Stable Internet Routing Without Global Coordination Lixin gao Jennifer Rexford omputer Science Internet and Networking Systems Smith Colleg at&T Labs- Research Northampton, MA 01060 Florham Park. NJ 0793 gao@cs. smith. edu jrex@research.att.com ABSTRACT reachability information using the Border Gateway Proto- The Border Gate way Protocol (BGP)allows an autonomous ol(BGP)[18: 19]. BGP is an interdomain rout ing pre ystem(As)to apply diverse local policies for selecting rout tocol that allows ASes to apply local policies for se lecting d propagating reachability information to ot her domains. routes and propagat ing rout ing information, without reveal However, BGP permits ASes to have conflic ting policies that ng their policies or internal topology to ot hers. However an lead to routing instability. This paper proposes a set of recent st udies have shown that a collec tion of A ses may have guidelines for an As to follow in set ting its rout ing policies, conflicting BGP policies that lead to route divergence [10 without requiring coordination with other ASes. Our ap- 20]. Route divergence can result in roach exploits the Internet's hierarchical st ruct ure and the can significant ly degrade the end-to-end performance of th commercial re lat ionships between ASes to impose a partial Internet. A voiding these conflicting BGP policies is cr rder on the set of routes to each destination. The guide cial for the stability of the Internet routing infrastructure lines conform to convent ional traffic-engineering practices of Yet, to be practical, any technique for ensuring convergence ISPs, and S with significant flexibility in se should not sacrifice the ability of each as to apply complex lect ing its local policies. Furthe the guide line local policies routing policies. Drawing on a formal model of BGP and n the topolo A natural approach to the route convergence problem in rove that following our proposed policy guidelines guara olves the use of an Internet Rout ing Registry (RR),a ees route convergence. We also describe how our met hod epository of routing policies specified in a st andard lan ology can be applied to new types of relationships between guage [16]. A complete and up-to-date registry could check ASes, how to verify the hierarchical AS re lationships, and if the set of routing policies has any potential convergence how to realize our policy guidelines. Our approach has al value since it problems. Howe ver, this global coordination effort faces al ISPs may be ng as to apply complex local policies wi thout divulging its eveal their local policies to ot hers, and may not keep the BGP configurations to others. registry up-to-date. Second, and perhaps more importantly even if ISPs decide to reveal their local polices, recent work 1. INTRODUCTION has shown that st at ically checking for convergence proper ties is an NP-complete problem [10]. Third, even if the reg Inects thousands of Autonomous Systems istry could ensure convergent routes under a given to (ASes) operated by difTerent institutions, such as Internet BGP still might not converge under router or link failures rvice Providers(ISPs), companies, and universities. Rout ng wit hin an As is cont rolled by intradomain protocols or a policy change. Hence, rather than requiring global ce such as oSPF, Is-Is, and RiP, A Ses interconnect via dedi- ordinat ion, we believe that convergence should be achie ved cated links and public net work access point s, and exchange by rest ricting the set of policies that each AS can apply. In this paper, we propose a set of guidelines for an As to fol 9977555, and NSF CAREER Award grant ANI-9875513 low in set ting its routing policies, wit hout requiring coordi nat ion with other ASes. Our approach capit alizes d in this material are tI he authors and do not cial relation ecessarily reflect the of the Nat ional Science Foun- ships between ASes. These re lat ionships include custome dation and backi provider for connectivity to the rest of the Internet, whe peers agree to exchange traffic between their respective tomers free of charge; an As may also provide backup cor nectivity to the Internet in the event of a failure. Under o guide lines, rout ing via a peer or a provider is never prefer able to routing via a customer link; furthermore, routes via backup links have the lowest preference. An As is free to ap ply any local policies to the routes learned from neighbors within each preference class. These guidelines conform t
Stable Internet Routing Without Global Coordination Lixin Gao Computer Science Smith College Northampton, MA 01060 gao@cs.smith.edu Jennifer Rexford Internet and Networking Systems AT&T Labs – Research Florham Park, NJ 07932 jrex@research.att.com ABSTRACT ✁ ✂ ✄ ☎ ✆ ✝ ✞ ✄ ✝ ✟ ✠ ✡ ✄ ☛ ✠ ☞ ✌ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✏ ☎ ✟ ✌ ✑ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✓ ✠ ✔ ✡ ✆ ✓ ✆ ✕ ✆ ✔ ✒ ✒ ☞ ✒ ✡ ✄ ✕ ✏ ✖ ✗ ✑ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✞ ✙ ✚ ✄ ✝ ✒ ✄ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✛ ✆ ✝ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✙ ✓ ✜ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ☎ ✟ ✌ ✘ ✄ ✝ ✕ ✙ ✡ ✒ ✖ ✗ ✄ ✒ ✡ ✆ ✂ ✠ ✚ ✄ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✍ ✠ ✓ ✎ ✄ ✠ ✞ ✡ ✆ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ✁ ✂ ✙ ✒ ✘ ✠ ✘ ✄ ✝ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✒ ✠ ✒ ✄ ✡ ✆ ✛ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✛ ✆ ✝ ✠ ✓ ✖ ✗ ✡ ✆ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✒ ✄ ✡ ✡ ✙ ✓ ✜ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✙ ✓ ✜ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✣ ★ ✔ ✝ ✠ ✘ ✩ ✘ ✝ ✆ ✠ ✍ ✂ ✄ ✪ ✘ ✎ ✆ ✙ ✡ ✒ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✬ ✒ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✠ ✓ ✞ ✡ ✂ ✄ ✍ ✆ ✕ ✕ ✄ ✝ ✍ ✙ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✡ ✆ ✙ ✕ ✘ ✆ ✒ ✄ ✠ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✆ ✓ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✄ ✠ ✍ ✂ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✣ ✁ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✩ ✎ ✙ ✓ ✄ ✒ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✡ ✆ ✍ ✆ ✓ ✚ ✄ ✓ ✡ ✙ ✆ ✓ ✠ ✎ ✡ ✝ ✠ ✭ ✍ ✩ ✄ ✓ ✜ ✙ ✓ ✄ ✄ ✝ ✙ ✓ ✜ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✒ ✆ ✛ ✫ ✗ ✌ ✒ ✥ ✠ ✓ ✞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✄ ✠ ✍ ✂ ✖ ✗ ☛ ✙ ✡ ✂ ✒ ✙ ✜ ✓ ✙ ✮ ✍ ✠ ✓ ✡ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✒ ✄ ✩ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✙ ✡ ✒ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✯ ✔ ✝ ✡ ✂ ✄ ✝ ✕ ✆ ✝ ✄ ✥ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✄ ✓ ✒ ✔ ✝ ✄ ✝ ✆ ✔ ✡ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✄ ✚ ✄ ✓ ✔ ✓ ✞ ✄ ✝ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✰ ✝ ✠ ☛ ✙ ✓ ✜ ✆ ✓ ✠ ✛ ✆ ✝ ✕ ✠ ✎ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✆ ✔ ✝ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✞ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✜ ✔ ✠ ✝ ✠ ✓ ✩ ✡ ✄ ✄ ✒ ✝ ✆ ✔ ✡ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✣ ✱ ✄ ✠ ✎ ✒ ✆ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✂ ✆ ☛ ✆ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✩ ✆ ✎ ✆ ✜ ☞ ✍ ✠ ✓ ✢ ✄ ✠ ✘ ✘ ✎ ✙ ✄ ✞ ✡ ✆ ✓ ✄ ☛ ✡ ☞ ✘ ✄ ✒ ✆ ✛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✥ ✂ ✆ ☛ ✡ ✆ ✚ ✄ ✝ ✙ ✛ ☞ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✖ ✗ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✥ ✠ ✓ ✞ ✂ ✆ ☛ ✡ ✆ ✝ ✄ ✠ ✎ ✙ ✲ ✄ ✆ ✔ ✝ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✣ ★ ✔ ✝ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✂ ✠ ✒ ✒ ✙ ✜ ✩ ✓ ✙ ✮ ✍ ✠ ✓ ✡ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✠ ✎ ✚ ✠ ✎ ✔ ✄ ✒ ✙ ✓ ✍ ✄ ✙ ✡ ✘ ✝ ✄ ✒ ✄ ✝ ✚ ✄ ✒ ✡ ✂ ✄ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✄ ✠ ✍ ✂ ✖ ✗ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✞ ✙ ✚ ✔ ✎ ✜ ✙ ✓ ✜ ✙ ✡ ✒ ☎ ✟ ✌ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✒ ✣ 1. INTRODUCTION ✁ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✡ ✂ ✆ ✔ ✒ ✠ ✓ ✞ ✒ ✆ ✛ ✖ ✔ ✡ ✆ ✓ ✆ ✕ ✆ ✔ ✒ ✗ ☞ ✒ ✡ ✄ ✕ ✒ ✏ ✖ ✗ ✄ ✒ ✑ ✆ ✘ ✄ ✝ ✠ ✡ ✄ ✞ ✢ ☞ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✙ ✓ ✒ ✡ ✙ ✡ ✔ ✡ ✙ ✆ ✓ ✒ ✥ ✒ ✔ ✍ ✂ ✠ ✒ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✗ ✄ ✝ ✚ ✙ ✍ ✄ ✌ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✏ ✫ ✗ ✌ ✒ ✑ ✥ ✍ ✆ ✕ ✘ ✠ ✓ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✔ ✓ ✙ ✚ ✄ ✝ ✒ ✙ ✡ ✙ ✄ ✒ ✣ ✴ ✆ ✔ ✡ ✩ ✙ ✓ ✜ ☛ ✙ ✡ ✂ ✙ ✓ ✠ ✓ ✖ ✗ ✙ ✒ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✎ ✄ ✞ ✢ ☞ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✕ ✠ ✙ ✓ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✒ ✒ ✔ ✍ ✂ ✠ ✒ ★ ✗ ✌ ✯ ✥ ✫ ✗ ✩ ✫ ✗ ✥ ✠ ✓ ✞ ✴ ✫ ✌ ✣ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✚ ✙ ✠ ✞ ✄ ✞ ✙ ✩ ✍ ✠ ✡ ✄ ✞ ✎ ✙ ✓ ✵ ✒ ✠ ✓ ✞ ✘ ✔ ✢ ✎ ✙ ✍ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✠ ✍ ✍ ✄ ✒ ✒ ✘ ✆ ✙ ✓ ✡ ✒ ✥ ✠ ✓ ✞ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✁ ✂ ✄ ✮ ✝ ✒ ✡ ✠ ✔ ✡ ✂ ✆ ✝ ☛ ✠ ✒ ✒ ✔ ✘ ✘ ✆ ✝ ✡ ✄ ✞ ✙ ✓ ✘ ✠ ✝ ✡ ✢ ☞ ✶ ✗ ✯ ✜ ✝ ✠ ✓ ✡ ✶ ✷ ✴ ✩ ✸ ✸ ✹ ✹ ✺ ✺ ✺ ✥ ✠ ✓ ✞ ✶ ✗ ✯ ✷ ✖ ✴ ✻ ✻ ✴ ✖ ☛ ✠ ✝ ✞ ✜ ✝ ✠ ✓ ✡ ✖ ✶ ✫ ✩ ✸ ✼ ✹ ✺ ✺ ✽ ✾ ✣ ✖ ✓ ☞ ✆ ✘ ✙ ✓ ✙ ✆ ✓ ✒ ✥ ✮ ✓ ✞ ✙ ✓ ✜ ✒ ✥ ✠ ✓ ✞ ✍ ✆ ✓ ✍ ✎ ✔ ✒ ✙ ✆ ✓ ✒ ✆ ✝ ✝ ✄ ✍ ✆ ✕ ✕ ✄ ✓ ✞ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✪ ✘ ✝ ✄ ✒ ✒ ✄ ✞ ✙ ✓ ✡ ✂ ✙ ✒ ✕ ✠ ✡ ✄ ✝ ✙ ✠ ✎ ✠ ✝ ✄ ✡ ✂ ✆ ✒ ✄ ✆ ✛ ✡ ✂ ✄ ✠ ✔ ✡ ✂ ✆ ✝ ✒ ✠ ✓ ✞ ✞ ✆ ✓ ✆ ✡ ✓ ✄ ✍ ✄ ✒ ✒ ✠ ✝ ✙ ✎ ☞ ✝ ✄ ✦ ✄ ✍ ✡ ✡ ✂ ✄ ✚ ✙ ✄ ☛ ✒ ✆ ✛ ✡ ✂ ✄ ✶ ✠ ✡ ✙ ✆ ✓ ✠ ✎ ✗ ✍ ✙ ✄ ✓ ✍ ✄ ✯ ✆ ✔ ✓ ✩ ✞ ✠ ✡ ✙ ✆ ✓ ✣ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ☎ ✆ ✝ ✞ ✄ ✝ ✟ ✠ ✡ ✄ ☛ ✠ ☞ ✌ ✝ ✆ ✡ ✆ ✩ ✍ ✆ ✎ ✏ ☎ ✟ ✌ ✑ ✿ ✽ ✼ ❀ ✽ ✸ ❁ ✣ ☎ ✟ ✌ ✙ ✒ ✠ ✓ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✩ ✡ ✆ ✍ ✆ ✎ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ✆ ☛ ✒ ✖ ✗ ✄ ✒ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✛ ✆ ✝ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✝ ✄ ✚ ✄ ✠ ✎ ✩ ✙ ✓ ✜ ✡ ✂ ✄ ✙ ✝ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✝ ✙ ✓ ✡ ✄ ✝ ✓ ✠ ✎ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✝ ✄ ✍ ✄ ✓ ✡ ✒ ✡ ✔ ✞ ✙ ✄ ✒ ✂ ✠ ✚ ✄ ✒ ✂ ✆ ☛ ✓ ✡ ✂ ✠ ✡ ✠ ✍ ✆ ✎ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✖ ✗ ✄ ✒ ✕ ✠ ☞ ✂ ✠ ✚ ✄ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✎ ✄ ✠ ✞ ✡ ✆ ✝ ✆ ✔ ✡ ✄ ✞ ✙ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✿ ✽ ❂ ❀ ❃ ❂ ❁ ✣ ✴ ✆ ✔ ✡ ✄ ✞ ✙ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✍ ✠ ✓ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✝ ✆ ✔ ✡ ✄ ✆ ✒ ✍ ✙ ✎ ✎ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✂ ✙ ✍ ✂ ✍ ✠ ✓ ✒ ✙ ✜ ✓ ✙ ✮ ✍ ✠ ✓ ✡ ✎ ☞ ✞ ✄ ✜ ✝ ✠ ✞ ✄ ✡ ✂ ✄ ✄ ✓ ✞ ✩ ✡ ✆ ✩ ✄ ✓ ✞ ✘ ✄ ✝ ✛ ✆ ✝ ✕ ✠ ✓ ✍ ✄ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✣ ✖ ✚ ✆ ✙ ✞ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✙ ✒ ✍ ✝ ✔ ✩ ✍ ✙ ✠ ✎ ✛ ✆ ✝ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✝ ✠ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✣ ❄ ✄ ✡ ✥ ✡ ✆ ✢ ✄ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✠ ✎ ✥ ✠ ✓ ☞ ✡ ✄ ✍ ✂ ✓ ✙ ✧ ✔ ✄ ✛ ✆ ✝ ✄ ✓ ✒ ✔ ✝ ✙ ✓ ✜ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✒ ✂ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✒ ✠ ✍ ✝ ✙ ✮ ✍ ✄ ✡ ✂ ✄ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✄ ✠ ✍ ✂ ✖ ✗ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✖ ✓ ✠ ✡ ✔ ✝ ✠ ✎ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✡ ✆ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✙ ✓ ✩ ✚ ✆ ✎ ✚ ✄ ✒ ✡ ✂ ✄ ✔ ✒ ✄ ✆ ✛ ✠ ✓ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✴ ✆ ✔ ✡ ✙ ✓ ✜ ✴ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✏ ✫ ✴ ✴ ✑ ✥ ✠ ✝ ✄ ✘ ✆ ✒ ✙ ✡ ✆ ✝ ☞ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✒ ✘ ✄ ✍ ✙ ✮ ✄ ✞ ✙ ✓ ✠ ✒ ✡ ✠ ✓ ✞ ✠ ✝ ✞ ✎ ✠ ✓ ✩ ✜ ✔ ✠ ✜ ✄ ✿ ✽ ❅ ❁ ✣ ✖ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✠ ✓ ✞ ✔ ✘ ✩ ✡ ✆ ✩ ✞ ✠ ✡ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✆ ✔ ✎ ✞ ✍ ✂ ✄ ✍ ✵ ✙ ✛ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✂ ✠ ✒ ✠ ✓ ☞ ✘ ✆ ✡ ✄ ✓ ✡ ✙ ✠ ✎ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✡ ✂ ✙ ✒ ✜ ✎ ✆ ✢ ✠ ✎ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✄ ✳ ✆ ✝ ✡ ✛ ✠ ✍ ✄ ✒ ✒ ✄ ✚ ✩ ✄ ✝ ✠ ✎ ✙ ✕ ✘ ✄ ✞ ✙ ✕ ✄ ✓ ✡ ✒ ✣ ✯ ✙ ✝ ✒ ✡ ✥ ✕ ✠ ✓ ☞ ✫ ✗ ✌ ✒ ✕ ✠ ☞ ✢ ✄ ✔ ✓ ☛ ✙ ✎ ✎ ✙ ✓ ✜ ✡ ✆ ✝ ✄ ✚ ✄ ✠ ✎ ✡ ✂ ✄ ✙ ✝ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✒ ✥ ✠ ✓ ✞ ✕ ✠ ☞ ✓ ✆ ✡ ✵ ✄ ✄ ✘ ✡ ✂ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✔ ✘ ✩ ✡ ✆ ✩ ✞ ✠ ✡ ✄ ✣ ✗ ✄ ✍ ✆ ✓ ✞ ✥ ✠ ✓ ✞ ✘ ✄ ✝ ✂ ✠ ✘ ✒ ✕ ✆ ✝ ✄ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✡ ✎ ☞ ✥ ✄ ✚ ✄ ✓ ✙ ✛ ✫ ✗ ✌ ✒ ✞ ✄ ✍ ✙ ✞ ✄ ✡ ✆ ✝ ✄ ✚ ✄ ✠ ✎ ✡ ✂ ✄ ✙ ✝ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✄ ✒ ✥ ✝ ✄ ✍ ✄ ✓ ✡ ☛ ✆ ✝ ✵ ✂ ✠ ✒ ✒ ✂ ✆ ☛ ✓ ✡ ✂ ✠ ✡ ✒ ✡ ✠ ✡ ✙ ✍ ✠ ✎ ✎ ☞ ✍ ✂ ✄ ✍ ✵ ✙ ✓ ✜ ✛ ✆ ✝ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✩ ✡ ✙ ✄ ✒ ✙ ✒ ✠ ✓ ✶ ✌ ✩ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✿ ✽ ❂ ❁ ✣ ✁ ✂ ✙ ✝ ✞ ✥ ✄ ✚ ✄ ✓ ✙ ✛ ✡ ✂ ✄ ✝ ✄ ✜ ✩ ✙ ✒ ✡ ✝ ☞ ✍ ✆ ✔ ✎ ✞ ✄ ✓ ✒ ✔ ✝ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✔ ✓ ✞ ✄ ✝ ✠ ✜ ✙ ✚ ✄ ✓ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✥ ☎ ✟ ✌ ✒ ✡ ✙ ✎ ✎ ✕ ✙ ✜ ✂ ✡ ✓ ✆ ✡ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✔ ✓ ✞ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✝ ✆ ✝ ✎ ✙ ✓ ✵ ✛ ✠ ✙ ✎ ✔ ✝ ✄ ✒ ✥ ✆ ✝ ✠ ✘ ✆ ✎ ✙ ✍ ☞ ✍ ✂ ✠ ✓ ✜ ✄ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✝ ✠ ✡ ✂ ✄ ✝ ✡ ✂ ✠ ✓ ✝ ✄ ✧ ✔ ✙ ✝ ✙ ✓ ✜ ✜ ✎ ✆ ✢ ✠ ✎ ✍ ✆ ✩ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✢ ✄ ✎ ✙ ✄ ✚ ✄ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✒ ✂ ✆ ✔ ✎ ✞ ✢ ✄ ✠ ✍ ✂ ✙ ✄ ✚ ✄ ✞ ✢ ☞ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✄ ✠ ✍ ✂ ✖ ✗ ✍ ✠ ✓ ✠ ✘ ✘ ✎ ☞ ✣ ✫ ✓ ✡ ✂ ✙ ✒ ✘ ✠ ✘ ✄ ✝ ✥ ☛ ✄ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✠ ✒ ✄ ✡ ✆ ✛ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✛ ✆ ✝ ✠ ✓ ✖ ✗ ✡ ✆ ✛ ✆ ✎ ✩ ✎ ✆ ☛ ✙ ✓ ✒ ✄ ✡ ✡ ✙ ✓ ✜ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✙ ✓ ✜ ✍ ✆ ✆ ✝ ✞ ✙ ✩ ✓ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✣ ★ ✔ ✝ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✍ ✠ ✘ ✙ ✡ ✠ ✎ ✙ ✲ ✄ ✒ ✆ ✓ ✡ ✂ ✄ ✫ ✓ ✩ ✡ ✄ ✝ ✓ ✄ ✡ ✬ ✒ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✠ ✓ ✞ ✡ ✂ ✄ ✍ ✆ ✕ ✕ ✄ ✝ ✍ ✙ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✩ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ ✁ ✂ ✄ ✒ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✥ ✠ ✓ ✞ ✢ ✠ ✍ ✵ ✔ ✘ ✣ ✖ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✘ ✠ ☞ ✒ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✛ ✆ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✡ ✆ ✡ ✂ ✄ ✝ ✄ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✥ ☛ ✂ ✄ ✝ ✄ ✠ ✒ ✘ ✄ ✄ ✝ ✒ ✠ ✜ ✝ ✄ ✄ ✡ ✆ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ✂ ✄ ✙ ✝ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✍ ✔ ✒ ✩ ✡ ✆ ✕ ✄ ✝ ✒ ✛ ✝ ✄ ✄ ✆ ✛ ✍ ✂ ✠ ✝ ✜ ✄ ❀ ✠ ✓ ✖ ✗ ✕ ✠ ☞ ✠ ✎ ✒ ✆ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✍ ✆ ✓ ✩ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✡ ✆ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✙ ✓ ✡ ✂ ✄ ✄ ✚ ✄ ✓ ✡ ✆ ✛ ✠ ✛ ✠ ✙ ✎ ✔ ✝ ✄ ✣ ❆ ✓ ✞ ✄ ✝ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✥ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✚ ✙ ✠ ✠ ✘ ✄ ✄ ✝ ✆ ✝ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✙ ✒ ✓ ✄ ✚ ✄ ✝ ✘ ✝ ✄ ✛ ✄ ✝ ✩ ✠ ✢ ✎ ✄ ✡ ✆ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✚ ✙ ✠ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✎ ✙ ✓ ✵ ❀ ✛ ✔ ✝ ✡ ✂ ✄ ✝ ✕ ✆ ✝ ✄ ✥ ✝ ✆ ✔ ✡ ✄ ✒ ✚ ✙ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✂ ✠ ✚ ✄ ✡ ✂ ✄ ✎ ✆ ☛ ✄ ✒ ✡ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✣ ✖ ✓ ✖ ✗ ✙ ✒ ✛ ✝ ✄ ✄ ✡ ✆ ✠ ✘ ✩ ✘ ✎ ☞ ✠ ✓ ☞ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ☛ ✙ ✡ ✂ ✙ ✓ ✄ ✠ ✍ ✂ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✍ ✎ ✠ ✒ ✒ ✣ ✁ ✂ ✄ ✒ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✡ ✆
convent ional traffic-engineering practices of ISPs, and this consist ing of a 32-bit IP address and a mask length(e.g. ght well explain why Internet ce has not 1.2.3 724). An AS employs an intradomain rout ing pro occurred vet. Howe ver, it is cruci ake these guidelines tocol (such as OSPF or Is-Is)to determine how to reach xplicit since BGP itself does no ain rout ing policies each customer prefix, and employs an interdomain rout ing m e convergence. Based on our results, we propose protocol (BGP) to advert ise the reachability of these pre outing registry that requires each As to disclos fixes to neighboring ASes. BGP is a dist ance-vector protocol relationship with each of its ne igh rat her than that constructs pat hs by successi vely propagat ing advertise the entire set of rout ing policies. ments bet s of routers t hat are configured as BGP peers [18: 19]. Each advertisement The remainder of the paper is structured as follows. S prefix and includes the list of the A Ses along the path(the tion 2 presents an overview of interdomain routing and di As path). Upon receiving an adver tisement, a BGP speaker cusses pre vious work on BGP protocol dynamics. Then, See must decide whe ther or not to use this path and, if the path on 3 presents a formal model of BGP that includes ASes is chosen, whet her or not to propagate the adver tisement with multiple BGP speakers, both interior BGP (BGP)and to neighboring A Ses (after adding its own AS number to exterior BGP(e BGP), and additional BGP at tributes. We the As path). A BGP speaker withdraws an adver tisement de fine the ty pes of relationships between ASes and describe when the prefix is no longer reachable with this route, which the hierarchical structure of the As ph in Secti on 4. In leads to a sequence of wit drawals by upstream ASes that ection 5, we present our policy guidelines and formally are using this path prove that adherence to these guidelines guarantees conver- ence for all possible init ial states. We show how to The simplest dist ance-vec tor protocol would employ shortest mit addit ional flexibility in choosing bet ween routes through path routing. BGP allows a much wider range of policie customers and routes through peers by making realistic as- based on how the routers are configured. An As can favor sumpt ions about peer-to-peer relationships. Then, Section 6 one path over anot her by assigning a local preference. BGP discusses the rob usiness of our guide lines to changes in net also allows an As to send a hint to a neighbor on the prefer work topolo nd relationships between ence that should be gi ven to a route by using the communit ASes. We describe how to apply our me thodolo gy to ne at tribute. An as can control how traffic enters its network ypes of relat ionships that can arise between ASes, and how by assigning a different multiple erit discriminator(MED) n As pair can transition to a new relationship while pre- value to the advertisements it sends on each link to a neigh- serving BGP stabilit 7 concludes the paper with boring As. Ot her wise, the neighboring As would select the a discussion of future research direct ions link based on its own intradomain rout ing protocol. An AS 2. INTERDOMAIN ROUTING forming As prepending, which inflates the length of the AS pat h by listing an As number multiple times. Processing an ternet architect ure [11] and the use of BGP for interdom air advertisement involves three steps import policies that outing [18; 19]. We also decide which routes to consider, path selection that decide protocol dynamics of BGP. which route to use, and export policies that decide whet her and what)t vermis t hat are 2.1 Internet architecture detail in se 3 The Internet consists of a large collection of hosts intercon- nected by networks of links and routers. The Internet 2.2 Protocol Dynamics divided into thousands of dist inct regions of ad minist rat lexit y of the Internet rout- control, referred to as aut derstanding BGP ples range from college campuses and corporate net works to protocol dynamics. Previous work consists of measurement o, Se Internet Service Providers(ISPs). An AS has its ov based st udies of BGP protocol traffic and theoret ical analy lters and routing policies, and connects to other ASes to sis of BGP convergence properties. Extensi ve traces of Bo exchange traffic with remote hosts. A router t ypically has update messages have been used to characterize the struc very detailed knowledge of the topology within its AS, and ture(and growth)of the Internet tond\: 13: 14; 15]. In ge points(IXPs)or ch on bGP convergence has focused on dedicated point-to-point links. Public exchange points typ termining what combinat cally consist of a shared medium, such as a FDDI ring or ar group of A Ses to continually advertise and withdraw routes TM switch, that interconnects routers from several differ to a given prefix [6;8; 9; 10; 20]. BGP conve nt ASes. Physical connectivity at the IXP does not neces lems would not arise if every As selects shortest-path routes sarily imply that every pair of ASes exchanges traffic with However, ASes can have conflicting local policies when they ach other as pairs ne got iate cont ractual ts that tribute to fa route with control the exchange of traffic. These relationships include non-minimal AS path. This can result in route oscillat ion, Section 4 to its neighbors, whic eighbors to change their de en,these A Ses withdraw thei ous route and Each As has responsibility for carrying traffic to and from advertise new ones, and the process repeats a set of customer ip addr ternet routing infrast ructure depends on the aggregation Previous research has studied route convergence under of IP addresses in contiguous blocks, called prefires, each assumpt ion of global know ledge of the to polo gy and rout ing
✍ ✆ ✓ ✚ ✄ ✓ ✡ ✙ ✆ ✓ ✠ ✎ ✡ ✝ ✠ ✭ ✍ ✩ ✄ ✓ ✜ ✙ ✓ ✄ ✄ ✝ ✙ ✓ ✜ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✒ ✆ ✛ ✫ ✗ ✌ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✙ ✒ ✕ ✙ ✜ ✂ ✡ ☛ ✄ ✎ ✎ ✄ ✪ ✘ ✎ ✠ ✙ ✓ ☛ ✂ ☞ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✙ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✂ ✠ ✒ ✓ ✆ ✡ ✆ ✍ ✍ ✔ ✝ ✝ ✄ ✞ ☞ ✄ ✡ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✙ ✡ ✙ ✒ ✍ ✝ ✔ ✍ ✙ ✠ ✎ ✡ ✆ ✕ ✠ ✵ ✄ ✡ ✂ ✄ ✒ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✒ ✙ ✓ ✍ ✄ ☎ ✟ ✌ ✙ ✡ ✒ ✄ ✎ ✛ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✍ ✆ ✓ ✒ ✡ ✝ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✄ ✓ ✒ ✔ ✝ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✣ ☎ ✠ ✒ ✄ ✞ ✆ ✓ ✆ ✔ ✝ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✥ ☛ ✄ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✠ ✒ ✙ ✕ ✘ ✎ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✡ ✂ ✠ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✄ ✒ ✄ ✠ ✍ ✂ ✖ ✗ ✡ ✆ ✞ ✙ ✒ ✍ ✎ ✆ ✒ ✄ ✆ ✓ ✎ ☞ ✙ ✡ ✒ ✁ ✂ ✄ ☎ ✆ ✝ ✞ ✟ ✠ ✆ ✡ ☛ ✙ ✡ ✂ ✄ ✠ ✍ ✂ ✆ ✛ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✥ ✝ ✠ ✡ ✂ ✄ ✝ ✡ ✂ ✠ ✓ ✡ ✂ ✄ ✄ ✓ ✡ ✙ ✝ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✁ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✞ ✄ ✝ ✆ ✛ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✙ ✒ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✞ ✠ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✣ ✗ ✄ ✍ ✩ ✡ ✙ ✆ ✓ ❃ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✓ ✆ ✚ ✄ ✝ ✚ ✙ ✄ ☛ ✆ ✛ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✠ ✓ ✞ ✞ ✙ ✒ ✩ ✍ ✔ ✒ ✒ ✄ ✒ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✆ ✓ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✣ ✁ ✂ ✄ ✓ ✥ ✗ ✄ ✍ ✩ ✡ ✙ ✆ ✓ ✾ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✛ ✆ ✝ ✕ ✠ ✎ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✡ ✂ ✠ ✡ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✖ ✗ ✄ ✒ ☛ ✙ ✡ ✂ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ✢ ✆ ✡ ✂ ✙ ✓ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✙ ☎ ✟ ✌ ✑ ✠ ✓ ✞ ✄ ✪ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✄ ☎ ✟ ✌ ✑ ✥ ✠ ✓ ✞ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ☎ ✟ ✌ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✣ ✱ ✄ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✡ ☞ ✘ ✄ ✒ ✆ ✛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✠ ✓ ✞ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ☛ ✣ ✫ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✺ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✆ ✔ ✝ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✠ ✓ ✞ ✛ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✠ ✞ ✂ ✄ ✝ ✄ ✓ ✍ ✄ ✡ ✆ ✡ ✂ ✄ ✒ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✒ ✍ ✆ ✓ ✚ ✄ ✝ ✩ ✜ ✄ ✓ ✍ ✄ ✛ ✆ ✝ ✠ ✎ ✎ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✒ ✣ ✱ ✄ ✒ ✂ ✆ ☛ ✂ ✆ ☛ ✡ ✆ ✘ ✄ ✝ ✩ ✕ ✙ ✡ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✍ ✂ ✆ ✆ ✒ ✙ ✓ ✜ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✘ ✄ ✄ ✝ ✒ ✢ ☞ ✕ ✠ ✵ ✙ ✓ ✜ ✝ ✄ ✠ ✎ ✙ ✒ ✡ ✙ ✍ ✠ ✒ ✩ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✒ ✠ ✢ ✆ ✔ ✡ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✁ ✂ ✄ ✓ ✥ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ❅ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✄ ✒ ✡ ✂ ✄ ✝ ✆ ✢ ✔ ✒ ✡ ✓ ✄ ✒ ✒ ✆ ✛ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✓ ✄ ✡ ✩ ☛ ✆ ✝ ✵ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✥ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ ✱ ✄ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✂ ✆ ☛ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✆ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✆ ✎ ✆ ✜ ☞ ✡ ✆ ✓ ✄ ☛ ✡ ☞ ✘ ✄ ✒ ✆ ✛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✡ ✂ ✠ ✡ ✍ ✠ ✓ ✠ ✝ ✙ ✒ ✄ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✥ ✠ ✓ ✞ ✂ ✆ ☛ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✡ ✆ ✠ ✓ ✄ ☛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✂ ✙ ✎ ✄ ✘ ✝ ✄ ✩ ✒ ✄ ✝ ✚ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✹ ✍ ✆ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ☛ ✙ ✡ ✂ ✠ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✆ ✛ ✛ ✔ ✡ ✔ ✝ ✄ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✞ ✙ ✝ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✣ 2. INTERDOMAIN ROUTING ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✢ ✠ ✍ ✵ ✜ ✝ ✆ ✔ ✓ ✞ ✕ ✠ ✡ ✄ ✝ ✙ ✠ ✎ ✆ ✓ ✡ ✂ ✄ ✫ ✓ ✩ ✡ ✄ ✝ ✓ ✄ ✡ ✠ ✝ ✍ ✂ ✙ ✡ ✄ ✍ ✡ ✔ ✝ ✄ ✿ ✽ ✽ ❁ ✠ ✓ ✞ ✡ ✂ ✄ ✔ ✒ ✄ ✆ ✛ ☎ ✟ ✌ ✛ ✆ ✝ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✿ ✽ ✼ ❀ ✽ ✸ ❁ ✣ ✱ ✄ ✠ ✎ ✒ ✆ ✒ ✔ ✕ ✕ ✠ ✝ ✙ ✲ ✄ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✆ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✆ ✛ ☎ ✟ ✌ ✣ 2.1 Internet Architecture ✁ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✠ ✎ ✠ ✝ ✜ ✄ ✍ ✆ ✎ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✂ ✆ ✒ ✡ ✒ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✩ ✓ ✄ ✍ ✡ ✄ ✞ ✢ ☞ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✒ ✆ ✛ ✎ ✙ ✓ ✵ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✣ ✁ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✙ ✒ ✞ ✙ ✚ ✙ ✞ ✄ ✞ ✙ ✓ ✡ ✆ ✡ ✂ ✆ ✔ ✒ ✠ ✓ ✞ ✒ ✆ ✛ ✞ ✙ ✒ ✡ ✙ ✓ ✍ ✡ ✝ ✄ ✜ ✙ ✆ ✓ ✒ ✆ ✛ ✠ ✞ ✕ ✙ ✓ ✙ ✒ ✡ ✝ ✠ ✡ ✙ ✚ ✄ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✥ ✝ ✄ ✛ ✄ ✝ ✝ ✄ ✞ ✡ ✆ ✠ ✒ ✄ ☞ ☎ ✝ ✞ ✝ ✌ ✝ ☞ ✟ ✟ ✍ ✟ ☎ ✁ ✌ ✟ ✏ ✖ ✗ ✄ ✒ ✑ ✣ ✻ ✪ ✠ ✕ ✩ ✘ ✎ ✄ ✒ ✝ ✠ ✓ ✜ ✄ ✛ ✝ ✆ ✕ ✍ ✆ ✎ ✎ ✄ ✜ ✄ ✍ ✠ ✕ ✘ ✔ ✒ ✄ ✒ ✠ ✓ ✞ ✍ ✆ ✝ ✘ ✆ ✝ ✠ ✡ ✄ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✒ ✡ ✆ ✎ ✠ ✝ ✜ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✗ ✄ ✝ ✚ ✙ ✍ ✄ ✌ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✏ ✫ ✗ ✌ ✒ ✑ ✣ ✖ ✓ ✖ ✗ ✂ ✠ ✒ ✙ ✡ ✒ ✆ ☛ ✓ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✡ ✆ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✡ ✆ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ☛ ✙ ✡ ✂ ✝ ✄ ✕ ✆ ✡ ✄ ✂ ✆ ✒ ✡ ✒ ✣ ✖ ✝ ✆ ✔ ✡ ✄ ✝ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✂ ✠ ✒ ✚ ✄ ✝ ☞ ✞ ✄ ✡ ✠ ✙ ✎ ✄ ✞ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ☛ ✙ ✡ ✂ ✙ ✓ ✙ ✡ ✒ ✖ ✗ ✥ ✠ ✓ ✞ ✎ ✙ ✕ ✙ ✡ ✄ ✞ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✠ ✢ ✆ ✔ ✡ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✄ ✒ ✣ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✠ ✡ ✘ ✔ ✢ ✎ ✙ ✍ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✘ ✆ ✙ ✓ ✡ ✒ ✏ ✫ ✎ ✌ ✒ ✑ ✆ ✝ ✞ ✄ ✞ ✙ ✍ ✠ ✡ ✄ ✞ ✘ ✆ ✙ ✓ ✡ ✩ ✡ ✆ ✩ ✘ ✆ ✙ ✓ ✡ ✎ ✙ ✓ ✵ ✒ ✣ ✌ ✔ ✢ ✎ ✙ ✍ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✘ ✆ ✙ ✓ ✡ ✒ ✡ ☞ ✘ ✙ ✩ ✍ ✠ ✎ ✎ ☞ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✆ ✛ ✠ ✒ ✂ ✠ ✝ ✄ ✞ ✕ ✄ ✞ ✙ ✔ ✕ ✥ ✒ ✔ ✍ ✂ ✠ ✒ ✠ ✯ ✰ ✰ ✫ ✝ ✙ ✓ ✜ ✆ ✝ ✠ ✓ ✖ ✁ ✏ ✒ ☛ ✙ ✡ ✍ ✂ ✥ ✡ ✂ ✠ ✡ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✛ ✝ ✆ ✕ ✒ ✄ ✚ ✄ ✝ ✠ ✎ ✞ ✙ ✳ ✄ ✝ ✩ ✄ ✓ ✡ ✖ ✗ ✄ ✒ ✣ ✌ ✂ ☞ ✒ ✙ ✍ ✠ ✎ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✠ ✡ ✡ ✂ ✄ ✫ ✎ ✌ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✍ ✄ ✒ ✩ ✒ ✠ ✝ ✙ ✎ ☞ ✙ ✕ ✘ ✎ ☞ ✡ ✂ ✠ ✡ ✄ ✚ ✄ ✝ ☞ ✘ ✠ ✙ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✝ ✠ ✭ ✍ ☛ ✙ ✡ ✂ ✄ ✠ ✍ ✂ ✆ ✡ ✂ ✄ ✝ ✣ ✖ ✗ ✘ ✠ ✙ ✝ ✒ ✓ ✄ ✜ ✆ ✡ ✙ ✠ ✡ ✄ ✍ ✆ ✓ ✡ ✝ ✠ ✍ ✡ ✔ ✠ ✎ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✒ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✡ ✂ ✄ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✆ ✛ ✡ ✝ ✠ ✭ ✍ ✣ ✁ ✂ ✄ ✒ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✥ ✠ ✓ ✞ ✢ ✠ ✍ ✵ ✔ ✘ ✥ ✠ ✓ ✞ ✠ ✝ ✄ ✞ ✙ ✒ ✩ ✍ ✔ ✒ ✒ ✄ ✞ ✙ ✓ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ☛ ✣ ✻ ✠ ✍ ✂ ✖ ✗ ✂ ✠ ✒ ✝ ✄ ✒ ✘ ✆ ✓ ✒ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✛ ✆ ✝ ✍ ✠ ✝ ✝ ☞ ✙ ✓ ✜ ✡ ✝ ✠ ✭ ✍ ✡ ✆ ✠ ✓ ✞ ✛ ✝ ✆ ✕ ✠ ✒ ✄ ✡ ✆ ✛ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✄ ✒ ✣ ✁ ✂ ✄ ✒ ✍ ✠ ✎ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✩ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✝ ✠ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✞ ✄ ✘ ✄ ✓ ✞ ✒ ✆ ✓ ✡ ✂ ✄ ✠ ✜ ✜ ✝ ✄ ✜ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✄ ✒ ✙ ✓ ✍ ✆ ✓ ✡ ✙ ✜ ✔ ✆ ✔ ✒ ✢ ✎ ✆ ✍ ✵ ✒ ✥ ✍ ✠ ✎ ✎ ✄ ✞ ✡ ✁ ✑ ✒ ✁ ✟ ✥ ✄ ✠ ✍ ✂ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✙ ✓ ✜ ✆ ✛ ✠ ✾ ❃ ✩ ✢ ✙ ✡ ✫ ✌ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✠ ✓ ✞ ✠ ✕ ✠ ✒ ✵ ✎ ✄ ✓ ✜ ✡ ✂ ✏ ✄ ✣ ✜ ✣ ✥ ✽ ✓ ❃ ✓ ✾ ✓ ❂ ✔ ❃ ☛ ✑ ✣ ✖ ✓ ✖ ✗ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✠ ✓ ✆ ✞ ☎ ✄ ✕ ✝ ✌ ✄ ✆ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✩ ✡ ✆ ✍ ✆ ✎ ✏ ✒ ✔ ✍ ✂ ✠ ✒ ★ ✗ ✌ ✯ ✆ ✝ ✫ ✗ ✩ ✫ ✗ ✑ ✡ ✆ ✞ ✄ ✡ ✄ ✝ ✕ ✙ ✓ ✄ ✂ ✆ ☛ ✡ ✆ ✝ ✄ ✠ ✍ ✂ ✄ ✠ ✍ ✂ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✘ ✝ ✄ ✮ ✪ ✥ ✠ ✓ ✞ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✠ ✓ ✆ ✞ ☎ ✁ ✕ ✝ ✌ ✄ ✆ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✏ ☎ ✟ ✌ ✑ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✡ ✂ ✄ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✒ ✄ ✘ ✝ ✄ ✩ ✮ ✪ ✄ ✒ ✡ ✆ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ☎ ✟ ✌ ✙ ✒ ✠ ✞ ✙ ✒ ✡ ✠ ✓ ✍ ✄ ✩ ✚ ✄ ✍ ✡ ✆ ✝ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✒ ✘ ✠ ✡ ✂ ✒ ✢ ☞ ✒ ✔ ✍ ✍ ✄ ✒ ✒ ✙ ✚ ✄ ✎ ☞ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✙ ✓ ✜ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✩ ✕ ✄ ✓ ✡ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✘ ✠ ✙ ✝ ✒ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✞ ✠ ✒ ✖ ✗ ✘ ✡ ✁ ✁ ✟ ✿ ✽ ✼ ❀ ✽ ✸ ❁ ✣ ✻ ✠ ✍ ✂ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✍ ✆ ✓ ✍ ✄ ✝ ✓ ✒ ✠ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✘ ✝ ✄ ✮ ✪ ✠ ✓ ✞ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ✎ ✙ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✠ ✎ ✆ ✓ ✜ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✏ ✡ ✂ ✄ ✙ ✚ ✡ ✄ ☎ ✠ ✑ ✣ ❆ ✘ ✆ ✓ ✝ ✄ ✍ ✄ ✙ ✚ ✙ ✓ ✜ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✥ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✕ ✔ ✒ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✆ ✝ ✓ ✆ ✡ ✡ ✆ ✔ ✒ ✄ ✡ ✂ ✙ ✒ ✘ ✠ ✡ ✂ ✠ ✓ ✞ ✥ ✙ ✛ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✙ ✒ ✍ ✂ ✆ ✒ ✄ ✓ ✥ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✆ ✝ ✓ ✆ ✡ ✡ ✆ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✡ ✂ ✄ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✡ ✆ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✏ ✠ ✛ ✡ ✄ ✝ ✠ ✞ ✞ ✙ ✓ ✜ ✙ ✡ ✒ ✆ ☛ ✓ ✖ ✗ ✓ ✔ ✕ ✢ ✄ ✝ ✡ ✆ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✑ ✣ ✖ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✒ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ✘ ✝ ✄ ✮ ✪ ✙ ✒ ✓ ✆ ✎ ✆ ✓ ✜ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✠ ✢ ✎ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✙ ✒ ✝ ✆ ✔ ✡ ✄ ✥ ☛ ✂ ✙ ✍ ✂ ✎ ✄ ✠ ✞ ✒ ✡ ✆ ✠ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✠ ✎ ✒ ✢ ☞ ✔ ✘ ✒ ✡ ✝ ✄ ✠ ✕ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✙ ✒ ✘ ✠ ✡ ✂ ✣ ✁ ✂ ✄ ✒ ✙ ✕ ✘ ✎ ✄ ✒ ✡ ✞ ✙ ✒ ✡ ✠ ✓ ✍ ✄ ✩ ✚ ✄ ✍ ✡ ✆ ✝ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ☛ ✆ ✔ ✎ ✞ ✄ ✕ ✘ ✎ ✆ ☞ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✩ ✘ ✠ ✡ ✂ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✣ ☎ ✟ ✌ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✕ ✔ ✍ ✂ ☛ ✙ ✞ ✄ ✝ ✝ ✠ ✓ ✜ ✄ ✆ ✛ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✂ ✆ ☛ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✠ ✝ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✞ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✛ ✠ ✚ ✆ ✝ ✆ ✓ ✄ ✘ ✠ ✡ ✂ ✆ ✚ ✄ ✝ ✠ ✓ ✆ ✡ ✂ ✄ ✝ ✢ ☞ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✠ ✂ ✝ ✛ ✄ ✂ ✡ ✁ ✜ ✁ ✁ ✞ ✛ ✁ ✣ ☎ ✟ ✌ ✠ ✎ ✒ ✆ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✓ ✖ ✗ ✡ ✆ ✒ ✄ ✓ ✞ ✠ ✂ ✙ ✓ ✡ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✆ ✓ ✡ ✂ ✄ ✘ ✝ ✄ ✛ ✄ ✝ ✩ ✄ ✓ ✍ ✄ ✡ ✂ ✠ ✡ ✒ ✂ ✆ ✔ ✎ ✞ ✢ ✄ ✜ ✙ ✚ ✄ ✓ ✡ ✆ ✠ ✝ ✆ ✔ ✡ ✄ ✢ ☞ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ✛ ✝ ✌ ✌ ☞ ✞ ✆ ☎ ✍ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✍ ✆ ✓ ✡ ✝ ✆ ✎ ✂ ✆ ☛ ✡ ✝ ✠ ✭ ✍ ✄ ✓ ✡ ✄ ✝ ✒ ✙ ✡ ✒ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✢ ☞ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✠ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✌ ☞ ✂ ☎ ✆ ✡ ✂ ✁ ✁ ✒ ✆ ☎ ✕ ✆ ✟ ✛ ✆ ✌ ✆ ✞ ✄ ☎ ✝ ✏ ✏ ✻ ✰ ✑ ✚ ✠ ✎ ✔ ✄ ✡ ✆ ✡ ✂ ✄ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✒ ✙ ✡ ✒ ✄ ✓ ✞ ✒ ✆ ✓ ✄ ✠ ✍ ✂ ✎ ✙ ✓ ✵ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✩ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✣ ★ ✡ ✂ ✄ ✝ ☛ ✙ ✒ ✄ ✥ ✡ ✂ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ☛ ✆ ✔ ✎ ✞ ✒ ✄ ✎ ✄ ✍ ✡ ✡ ✂ ✄ ✎ ✙ ✓ ✵ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✙ ✡ ✒ ✆ ☛ ✓ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✠ ✎ ✒ ✆ ✞ ✙ ✒ ✍ ✆ ✔ ✝ ✠ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ✛ ✝ ✆ ✕ ✄ ✓ ✡ ✄ ✝ ✙ ✓ ✜ ✙ ✡ ✒ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✢ ☞ ✘ ✄ ✝ ✩ ✛ ✆ ✝ ✕ ✙ ✓ ✜ ✙ ✚ ✡ ✁ ✡ ✁ ✞ ✕ ✆ ✞ ✢ ✥ ☛ ✂ ✙ ✍ ✂ ✙ ✓ ✦ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ✎ ✄ ✓ ✜ ✡ ✂ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✢ ☞ ✎ ✙ ✒ ✡ ✙ ✓ ✜ ✠ ✓ ✖ ✗ ✓ ✔ ✕ ✢ ✄ ✝ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✡ ✙ ✕ ✄ ✒ ✣ ✌ ✝ ✆ ✍ ✄ ✒ ✒ ✙ ✓ ✜ ✠ ✓ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✒ ✡ ✂ ✝ ✄ ✄ ✒ ✡ ✄ ✘ ✒ ✣ ✆ ✌ ✡ ✝ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✥ ✡ ✄ ☎ ✠ ✟ ✁ ✂ ✁ ✛ ☎ ✆ ✝ ✞ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ✒ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✔ ✒ ✄ ✥ ✠ ✓ ✞ ✁ ✒ ✡ ✝ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✡ ✂ ✠ ✡ ✞ ✄ ✍ ✙ ✞ ✄ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✏ ✠ ✓ ✞ ☛ ✂ ✠ ✡ ✑ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✣ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✄ ✞ ✙ ✓ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✾ ✣ 2.2 Protocol Dynamics ✁ ✂ ✄ ✜ ✝ ✆ ☛ ✙ ✓ ✜ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✍ ✄ ✠ ✓ ✞ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✝ ✆ ✔ ✡ ✩ ✙ ✓ ✜ ✙ ✓ ✛ ✝ ✠ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✂ ✠ ✒ ✒ ✘ ✠ ✝ ✵ ✄ ✞ ✙ ✓ ✡ ✄ ✝ ✄ ✒ ✡ ✙ ✓ ✔ ✓ ✞ ✄ ✝ ✒ ✡ ✠ ✓ ✞ ✙ ✓ ✜ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✒ ✣ ✌ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ☛ ✆ ✝ ✵ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✕ ✄ ✠ ✒ ✔ ✝ ✄ ✕ ✄ ✓ ✡ ✩ ✢ ✠ ✒ ✄ ✞ ✒ ✡ ✔ ✞ ✙ ✄ ✒ ✆ ✛ ☎ ✟ ✌ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✡ ✝ ✠ ✭ ✍ ✠ ✓ ✞ ✡ ✂ ✄ ✆ ✝ ✄ ✡ ✙ ✍ ✠ ✎ ✠ ✓ ✠ ✎ ☞ ✩ ✒ ✙ ✒ ✆ ✛ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✣ ✻ ✪ ✡ ✄ ✓ ✒ ✙ ✚ ✄ ✡ ✝ ✠ ✍ ✄ ✒ ✆ ✛ ☎ ✟ ✌ ✔ ✘ ✞ ✠ ✡ ✄ ✕ ✄ ✒ ✒ ✠ ✜ ✄ ✒ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✔ ✒ ✄ ✞ ✡ ✆ ✍ ✂ ✠ ✝ ✠ ✍ ✡ ✄ ✝ ✙ ✲ ✄ ✡ ✂ ✄ ✒ ✡ ✝ ✔ ✍ ✩ ✡ ✔ ✝ ✄ ✏ ✠ ✓ ✞ ✜ ✝ ✆ ☛ ✡ ✂ ✑ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✥ ✠ ✒ ☛ ✄ ✎ ✎ ✠ ✒ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✿ ✹ ❀ ✽ ✾ ❀ ✽ ☛ ❀ ✽ ✺ ❁ ✣ ✫ ✓ ✍ ✆ ✓ ✡ ✝ ✠ ✒ ✡ ✥ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✆ ✓ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✂ ✠ ✒ ✛ ✆ ✍ ✔ ✒ ✄ ✞ ✆ ✓ ✞ ✄ ✩ ✡ ✄ ✝ ✕ ✙ ✓ ✙ ✓ ✜ ☛ ✂ ✠ ✡ ✍ ✆ ✕ ✢ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ☛ ✆ ✔ ✎ ✞ ✍ ✠ ✔ ✒ ✄ ✠ ✜ ✝ ✆ ✔ ✘ ✆ ✛ ✖ ✗ ✄ ✒ ✡ ✆ ✍ ✆ ✓ ✡ ✙ ✓ ✔ ✠ ✎ ✎ ☞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✠ ✓ ✞ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✜ ✙ ✚ ✄ ✓ ✘ ✝ ✄ ✮ ✪ ✿ ❅ ❀ ✼ ❀ ✸ ❀ ✽ ❂ ❀ ❃ ❂ ❁ ✣ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✩ ✎ ✄ ✕ ✒ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✝ ✙ ✒ ✄ ✙ ✛ ✄ ✚ ✄ ✝ ☞ ✖ ✗ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✩ ✘ ✠ ✡ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✖ ✗ ✄ ✒ ✍ ✠ ✓ ✂ ✠ ✚ ✄ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ☞ ✔ ✒ ✄ ✡ ✂ ✄ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✡ ✆ ✛ ✠ ✚ ✆ ✝ ✠ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✠ ✓ ✆ ✓ ✩ ✕ ✙ ✓ ✙ ✕ ✠ ✎ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ✁ ✂ ✙ ✒ ✍ ✠ ✓ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✝ ✆ ✔ ✡ ✄ ✆ ✒ ✍ ✙ ✎ ✎ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✂ ✄ ✝ ✄ ✠ ✓ ✖ ✗ ✕ ✠ ✵ ✄ ✒ ✠ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✠ ✓ ✞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✒ ✠ ✓ ✄ ☛ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✥ ☛ ✂ ✙ ✍ ✂ ✍ ✠ ✔ ✒ ✄ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✙ ✝ ✞ ✄ ✩ ✍ ✙ ✒ ✙ ✆ ✓ ✒ ❀ ✡ ✂ ✄ ✓ ✥ ✡ ✂ ✄ ✒ ✄ ✖ ✗ ✄ ✒ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✡ ✂ ✄ ✙ ✝ ✘ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ✝ ✆ ✔ ✡ ✄ ✠ ✓ ✞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✓ ✄ ☛ ✆ ✓ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✝ ✄ ✘ ✄ ✠ ✡ ✒ ✣ ✌ ✝ ✄ ✚ ✙ ✆ ✔ ✒ ✝ ✄ ✒ ✄ ✠ ✝ ✍ ✂ ✂ ✠ ✒ ✒ ✡ ✔ ✞ ✙ ✄ ✞ ✝ ✆ ✔ ✡ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✔ ✓ ✞ ✄ ✝ ✡ ✂ ✄ ✠ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✆ ✛ ✜ ✎ ✆ ✢ ✠ ✎ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜
policies. The work in [20] analyzes route oscillat ion in simple ring topologies, and suggests maint aining a global routing iBGP egistry of interdom ain policies that can be checked for po tent ial convergence problems [2; 6: 16; 20]. Expanding on these observations, the work in [10] presents a formal model of BGP that focuses on local-preference and AS-path-length OAS attributes. Since the paper proves negative results about BGP convergence properties, it is sufficient to consider a stricted subset of the protocol. In particular, the study stablishes that the problem of checking the convergence properties is NP-complete, even with full knowledge of the routing policies of each As. In addition, the paper presents Figure 1: An example of a BGP system topology several examples of conflicting BGP policies, including sce narios when the divergence occurs only after a link failure. A follow-up paper [9 presents a dynamic model that cap the updates to the immediate neighbors via tures the asynchronous processing of updates at each As e BGP session. BGP-speaker pairs in the same AS use iBGP The paper formalizes the notion of a stable state where ne to exchange routes learned from BGP peers. In practice AS would change its routes, and a safe BGP systerm that is an AS may configure its iBGP sessions to avoid a full ex- guaranteed to converge to a stable state. The paper presents a sufficient condi tion for a BG P system to be safe. However, usIng route re flector). These optimizat ions are intended test ing adherence to the condition requires full know ledge of to reduce ibGP traffic wit hout affecting the rout ing deci- the as graph and the set of routing policies for each As sions [11] and, hence, are not included in our model. Rout ng updates exchanged via eBGP sessions are transformed according to the bgp policies. We consider an eBGP session These results suggest that it may be possiBle to rest rict local /EE between two BGP speakers, u and v. BGP speaker v a way that antees bgP convergence, while still allowing greater flexibility than shortest-path rout ing receives a set of route updates R on l from u. BGP speaker Our paper focuses on construct v applies import policies to transform incoming route up dates, and app lies export policies before sending upda hanges in network topology and routing policies, wit hout t he neighbor u g coordination be An As can apply both implicit and explicit import poli 3. ABSTRACT MODEL OF BGP es. Let imimport(L,v)[R] denote the set of updates after applying the implicit import policy of v on edge L. Every In this sect esent an abstract model of bgp that edge has an implicit import policy that discards a rout ing we use in establishing the stability properties in Section 5 update when the receiving BGP speaker's As already ap The model extends the work in 19; 10 to include interior BGP GiBGP) and exterior BGP (eBGP), additional BGP a cycle in the AS path. That is, if a(v)E r as-path, IEo a pears in the as path; this is essential to avoid int roducing ttributes and oper (such as MED im-import (L, u)[r]= 0; otherwise im-import(L,UEr) d As sibility that an As has t(l,D[R represent the set of updates multiple BGP speakers. This more complete model of BG ter applying the explic as denying is necessary for est ablishing positive results about syste or permit ting an update, and assigning a local-preferene stability. value. For example, an explicit import policy could as- 3.1 BGP Routing sign rLocal-pref= 100 if As 1 appears in r as_pth or deny any update that includes As 2 in the path. Ulti The topology of a BGP system is modeled as a clustered mately, the import policy transforms the set of updates R graph G=(N, V, E), where the set N consists of ASes, as import (L, u)[R=ex-import (L, D )[im_imporI(L, D[R the vertex set V consists of all BGP-speaking routers, and the edge set E consists of all e bgP peering sessions. Each After applying the import policies for a route update from BGP speaker belongs to one AS and an As can have one or an eBGP session, v exchanges the update with all BGP ore BGP speakers. Let a(i)E N denote the AS that BGP spe akers in the same AS, using iBGP peaker i belongs to. each e bgp peering session involves a ss Select(S) pair of BGP speakers in different ASes. Each BGP-speaker that picks the best route for each prefix. The BGP speaker air in the same As has an iBGP session and a cost metric picks the route with the highest rlocal-pref, breaking ties that represents the dist ance between the two BGP speaker by selecting the route with the shor test r as_path. Note that based on the int radomain routing protocol. BGP speakers i local pre ference overrides the AS-path length. Amongst the d j in different ASes (i.e, a(i)ta() has a set of eBGP with the smallest r med, sions E(,)C E, which may be empty. Figure 1 shows breaking ties by select ing the route wit h the smallest cost to an example of the topology in a BGP systen the BGP speaker that passes the route via an iBGP session Note that, since the tie-breaking process draws on intrado A route update r includes the destination prefix (rprefis), main cost informat ion, t wo BGP speakers in the same AS lext-hop interface address(r nert-hop), AS path(ras-path) ay select difTerent best routes for the same prefix. If a tie U picks the route with the smallest r nert_ (r. med), and community set (. c-sen). Each BGP spe akd Each BGP speaker sends its best route(one best route for
✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✁ ✂ ✄ ☛ ✆ ✝ ✵ ✙ ✓ ✿ ❃ ❂ ❁ ✠ ✓ ✠ ✎ ☞ ✲ ✄ ✒ ✝ ✆ ✔ ✡ ✄ ✆ ✒ ✍ ✙ ✎ ✎ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✒ ✙ ✕ ✘ ✎ ✄ ✝ ✙ ✓ ✜ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✒ ✔ ✜ ✜ ✄ ✒ ✡ ✒ ✕ ✠ ✙ ✓ ✡ ✠ ✙ ✓ ✙ ✓ ✜ ✠ ✜ ✎ ✆ ✢ ✠ ✎ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✆ ✛ ✙ ✓ ✡ ✄ ✝ ✞ ✆ ✕ ✠ ✙ ✓ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✍ ✠ ✓ ✢ ✄ ✍ ✂ ✄ ✍ ✵ ✄ ✞ ✛ ✆ ✝ ✘ ✆ ✩ ✡ ✄ ✓ ✡ ✙ ✠ ✎ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✿ ❃ ❀ ❅ ❀ ✽ ❅ ❀ ❃ ❂ ❁ ✣ ✻ ✪ ✘ ✠ ✓ ✞ ✙ ✓ ✜ ✆ ✓ ✡ ✂ ✄ ✒ ✄ ✆ ✢ ✒ ✄ ✝ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✥ ✡ ✂ ✄ ☛ ✆ ✝ ✵ ✙ ✓ ✿ ✽ ❂ ❁ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✛ ✆ ✝ ✕ ✠ ✎ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✡ ✂ ✠ ✡ ✛ ✆ ✍ ✔ ✒ ✄ ✒ ✆ ✓ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✠ ✓ ✞ ✖ ✗ ✩ ✘ ✠ ✡ ✂ ✩ ✎ ✄ ✓ ✜ ✡ ✂ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✘ ✝ ✆ ✚ ✄ ✒ ✞ ✁ ✢ ✄ ☎ ✆ ✁ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✠ ✢ ✆ ✔ ✡ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✥ ✙ ✡ ✙ ✒ ✒ ✔ ✭ ✍ ✙ ✄ ✓ ✡ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✄ ✞ ✒ ✔ ✢ ✒ ✄ ✡ ✆ ✛ ✡ ✂ ✄ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✣ ✫ ✓ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✥ ✡ ✂ ✄ ✒ ✡ ✔ ✞ ☞ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✄ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✆ ✛ ✍ ✂ ✄ ✍ ✵ ✙ ✓ ✜ ✡ ✂ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✙ ✒ ✶ ✌ ✩ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✥ ✄ ✚ ✄ ✓ ☛ ✙ ✡ ✂ ✛ ✔ ✎ ✎ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✛ ✄ ✠ ✍ ✂ ✖ ✗ ✣ ✫ ✓ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✥ ✡ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✒ ✄ ✚ ✄ ✝ ✠ ✎ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✒ ✆ ✛ ✍ ✆ ✓ ✦ ✙ ✍ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✙ ✓ ✍ ✎ ✔ ✞ ✙ ✓ ✜ ✒ ✍ ✄ ✩ ✓ ✠ ✝ ✙ ✆ ✒ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ✞ ✙ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✆ ✍ ✍ ✔ ✝ ✒ ✆ ✓ ✎ ☞ ✠ ✛ ✡ ✄ ✝ ✠ ✎ ✙ ✓ ✵ ✛ ✠ ✙ ✎ ✔ ✝ ✄ ✣ ✖ ✛ ✆ ✎ ✎ ✆ ☛ ✩ ✔ ✘ ✘ ✠ ✘ ✄ ✝ ✿ ✸ ❁ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✕ ✆ ✞ ✄ ✎ ✡ ✂ ✠ ✡ ✍ ✠ ✘ ✩ ✡ ✔ ✝ ✄ ✒ ✡ ✂ ✄ ✠ ✒ ☞ ✓ ✍ ✂ ✝ ✆ ✓ ✆ ✔ ✒ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✙ ✓ ✜ ✆ ✛ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✠ ✡ ✄ ✠ ✍ ✂ ✖ ✗ ✣ ✁ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✛ ✆ ✝ ✕ ✠ ✎ ✙ ✲ ✄ ✒ ✡ ✂ ✄ ✓ ✆ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✟ ☎ ✄ ✁ ✂ ✁ ✟ ☎ ✄ ☎ ✁ ☛ ✂ ✄ ✝ ✄ ✓ ✆ ✖ ✗ ☛ ✆ ✔ ✎ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ✠ ✓ ✞ ✠ ✟ ✄ ✜ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✡ ✂ ✠ ✡ ✙ ✒ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✞ ✡ ✆ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✁ ✂ ✄ ✘ ✠ ✘ ✄ ✝ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✒ ✔ ✭ ✍ ✙ ✄ ✓ ✡ ✍ ✆ ✓ ✞ ✙ ✡ ✙ ✆ ✓ ✛ ✆ ✝ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✡ ✆ ✢ ✄ ✒ ✠ ✛ ✄ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✡ ✄ ✒ ✡ ✙ ✓ ✜ ✠ ✞ ✂ ✄ ✝ ✄ ✓ ✍ ✄ ✡ ✆ ✡ ✂ ✄ ✍ ✆ ✓ ✞ ✙ ✡ ✙ ✆ ✓ ✝ ✄ ✧ ✔ ✙ ✝ ✄ ✒ ✛ ✔ ✎ ✎ ✵ ✓ ✆ ☛ ✎ ✄ ✞ ✜ ✄ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ✠ ✓ ✞ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✖ ✗ ✣ ✁ ✂ ✄ ✒ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✒ ✔ ✜ ✜ ✄ ✒ ✡ ✡ ✂ ✠ ✡ ✙ ✡ ✕ ✠ ☞ ✢ ✄ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✡ ✆ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✙ ✓ ✠ ☛ ✠ ☞ ✡ ✂ ✠ ✡ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✒ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✥ ☛ ✂ ✙ ✎ ✄ ✒ ✡ ✙ ✎ ✎ ✠ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✜ ✝ ✄ ✠ ✡ ✄ ✝ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✡ ✂ ✠ ✓ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✩ ✘ ✠ ✡ ✂ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✣ ★ ✔ ✝ ✘ ✠ ✘ ✄ ✝ ✛ ✆ ✍ ✔ ✒ ✄ ✒ ✆ ✓ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✙ ✓ ✜ ✠ ✒ ✄ ✡ ✆ ✛ ✝ ✄ ✠ ✒ ✆ ✓ ✠ ✢ ✎ ✄ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✡ ✂ ✠ ✡ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✠ ✒ ✠ ✛ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✥ ✄ ✚ ✄ ✓ ✔ ✓ ✞ ✄ ✝ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✙ ✓ ✜ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ 3. ABSTRACT MODEL OF BGP ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✠ ✓ ✠ ✢ ✒ ✡ ✝ ✠ ✍ ✡ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✡ ✂ ✠ ✡ ☛ ✄ ✔ ✒ ✄ ✙ ✓ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✺ ✣ ✁ ✂ ✄ ✕ ✆ ✞ ✄ ✎ ✄ ✪ ✡ ✄ ✓ ✞ ✒ ✡ ✂ ✄ ☛ ✆ ✝ ✵ ✙ ✓ ✿ ✸ ❀ ✽ ❂ ❁ ✡ ✆ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✙ ✓ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✙ ☎ ✟ ✌ ✑ ✠ ✓ ✞ ✄ ✪ ✡ ✄ ✝ ✙ ✆ ✝ ☎ ✟ ✌ ✏ ✄ ☎ ✟ ✌ ✑ ✥ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ☎ ✟ ✌ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✆ ✘ ✄ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ✏ ✒ ✔ ✍ ✂ ✠ ✒ ✏ ✻ ✰ ✒ ✥ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✒ ✄ ✡ ✥ ✠ ✓ ✞ ✖ ✗ ✘ ✝ ✄ ✘ ✄ ✓ ✞ ✙ ✓ ✜ ✑ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✆ ✒ ✒ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✡ ✂ ✠ ✡ ✠ ✓ ✖ ✗ ✂ ✠ ✒ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✣ ✁ ✂ ✙ ✒ ✕ ✆ ✝ ✄ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✕ ✆ ✞ ✄ ✎ ✆ ✛ ☎ ✟ ✌ ✙ ✒ ✓ ✄ ✍ ✄ ✒ ✒ ✠ ✝ ☞ ✛ ✆ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✙ ✓ ✜ ✡ ✝ ✟ ✆ ☎ ✆ ✁ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✠ ✢ ✆ ✔ ✡ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ 3.1 BGP Routing ✁ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✆ ✛ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✕ ✆ ✞ ✄ ✎ ✄ ✞ ✠ ✒ ✠ ✍ ✎ ✔ ✒ ✡ ✄ ✝ ✄ ✞ ✜ ✝ ✠ ✘ ✂ ✂ ✄ ✏ ☎ ✆ ✝ ✆ ✞ ✑ ✥ ☛ ✂ ✄ ✝ ✄ ✡ ✂ ✄ ✒ ✄ ✡ ☎ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✖ ✗ ✄ ✒ ✥ ✡ ✂ ✄ ✚ ✄ ✝ ✡ ✄ ✪ ✒ ✄ ✡ ✝ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✠ ✎ ✎ ☎ ✟ ✌ ✩ ✒ ✘ ✄ ✠ ✵ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✄ ✞ ✜ ✄ ✒ ✄ ✡ ✞ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✠ ✎ ✎ ✄ ☎ ✟ ✌ ✘ ✄ ✄ ✝ ✙ ✓ ✜ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ ✻ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✢ ✄ ✎ ✆ ✓ ✜ ✒ ✡ ✆ ✆ ✓ ✄ ✖ ✗ ✠ ✓ ✞ ✠ ✓ ✖ ✗ ✍ ✠ ✓ ✂ ✠ ✚ ✄ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✣ ✟ ✄ ✡ ✠ ✏ ✡ ✑ ☛ ☎ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✡ ✂ ✠ ✡ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✢ ✄ ✎ ✆ ✓ ✜ ✒ ✡ ✆ ✣ ✻ ✠ ✍ ✂ ✄ ☎ ✟ ✌ ✘ ✄ ✄ ✝ ✙ ✓ ✜ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✒ ✠ ✘ ✠ ✙ ✝ ✆ ✛ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✖ ✗ ✄ ✒ ✣ ✻ ✠ ✍ ✂ ☎ ✟ ✌ ✩ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✘ ✠ ✙ ✝ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✂ ✠ ✒ ✠ ✓ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✠ ✓ ✞ ✠ ✍ ✆ ✒ ✡ ✕ ✄ ✡ ✝ ✙ ✍ ✡ ✂ ✠ ✡ ✝ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✡ ✂ ✄ ✞ ✙ ✒ ✡ ✠ ✓ ✍ ✄ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ✂ ✄ ✡ ☛ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✡ ✂ ✄ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✡ ✠ ✓ ✞ ☞ ✙ ✓ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✖ ✗ ✄ ✒ ✏ ✙ ✣ ✄ ✣ ✥ ✠ ✏ ✡ ✑ ✄✌ ✠ ✏ ☞ ✑ ✑ ✂ ✠ ✒ ✠ ✒ ✄ ✡ ✆ ✛ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✞ ✏ ✡ ✆ ☞ ✑ ✍ ✞ ✥ ☛ ✂ ✙ ✍ ✂ ✕ ✠ ☞ ✢ ✄ ✄ ✕ ✘ ✡ ☞ ✣ ✯ ✙ ✜ ✔ ✝ ✄ ✽ ✒ ✂ ✆ ☛ ✒ ✠ ✓ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✙ ✓ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✣ ✖ ✝ ✆ ✔ ✡ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ✎ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✏ ✎ ✓ ✏ ✎ ✑ ✒ ✡ ✓ ✑ ✥ ✓ ✄ ✪ ✡ ✩ ✂ ✆ ✘ ✙ ✓ ✡ ✄ ✝ ✛ ✠ ✍ ✄ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✏ ✎ ✓ ✔ ✑ ✓ ✕ ✖ ✗ ✏ ✑ ✥ ✖ ✗ ✘ ✠ ✡ ✂ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ✥ ✎ ✆ ✍ ✠ ✎ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✏ ✎ ✓ ✙ ✗ ✚ ✠ ✙ ✏ ✎ ✑ ✒ ✑ ✥ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✩ ✄ ✪ ✙ ✡ ✞ ✙ ✒ ✍ ✝ ✙ ✕ ✙ ✓ ✠ ✡ ✆ ✝ ✏ ✎ ✓ ✛ ✑ ✜ ✑ ✥ ✠ ✓ ✞ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✒ ✄ ✡ ✏ ✎ ✓ ✚ ✘ ✑ ✕ ✑ ✣ ✻ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✆ ✝ ✙ ✜ ✙ ✓ ✠ ✡ ✄ ✒ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✛ ✆ ✝ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✥ ✠ ✓ ✞ ✍ ✠ ✓ ✒ ✄ ✓ ✞ AS2 AS3 AS1 eBGP iBGP BGP speaker AS ✢ ✣ ✤ ✥ ✦ ✧ ★ ✩ ✪ ✫ ✧ ✬ ✭ ✮ ✯ ✰ ✧ ✱ ✲ ✭ ✳ ✴ ✵ ✶ ✷ ✶ ✸ ✧ ✮ ✸ ✱ ✯ ✱ ✰ ✱ ✤ ✷ ✡ ✂ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✙ ✕ ✕ ✄ ✞ ✙ ✠ ✡ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✚ ✙ ✠ ✠ ✓ ✙ ☎ ✟ ✌ ✆ ✝ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✣ ☎ ✟ ✌ ✩ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✘ ✠ ✙ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✔ ✒ ✄ ✙ ☎ ✟ ✌ ✡ ✆ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ☎ ✟ ✌ ✘ ✄ ✄ ✝ ✒ ✣ ✫ ✓ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✥ ✠ ✓ ✖ ✗ ✕ ✠ ☞ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✙ ✡ ✒ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✡ ✆ ✠ ✚ ✆ ✙ ✞ ✠ ✛ ✔ ✎ ✎ ✄ ✪ ✩ ✍ ✂ ✠ ✓ ✜ ✄ ✆ ✛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✘ ✠ ✙ ✝ ✒ ✏ ✄ ✣ ✜ ✣ ✥ ✢ ☞ ✔ ✒ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✝ ✄ ✦ ✄ ✍ ✡ ✆ ✝ ✒ ✑ ✣ ✁ ✂ ✄ ✒ ✄ ✆ ✘ ✡ ✙ ✕ ✙ ✲ ✠ ✡ ✙ ✆ ✓ ✒ ✠ ✝ ✄ ✙ ✓ ✡ ✄ ✓ ✞ ✄ ✞ ✡ ✆ ✝ ✄ ✞ ✔ ✍ ✄ ✙ ☎ ✟ ✌ ✡ ✝ ✠ ✭ ✍ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✠ ✳ ✄ ✍ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✩ ✒ ✙ ✆ ✓ ✒ ✿ ✽ ✽ ❁ ✠ ✓ ✞ ✥ ✂ ✄ ✓ ✍ ✄ ✥ ✠ ✝ ✄ ✓ ✆ ✡ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✞ ✙ ✓ ✆ ✔ ✝ ✕ ✆ ✞ ✄ ✎ ✣ ✴ ✆ ✔ ✡ ✩ ✙ ✓ ✜ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✞ ✚ ✙ ✠ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✠ ✝ ✄ ✡ ✝ ✠ ✓ ✒ ✛ ✆ ✝ ✕ ✄ ✞ ✠ ✍ ✍ ✆ ✝ ✞ ✙ ✓ ✜ ✡ ✆ ✡ ✂ ✄ ☎ ✟ ✌ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✱ ✄ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ✓ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✙ ☛ ✞ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ✹ ✠ ✓ ✞ ✺ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✺ ✝ ✄ ✍ ✄ ✙ ✚ ✄ ✒ ✠ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✻ ✆ ✓ ✙ ✛ ✝ ✆ ✕ ✹ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✺ ✠ ✘ ✘ ✎ ✙ ✄ ✒ ✆ ✌ ✡ ✝ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✡ ✆ ✡ ✝ ✠ ✓ ✒ ✛ ✆ ✝ ✕ ✙ ✓ ✍ ✆ ✕ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✔ ✘ ✩ ✞ ✠ ✡ ✄ ✒ ✥ ✠ ✓ ✞ ✠ ✘ ✘ ✎ ✙ ✄ ✒ ✁ ✒ ✡ ✝ ☎ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✢ ✄ ✛ ✆ ✝ ✄ ✒ ✄ ✓ ✞ ✙ ✓ ✜ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✹ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✠ ✘ ✘ ✎ ☞ ✢ ✆ ✡ ✂ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ✠ ✓ ✞ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✩ ✍ ✙ ✄ ✒ ✣ ✟ ✄ ✡ ✡ ✛ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✻ ❁ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✠ ✛ ✡ ✄ ✝ ✠ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✡ ✂ ✄ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✆ ✛ ✺ ✆ ✓ ✄ ✞ ✜ ✄ ✙ ✣ ✻ ✚ ✄ ✝ ☞ ✄ ✞ ✜ ✄ ✂ ✠ ✒ ✠ ✓ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✡ ✂ ✠ ✡ ✞ ✙ ✒ ✍ ✠ ✝ ✞ ✒ ✠ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✔ ✘ ✞ ✠ ✡ ✄ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ✝ ✄ ✍ ✄ ✙ ✚ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✬ ✒ ✖ ✗ ✠ ✎ ✝ ✄ ✠ ✞ ☞ ✠ ✘ ✩ ✘ ✄ ✠ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ❀ ✡ ✂ ✙ ✒ ✙ ✒ ✄ ✒ ✒ ✄ ✓ ✡ ✙ ✠ ✎ ✡ ✆ ✠ ✚ ✆ ✙ ✞ ✙ ✓ ✡ ✝ ✆ ✞ ✔ ✍ ✙ ✓ ✜ ✠ ✍ ☞ ✍ ✎ ✄ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ✙ ✛ ✠ ✏ ✺ ✑ ☛ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✥ ✡ ✂ ✄ ✓ ✡ ✛ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✼ ✎ ✽ ❁ ✄ ✼ ✽ ❀ ✆ ✡ ✂ ✄ ✝ ☛ ✙ ✒ ✄ ✡ ✛ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✼ ✎ ✽ ❁ ✄ ✼ ✎ ✽ ✓ ✟ ✄ ✡ ✑ ✓ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✻ ❁ ✝ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✠ ✛ ✩ ✡ ✄ ✝ ✠ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✡ ✂ ✄ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✥ ✒ ✔ ✍ ✂ ✠ ✒ ✞ ✄ ✓ ☞ ✙ ✓ ✜ ✆ ✝ ✘ ✄ ✝ ✕ ✙ ✡ ✡ ✙ ✓ ✜ ✠ ✓ ✔ ✘ ✞ ✠ ✡ ✄ ✥ ✠ ✓ ✞ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✠ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✚ ✠ ✎ ✔ ✄ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✠ ✓ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✍ ✆ ✔ ✎ ✞ ✠ ✒ ✩ ✒ ✙ ✜ ✓ ✎ ✓ ✙ ✗ ✚ ✠ ✙ ✏ ✎ ✑ ✒ ✄ ✽ ❂ ❂ ✙ ✛ ✖ ✗ ✽ ✠ ✘ ✘ ✄ ✠ ✝ ✒ ✙ ✓ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✆ ✝ ✞ ✄ ✓ ☞ ✠ ✓ ☞ ✔ ✘ ✞ ✠ ✡ ✄ ✡ ✂ ✠ ✡ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✖ ✗ ❃ ✙ ✓ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✣ ❆ ✎ ✡ ✙ ✩ ✕ ✠ ✡ ✄ ✎ ☞ ✥ ✡ ✂ ✄ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✡ ✝ ✠ ✓ ✒ ✛ ✆ ✝ ✕ ✒ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✻ ✠ ✒ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✻ ❁ ✄ ✑ ✓ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✡ ✛ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✺ ✑ ✿ ✻ ❁ ❁ ✣ ✖ ✛ ✡ ✄ ✝ ✠ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✡ ✂ ✄ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✛ ✆ ✝ ✠ ✝ ✆ ✔ ✡ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ✛ ✝ ✆ ✕ ✠ ✓ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✥ ✺ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✂ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ☛ ✙ ✡ ✂ ✠ ✎ ✎ ✆ ✡ ✂ ✄ ✝ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✥ ✔ ✒ ✙ ✓ ✜ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ ✻ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✺ ✡ ✂ ✄ ✓ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✠ ✝ ✆ ✔ ✡ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✾ ✑ ✙ ✑ ✚ ✕ ✏ ✾ ✑ ✡ ✂ ✠ ✡ ✘ ✙ ✍ ✵ ✒ ✡ ✂ ✄ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✘ ✝ ✄ ✮ ✪ ✣ ✁ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✘ ✙ ✍ ✵ ✒ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✄ ✂ ✙ ✜ ✂ ✄ ✒ ✡ ✎ ✓ ✙ ✗ ✚ ✠ ✙ ✏ ✎ ✑ ✒ ✥ ✢ ✝ ✄ ✠ ✵ ✙ ✓ ✜ ✡ ✙ ✄ ✒ ✢ ☞ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✄ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✎ ✆ ✍ ✠ ✎ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✆ ✚ ✄ ✝ ✝ ✙ ✞ ✄ ✒ ✡ ✂ ✄ ✖ ✗ ✩ ✘ ✠ ✡ ✂ ✎ ✄ ✓ ✜ ✡ ✂ ✣ ✖ ✕ ✆ ✓ ✜ ✒ ✡ ✡ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ✺ ✘ ✙ ✍ ✵ ✒ ✡ ✂ ✄ ✆ ✓ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✄ ✒ ✕ ✠ ✎ ✎ ✄ ✒ ✡ ✎ ✓ ✛ ✑ ✜ ✥ ✢ ✝ ✄ ✠ ✵ ✙ ✓ ✜ ✡ ✙ ✄ ✒ ✢ ☞ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✡ ✂ ✄ ✒ ✕ ✠ ✎ ✎ ✄ ✒ ✡ ✍ ✆ ✒ ✡ ✡ ✆ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✂ ✠ ✡ ✘ ✠ ✒ ✒ ✄ ✒ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✚ ✙ ✠ ✠ ✓ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✥ ✒ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✡ ✙ ✄ ✩ ✢ ✝ ✄ ✠ ✵ ✙ ✓ ✜ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✞ ✝ ✠ ☛ ✒ ✆ ✓ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✩ ✕ ✠ ✙ ✓ ✍ ✆ ✒ ✡ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✥ ✡ ☛ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✕ ✠ ☞ ✒ ✄ ✎ ✄ ✍ ✡ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✛ ✆ ✝ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✘ ✝ ✄ ✮ ✪ ✣ ✫ ✛ ✠ ✡ ✙ ✄ ✒ ✡ ✙ ✎ ✎ ✄ ✪ ✙ ✒ ✡ ✒ ✥ ✺ ✘ ✙ ✍ ✵ ✒ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ 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each prefix) via eBGP sessions. The BGP p session route is immediately available and that these routes are implicit and explicit export policies on each eB propagated via iBGP sessions. This si assump to a neighboring BGP speaker v, defined as im_rport(, u) tion does not affect the BGP converger and er_rport(L, u), respectively. Each BGP speaker u ap neighbors updates would eventually be ble(e. g lies an implicit policy that sets r local-pref and r med to after finite propagation de lay) default values, assigns rnert_hop to us interface connecting to l, and prepends u to r, as-path. Explicit export policies Since each BGP speaker operates independent ly, we cannot include permit ting or denying the route, assigning r. med, assume that every BGP speaker is ac tivated at the same g r C-set, and prepending u one or more times to time. Instead, as in [9, we consider a subset A c V of ath. For example, as u could dec line to advert ise speakers that are activated at a given time. The remaining routes to as u that have community 10 in the com mt BGP speakers do not apply the pat h-select ion process and nity set. Also, As u could prepend u two times to the hence, do not change their best route. Therefore, the next As path for prefix 1.2.3.0/ 24 and for any route that in- state s =(si, $2,...,n)has si= Best Route(i, s)for i E A, des As 2 in the As path. Ultimately, the export pol y transforms the set of updates R as export(,u)(R]= from state s to given the activation set A. The definition of the state of a bgP system, and the notion of an act iva- transformed updates to u using e BGP sessions. tion set, allows us to precisely de fine the not ion of stability 3.2 Distributed Path Selection For mally, a state s is stable if and only if s i s for any activation set A. That is, when the system is in stat The route-selection process proceeds in a distributed and AS would change to a different route synchronous fashion, triggered by advertisements and with- drawals of routes. Rat her than modeling the exact timing To study convergence, we define an activation sequence as rocess of each BGP speaker. For the sake of simplici (possibly infinite)sequence of ac tivations. Let a denot e the act ivation sequence and ad) denote the jth ac ti efix d tha vation in o. In st udying c gence, we need to consider ASd; since address aggregation does not affect the conver- sequences that ac tivate each AS several times. In particular, nce properties, it is sufficient to consider the set of routes a fair activation sequence a is an infinite sequence that has to a single do estination prefix. Each speaker applies the Bgi infinitely many elements j such that n E o(), for each BGP import policies to the routes that have been exported by speaker n E V. A BGP system converge equence and an initial state if it arrives at a st able s neighbors. BGP is an incremental protocol, where each after the activation sequence. Formally, for an activation speaker reme mbers the routes advertised by neighbors until sequence a and an initial state s, a BGP system converges they are wit drawn, and se lects a best path from this set In a st able st ate, a BGP speaker remembers precise ly those if there is a finite j such that so 4 l a outes that have been chosen by its neighbors. Hence, for studying convergence properties, it is sufficient to define the tate of the bgp system in terms of the route chosen by Thus far, we have defined the not ion of a stable state. But ach BGP speaker. That is, we assume that each speaker some bgP systems have a stable st ate without necessarily e members only its own best route, selected from the set of onverging. For example, Figure 2 shows an example where outes exported by its neighbors. As such, we define the three ASes are connec ted pairwise and As O originates desti- n), where si denotes nat ion prefix d [10]; with each As, we list the set of possible the route chosen by speaker i =1, 2,...,n routes in order of pre ference. Both As 1 and As 2 prefer the pat h through the neighbor over the direct route to reach he system state occur when one or more BGP d. The system has a st able st ate. For example, AS 2 could speakers apply the route selectio use the direct route(0)and As 1 could use the route(2,0) tivating a speaker applies the export policies of the BGP Ho he system could also oscillate bet peakers in neighboring A Ses the speakers import policies ble states. In the first state, both A Ses have selected the di- d the bgP path-se lec tion t route(0). Then, if activated simultaneously, both Ase the BgP speaker resides in ASa, the route to d is a ro (e.g, As2 switches to (1,0)) (denoted as ro) that cont ains a null As path. Ot Then, if ac tivated again, both ASes return to their direct the selection of si can be affected by the route chosen by routes, and the process repeats. Whether or not the sys- at has a BGP tem eventually reaches a stable state depends on the k∈a(), This includes the BGP peers of speaker,画Hm, we define a st ronger notion of a小BCPm essing of the since i could learn about t hese routes via ibGP sessio stem is safe if it has a stable The choices available to speaker i depend on the route s ler any fair act ivat ion sequence and any initial state the export policies of j, and the import policies of k if a(i)=Asd Choices(, s) UIEE(kj)AkEa(i import(L, k )[export(L, )(s, 4. HIERARCHICAL AS GRAPH Our policy configuration guidelines capitalize on the fact t hat A Ses are interconnected in a hierarchical fashion. In Then, i selects a route Best Route(i, s)=Select (C hoices(i, s)). this section, we describe the relat ionships bet ween ASes and Note that the model assumes that each external neighbors the result ing hierarchical structure
✄ ✠ ✍ ✂ ✘ ✝ ✄ ✮ ✪ ✑ ✚ ✙ ✠ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ ✁ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✹ ✠ ✘ ✘ ✎ ✙ ✄ ✒ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ✠ ✓ ✞ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✓ ✄ ✠ ✍ ✂ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✙ ✡ ✆ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✺ ✥ ✞ ✄ ✮ ✓ ✄ ✞ ✠ ✒ ✡ ✛ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✠ ✓ ✞ ✑ ✓ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✥ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✎ ☞ ✣ ✻ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✹ ✠ ✘ ✩ ✘ ✎ ✙ ✄ ✒ ✠ ✓ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✡ ✂ ✠ ✡ ✒ ✄ ✡ ✒ ✎ ✓ ✙ ✗ ✚ ✠ ✙ ✏ ✎ ✑ ✒ ✠ ✓ ✞ ✎ ✓ ✛ ✑ ✜ ✡ ✆ ✞ ✄ ✛ ✠ ✔ ✎ ✡ ✚ ✠ ✎ ✔ ✄ ✒ ✥ ✠ ✒ ✒ ✙ ✜ ✓ ✒ ✎ ✓ ✔ ✑ ✓ ✕ ✖ ✗ ✏ ✡ ✆ ✹ ✬ ✒ ✙ ✓ ✡ ✄ ✝ ✛ ✠ ✍ ✄ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✓ ✜ ✡ ✆ ✙ ✥ ✠ ✓ ✞ ✘ ✝ ✄ ✘ ✄ ✓ ✞ ✒ ✹ ✡ ✆ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✣ ✻ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✘ ✄ ✝ ✕ ✙ ✡ ✡ ✙ ✓ ✜ ✆ ✝ ✞ ✄ ✓ ☞ ✙ ✓ ✜ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✥ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✎ ✓ ✛ ✑ ✜ ✥ ✠ ✒ ✒ ✙ ✜ ✓ ✙ ✓ ✜ ✎ ✓ ✚ ✘ ✑ ✕ ✥ ✠ ✓ ✞ ✘ ✝ ✄ ✘ ✄ ✓ ✞ ✙ ✓ ✜ ✹ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ✡ ✙ ✕ ✄ ✒ ✡ ✆ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✖ ✗ ✹ ✍ ✆ ✔ ✎ ✞ ✞ ✄ ✍ ✎ ✙ ✓ ✄ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✖ ✗ ✺ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✽ ❂ ✙ ✓ ✡ ✂ ✄ ✍ ✆ ✕ ✕ ✔ ✩ ✓ ✙ ✡ ☞ ✒ ✄ ✡ ✣ ✖ ✎ ✒ ✆ ✥ ✖ ✗ ✹ ✍ ✆ ✔ ✎ ✞ ✘ ✝ ✄ ✘ ✄ ✓ ✞ ✹ ✡ ☛ ✆ ✡ ✙ ✕ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✛ ✆ ✝ ✘ ✝ ✄ ✮ ✪ ✽ ✓ ❃ ✓ ✾ ✓ ❂ ✔ ❃ ☛ ✠ ✓ ✞ ✛ ✆ ✝ ✠ ✓ ☞ ✝ ✆ ✔ ✡ ✄ ✡ ✂ ✠ ✡ ✙ ✓ ✩ ✍ ✎ ✔ ✞ ✄ ✒ ✖ ✗ ❃ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ❆ ✎ ✡ ✙ ✕ ✠ ✡ ✄ ✎ ☞ ✥ ✡ ✂ ✄ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✩ ✙ ✍ ☞ ✡ ✝ ✠ ✓ ✒ ✛ ✆ ✝ ✕ ✒ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✻ ✠ ✒ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✿ ✻ ❁ ✄ ✑ ✓ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✿ ✡ ✛ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✿ ✻ ❁ ❁ ✣ ✁ ✂ ✄ ✓ ✥ ✹ ✡ ✝ ✠ ✓ ✒ ✕ ✙ ✡ ✒ ✡ ✂ ✄ ✒ ✄ ✡ ✝ ✠ ✓ ✒ ✛ ✆ ✝ ✕ ✄ ✞ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✡ ✆ ✺ ✔ ✒ ✙ ✓ ✜ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ 3.2 Distributed Path Selection ✁ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✩ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✘ ✝ ✆ ✍ ✄ ✄ ✞ ✒ ✙ ✓ ✠ ✞ ✙ ✒ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✞ ✠ ✓ ✞ ✠ ✒ ☞ ✓ ✍ ✂ ✝ ✆ ✓ ✆ ✔ ✒ ✛ ✠ ✒ ✂ ✙ ✆ ✓ ✥ ✡ ✝ ✙ ✜ ✜ ✄ ✝ ✄ ✞ ✢ ☞ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✒ ✠ ✓ ✞ ☛ ✙ ✡ ✂ ✩ ✞ ✝ ✠ ☛ ✠ ✎ ✒ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✴ ✠ ✡ ✂ ✄ ✝ ✡ ✂ ✠ ✓ ✕ ✆ ✞ ✄ ✎ ✙ ✓ ✜ ✡ ✂ ✄ ✄ ✪ ✠ ✍ ✡ ✡ ✙ ✕ ✙ ✓ ✜ ✆ ✛ ✕ ✄ ✒ ✒ ✠ ✜ ✄ ✡ ✝ ✠ ✓ ✒ ✕ ✙ ✒ ✒ ✙ ✆ ✓ ✒ ✥ ☛ ✄ ✛ ✆ ✍ ✔ ✒ ✆ ✓ ✡ ✂ ✄ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✩ ✕ ✠ ✵ ✙ ✓ ✜ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✆ ✛ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✣ ✯ ✆ ✝ ✡ ✂ ✄ ✒ ✠ ✵ ✄ ✆ ✛ ✒ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ☞ ✥ ☛ ✄ ✛ ✆ ✍ ✔ ✒ ✆ ✓ ✠ ✒ ✙ ✓ ✜ ✎ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✜ ✡ ✂ ✠ ✡ ✆ ✝ ✙ ✜ ✙ ✓ ✠ ✡ ✄ ✒ ✛ ✝ ✆ ✕ ✾ ✁ ❀ ✒ ✙ ✓ ✍ ✄ ✠ ✞ ✞ ✝ ✄ ✒ ✒ ✠ ✜ ✜ ✝ ✄ ✜ ✠ ✡ ✙ ✆ ✓ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✡ ✂ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✩ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✥ ✙ ✡ ✙ ✒ ✒ ✔ ✭ ✍ ✙ ✄ ✓ ✡ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✒ ✙ ✓ ✜ ✎ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✣ ✻ ✠ ✍ ✂ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✠ ✘ ✘ ✎ ✙ ✄ ✒ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✡ ✆ ✘ ✙ ✍ ✵ ✙ ✡ ✒ ✢ ✄ ✒ ✡ ✘ ✠ ✡ ✂ ✡ ✆ ✜ ✥ ✠ ✛ ✡ ✄ ✝ ✠ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✄ ✪ ✘ ✆ ✝ ✡ ✄ ✞ ✢ ☞ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✣ ☎ ✟ ✌ ✙ ✒ ✠ ✓ ✙ ✓ ✍ ✝ ✄ ✕ ✄ ✓ ✡ ✠ ✎ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✥ ☛ ✂ ✄ ✝ ✄ ✄ ✠ ✍ ✂ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✕ ✄ ✕ ✢ ✄ ✝ ✒ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✞ ✢ ☞ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✔ ✓ ✡ ✙ ✎ ✡ ✂ ✄ ☞ ✠ ✝ ✄ ☛ ✙ ✡ ✂ ✞ ✝ ✠ ☛ ✓ ✥ ✠ ✓ ✞ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✠ ✢ ✄ ✒ ✡ ✘ ✠ ✡ ✂ ✛ ✝ ✆ ✕ ✡ ✂ ✙ ✒ ✒ ✄ ✡ ✣ ✫ ✓ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✥ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✕ ✄ ✕ ✢ ✄ ✝ ✒ ✘ ✝ ✄ ✍ ✙ ✒ ✄ ✎ ☞ ✡ ✂ ✆ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✍ ✂ ✆ ✒ ✄ ✓ ✢ ☞ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✛ ✆ ✝ ✒ ✡ ✔ ✞ ☞ ✙ ✓ ✜ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✥ ✙ ✡ ✙ ✒ ✒ ✔ ✭ ✍ ✙ ✄ ✓ ✡ ✡ ✆ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✒ ✡ ✠ ✡ ✄ ✆ ✛ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✓ ✡ ✄ ✝ ✕ ✒ ✆ ✛ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✍ ✂ ✆ ✒ ✄ ✓ ✢ ☞ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ☛ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✄ ✠ ✍ ✂ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✕ ✄ ✕ ✢ ✄ ✝ ✒ ✆ ✓ ✎ ☞ ✙ ✡ ✒ ✆ ☛ ✓ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✥ ✒ ✄ ✎ ✄ ✍ ✡ ✄ ✞ ✛ ✝ ✆ ✕ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✄ ✪ ✘ ✆ ✝ ✡ ✄ ✞ ✢ ☞ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✣ ✖ ✒ ✒ ✔ ✍ ✂ ✥ ☛ ✄ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✡ ✄ ✠ ✒ ✠ ✚ ✄ ✍ ✡ ✆ ✝ ✘ ✄ ✏ ✘ ✂ ✆ ✘ ✄ ✆ ✓ ✓ ✓ ✆ ✘ ☎ ✑ ✥ ☛ ✂ ✄ ✝ ✄ ✘ ✆ ✞ ✄ ✓ ✆ ✡ ✄ ✒ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✍ ✂ ✆ ✒ ✄ ✓ ✢ ☞ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✄ ✽ ✆ ❃ ✆ ✓ ✓ ✓ ✆ ✔ ✣ ✷ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✡ ✄ ✆ ✍ ✍ ✔ ✝ ☛ ✂ ✄ ✓ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✠ ✘ ✘ ✎ ☞ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ✄ ✛ ✝ ☎ ✆ ✄ ☎ ✆ ✞ ✢ ✠ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✠ ✘ ✘ ✎ ✙ ✄ ✒ ✡ ✂ ✄ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✛ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✥ ✡ ✂ ✄ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✬ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ☎ ✟ ✌ ✘ ✠ ✡ ✂ ✩ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✿ ✸ ❁ ✣ ✫ ✓ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✥ ✙ ✛ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✒ ✙ ✞ ✄ ✒ ✙ ✓ ✾ ✁ ✥ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✜ ✙ ✒ ✠ ✝ ✆ ✔ ✡ ✄ ✏ ✞ ✄ ✓ ✆ ✡ ✄ ✞ ✠ ✒ ✎ ✞ ✑ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✒ ✠ ✓ ✔ ✎ ✎ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ★ ✡ ✂ ✄ ✝ ☛ ✙ ✒ ✄ ✥ ✡ ✂ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✘ ✆ ✍ ✠ ✓ ✢ ✄ ✠ ✳ ✄ ✍ ✡ ✄ ✞ ✢ ☞ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✍ ✂ ✆ ✒ ✄ ✓ ✢ ☞ ✠ ✓ ☞ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ☞ ✡ ✂ ✠ ✡ ✂ ✠ ✒ ✠ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✠ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✟ ☛ ✠ ✏ ✡ ✑ ✣ ✁ ✂ ✙ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✡ ✂ ✄ ☎ ✟ ✌ ✘ ✄ ✄ ✝ ✒ ✆ ✛ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✥ ✠ ✒ ☛ ✄ ✎ ✎ ✠ ✒ ✡ ✂ ✄ ☎ ✟ ✌ ✘ ✄ ✄ ✝ ✒ ✆ ✛ ✡ ✂ ✄ ✆ ✡ ✂ ✄ ✝ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✥ ✒ ✙ ✓ ✍ ✄ ✡ ✍ ✆ ✔ ✎ ✞ ✎ ✄ ✠ ✝ ✓ ✠ ✢ ✆ ✔ ✡ ✡ ✂ ✄ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✚ ✙ ✠ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ ✁ ✂ ✄ ✍ ✂ ✆ ✙ ✍ ✄ ✒ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✡ ✆ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✞ ✄ ✘ ✄ ✓ ✞ ✆ ✓ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✘ ✠ ✥ ✡ ✂ ✄ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✛ ☞ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✛ ✟ ✡ ☛ ✖ ✗ ✡ ✚ ✑ ✘ ✏ ✡ ✆ ✘ ✑ ✄ ☞ ✌ ✍ ✎ ✞ ✆ ✙ ✛ ✠ ✏ ✡ ✑ ✄ ✾ ✁ ✎ ✏ ✑ ✒ ✓ ✔ ✕ ✠ ✖ ✗ ✔ ✑ ✘ ✓ ✆ ✖ ✡ ✛ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✟ ✑ ✿ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ☞ ✑ ✏ ✘ ✠ ✑ ❁ ✆ ✆ ✡ ✂ ✄ ✝ ☛ ✙ ✒ ✄ ✁ ✂ ✄ ✓ ✥ ✡ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✠ ✝ ✆ ✔ ✡ ✄ ✙ ✑ ✘ ✕ ✻ ✗ ✹ ✕ ✑ ✏ ✡ ✆ ✘ ✑ ✄ ✾ ✑ ✙ ✑ ✚ ✕ ✏ ☛ ✖ ✗ ✡ ✚ ✑ ✘ ✏ ✡ ✆ ✘ ✑ ✑ ✓ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✕ ✆ ✞ ✄ ✎ ✠ ✒ ✒ ✔ ✕ ✄ ✒ ✡ ✂ ✠ ✡ ✄ ✠ ✍ ✂ ✄ ✪ ✡ ✄ ✝ ✓ ✠ ✎ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✬ ✒ ✝ ✆ ✔ ✡ ✄ ✙ ✒ ✙ ✕ ✕ ✄ ✞ ✙ ✠ ✡ ✄ ✎ ☞ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✠ ✓ ✞ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✝ ✄ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✞ ✚ ✙ ✠ ✙ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✣ ✁ ✂ ✙ ✒ ✒ ✙ ✕ ✘ ✎ ✙ ✛ ☞ ✙ ✓ ✜ ✠ ✒ ✒ ✔ ✕ ✘ ✩ ✡ ✙ ✆ ✓ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✥ ✠ ✒ ✡ ✂ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✬ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ☛ ✆ ✔ ✎ ✞ ✄ ✚ ✄ ✓ ✡ ✔ ✠ ✎ ✎ ☞ ✢ ✄ ✍ ✆ ✕ ✄ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✏ ✄ ✣ ✜ ✣ ✥ ✠ ✛ ✡ ✄ ✝ ✮ ✓ ✙ ✡ ✄ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✙ ✆ ✓ ✞ ✄ ✎ ✠ ☞ ✑ ✣ ✗ ✙ ✓ ✍ ✄ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✆ ✘ ✄ ✝ ✠ ✡ ✄ ✒ ✙ ✓ ✞ ✄ ✘ ✄ ✓ ✞ ✄ ✓ ✡ ✎ ☞ ✥ ☛ ✄ ✍ ✠ ✓ ✓ ✆ ✡ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✄ ✚ ✄ ✝ ☞ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✙ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✠ ✡ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✡ ✙ ✕ ✄ ✣ ✫ ✓ ✒ ✡ ✄ ✠ ✞ ✥ ✠ ✒ ✙ ✓ ✿ ✸ ❁ ✥ ☛ ✄ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ✒ ✔ ✢ ✒ ✄ ✡ ✍ ✝ ✆ ✛ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✠ ✝ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✠ ✡ ✠ ✜ ✙ ✚ ✄ ✓ ✡ ✙ ✕ ✄ ✣ ✁ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✞ ✆ ✓ ✆ ✡ ✠ ✘ ✘ ✎ ☞ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✩ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✠ ✓ ✞ ✥ ✂ ✄ ✓ ✍ ✄ ✥ ✞ ✆ ✓ ✆ ✡ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✙ ✝ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ✡ ✂ ✄ ✓ ✄ ✪ ✡ ✒ ✡ ✠ ✡ ✄ ✘ ✚ ✄ ✏ ✘ ✚✂ ✆ ✘ ✄✚ ✆ ✓ ✓ ✓ ✆ ✘ ✚☎ ✑ ✂ ✠ ✒ ✘ ✚✆ ✄ ✙ ✑ ✘ ✕ ✻ ✗ ✹ ✕ ✑ ✏ ✡ ✆ ✘ ✑ ✛ ✆ ✝ ✡ ☛ ✥ ✠ ✓ ✞ ✘ ✚✆ ✄ ✘ ✆ ✛ ✆ ✝ ✡ ☛✌ ✣ ✱ ✄ ✎ ✄ ✡ ✘ ✜✛ ✘ ✚ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✛ ✝ ✆ ✕ ✒ ✡ ✠ ✡ ✄ ✘ ✡ ✆ ✘ ✚ ✜ ✙ ✚ ✄ ✓ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✡ ✣ ✁ ✂ ✄ ✞ ✄ ✮ ✓ ✙ ✡ ✙ ✆ ✓ ✆ ✛ ✡ ✂ ✄ ✒ ✡ ✠ ✡ ✄ ✆ ✛ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✓ ✆ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✩ ✡ ✙ ✆ ✓ ✒ ✄ ✡ ✥ ✠ ✎ ✎ ✆ ☛ ✒ ✔ ✒ ✡ ✆ ✘ ✝ ✄ ✍ ✙ ✒ ✄ ✎ ☞ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✓ ✆ ✡ ✙ ✆ ✓ ✆ ✛ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ✠ ✒ ✡ ✠ ✡ ✄ ✘ ✙ ✒ ✟ ☎ ✄ ✁ ✂ ✁ ✙ ✛ ✠ ✓ ✞ ✆ ✓ ✎ ☞ ✙ ✛ ✘ ✜✛ ✘ ✛ ✆ ✝ ✠ ✓ ☞ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✡ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ☛ ✂ ✄ ✓ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✙ ✓ ✒ ✡ ✠ ✡ ✄ ✘ ✥ ✓ ✆ ✖ ✗ ☛ ✆ ✔ ✎ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✆ ✠ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✝ ✆ ✔ ✡ ✄ ✣ ✁ ✆ ✒ ✡ ✔ ✞ ☞ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✥ ☛ ✄ ✞ ✄ ✮ ✓ ✄ ✠ ✓ ✄ ✛ ☎ ✆ ✄ ☎ ✆ ✝ ✞ ✟ ✁ ✢ ☞ ✁ ✞ ✛ ✁ ✠ ✒ ✠ ✏ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ☞ ✙ ✓ ✮ ✓ ✙ ✡ ✄ ✑ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✣ ✟ ✄ ✡ ✣ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✠ ✓ ✞ ✣ ✏ ☞ ✑ ✍ ✝ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ☞ ✡ ✂ ✠ ✍ ✡ ✙ ✩ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✣ ✣ ✫ ✓ ✒ ✡ ✔ ✞ ☞ ✙ ✓ ✜ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✥ ☛ ✄ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✄ ✠ ✍ ✂ ✖ ✗ ✒ ✄ ✚ ✄ ✝ ✠ ✎ ✡ ✙ ✕ ✄ ✒ ✣ ✫ ✓ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✥ ✠ ✜ ✄ ✆ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✙ ✒ ✠ ✓ ✙ ✓ ✮ ✓ ✙ ✡ ✄ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✡ ✂ ✠ ✡ ✂ ✠ ✒ ✙ ✓ ✮ ✓ ✙ ✡ ✄ ✎ ☞ ✕ ✠ ✓ ☞ ✄ ✎ ✄ ✕ ✄ ✓ ✡ ✒ ☞ ✒ ✔ ✍ ✂ ✡ ✂ ✠ ✡ ✔ ☛ ✣ ✏ ☞ ✑ ✥ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✔ ☛ ✝ ✣ ✖ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✛ ✝ ✞ ✁ ✢ ✁ ✟ ✆ ✓ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✠ ✓ ✞ ✠ ✓ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✙ ✛ ✙ ✡ ✠ ✝ ✝ ✙ ✚ ✄ ✒ ✠ ✡ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ✛ ✆ ✝ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✠ ✓ ✞ ✠ ✓ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✘ ✞ ✥ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✙ ✛ ✡ ✂ ✄ ✝ ✄ ✙ ✒ ✠ ✮ ✓ ✙ ✡ ✄ ☞ ✒ ✔ ✍ ✂ ✡ ✂ ✠ ✡ ✘ ✞ ✤ ✓ ✂ ✖ ✜ ✘ ✂ ✤ ✓ ✄ ✖ ✜ ✓ ✓ ✓ ✤ ✓ ✠ ✖ ✜ ✘ ✠ ✠ ✓ ✞ ✘ ✠ ✙ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✁ ✂ ✔ ✒ ✛ ✠ ✝ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✞ ✄ ✮ ✓ ✄ ✞ ✡ ✂ ✄ ✓ ✆ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ☎ ✔ ✡ ✥ ✒ ✆ ✕ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✂ ✠ ✚ ✄ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✓ ✄ ✍ ✄ ✒ ✒ ✠ ✝ ✙ ✎ ☞ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✙ ✓ ✜ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✯ ✙ ✜ ✔ ✝ ✄ ❃ ✒ ✂ ✆ ☛ ✒ ✠ ✓ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ☛ ✂ ✄ ✝ ✄ ✡ ✂ ✝ ✄ ✄ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✄ ✞ ✘ ✠ ✙ ✝ ☛ ✙ ✒ ✄ ✠ ✓ ✞ ✖ ✗ ❂ ✆ ✝ ✙ ✜ ✙ ✓ ✠ ✡ ✄ ✒ ✞ ✄ ✒ ✡ ✙ ✩ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✜ ✿ ✽ ❂ ❁ ❀ ☛ ✙ ✡ ✂ ✄ ✠ ✍ ✂ ✖ ✗ ✥ ☛ ✄ ✎ ✙ ✒ ✡ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✙ ✓ ✆ ✝ ✞ ✄ ✝ ✆ ✛ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✣ ☎ ✆ ✡ ✂ ✖ ✗ ✽ ✠ ✓ ✞ ✖ ✗ ❃ ✘ ✝ ✄ ✛ ✄ ✝ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✡ ✂ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✆ ✚ ✄ ✝ ✡ ✂ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✝ ✄ ✠ ✍ ✂ ✜ ✣ ✁ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✂ ✠ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✖ ✗ ❃ ✍ ✆ ✔ ✎ ✞ ✔ ✒ ✄ ✡ ✂ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✏ ❂ ✑ ✠ ✓ ✞ ✖ ✗ ✽ ✍ ✆ ✔ ✎ ✞ ✔ ✒ ✄ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✏ ❃ ✆ ❂ ✑ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✍ ✆ ✔ ✎ ✞ ✠ ✎ ✒ ✆ ✆ ✒ ✍ ✙ ✎ ✎ ✠ ✡ ✄ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ✔ ✓ ✒ ✡ ✠ ✩ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✒ ✣ ✫ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✒ ✡ ✠ ✡ ✄ ✥ ✢ ✆ ✡ ✂ ✖ ✗ ✄ ✒ ✂ ✠ ✚ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✄ ✞ ✡ ✂ ✄ ✞ ✙ ✩ ✝ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✏ ❂ ✑ ✣ ✁ ✂ ✄ ✓ ✥ ✙ ✛ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✒ ✙ ✕ ✔ ✎ ✡ ✠ ✓ ✄ ✆ ✔ ✒ ✎ ☞ ✥ ✢ ✆ ✡ ✂ ✖ ✗ ✄ ✒ ✒ ☛ ✙ ✡ ✍ ✂ ✡ ✆ ✡ ✂ ✄ ✙ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✏ ✄ ✣ ✜ ✣ ✥ ✖ ✗ ❃ ✒ ☛ ✙ ✡ ✍ ✂ ✄ ✒ ✡ ✆ ✏ ✽ ✆ ❂ ✑ ✑ ✣ ✁ ✂ ✄ ✓ ✥ ✙ ✛ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✠ ✜ ✠ ✙ ✓ ✥ ✢ ✆ ✡ ✂ ✖ ✗ ✄ ✒ ✝ ✄ ✡ ✔ ✝ ✓ ✡ ✆ ✡ ✂ ✄ ✙ ✝ ✞ ✙ ✝ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✝ ✄ ✘ ✄ ✠ ✡ ✒ ✣ ✱ ✂ ✄ ✡ ✂ ✄ ✝ ✆ ✝ ✓ ✆ ✡ ✡ ✂ ✄ ✒ ☞ ✒ ✩ ✡ ✄ ✕ ✄ ✚ ✄ ✓ ✡ ✔ ✠ ✎ ✎ ☞ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✞ ✄ ✘ ✄ ✓ ✞ ✒ ✆ ✓ ✡ ✂ ✄ ✄ ✪ ✠ ✍ ✡ ✡ ✙ ✕ ✙ ✓ ✜ ✆ ✛ ✡ ✂ ✄ ✝ ✄ ✍ ✄ ✘ ✡ ✙ ✆ ✓ ✠ ✓ ✞ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✙ ✓ ✜ ✆ ✛ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ☛ ✄ ✞ ✄ ✮ ✓ ✄ ✠ ✒ ✡ ✝ ✆ ✓ ✜ ✄ ✝ ✓ ✆ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✟ ✄ ✜ ✁ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✿ ✸ ❁ ✣ ✖ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✟ ✄ ✜ ✁ ✙ ✛ ✙ ✡ ✂ ✠ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✓ ✞ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✔ ✓ ✞ ✄ ✝ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✠ ✓ ✞ ✠ ✓ ☞ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✣ 4. HIERARCHICAL AS GRAPH ★ ✔ ✝ ✘ ✆ ✎ ✙ ✍ ☞ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✍ ✠ ✘ ✙ ✡ ✠ ✎ ✙ ✲ ✄ ✆ ✓ ✡ ✂ ✄ ✛ ✠ ✍ ✡ ✡ ✂ ✠ ✡ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✄ ✞ ✙ ✓ ✠ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✛ ✠ ✒ ✂ ✙ ✆ ✓ ✣ ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✡ ✂ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✣
ASI backup link Figure 2: A BGP system has a stable state but Figure 3: A hierarchical As interconnection might not converge 4.1 Clients Providers and Peers We assume t hat t here is a hierarchical customer er re. S relat ionships arise from contracts that define the pricing lat ionship among ASes. The hierarchical struct ure arises be model and the exchange of traffic. In a fy(hPT-tTUamI cause an aS typically uses an AS of larger size as a provider relationship, the customer is typically a smaller As that An As u serving a metropol tan area is likely to have a re- ays a larger AS for access to the rest of the Internet. The gional provider U, and a regional AS v is likely to have a provider may, in turn, be a customer of an even larger AS nat ional der w; it is very unlikely that a nationwide In a tT*-B-tTP relationship, the t wo peers are typically AS w would be a customer of a metropolit an-area AS u ble size and find it mut ually advantageous to That is, if u E customer(u) and u E customer(w), then w 6 xchange traffic between the ir respective customers. Eac customer(u). AS U is a mo'I Bprovider of u, whereas As w BGP session defines a rel wo A Ses it is an adnoMI Bprovider of w. Any direct or indirect provide onnects. Alt hough there might be multiple eBGP sessions of u cannot be a customer of u. To simplify the discus bet ween two ASes, the relationship bet ween the two A Ses sion, we define two directed graphs formed by the customer should be uniquely defined. An As a may have multiple provider re lationships. In the t rumi*-B-fyPTb'et a customers, providers, and peers. We define customer(a), the edges are directed from provider to customer. The re peer(a), and provider(a)as the set of customers, peers, an graph formed b only provider-cust omer relation- providers of a, respectively. We let first(rra s-path )denote ships should no"Il Bime fcfld bet a (DAG), as shown in the first AS in rIms_path. A route r is classified as a t he example in Figure 3. In the fy(B PT-B-troamlbet a tomer route of a if first(rns-path)e customer(a), a peer the edges are directed from customer to provider route if first(rras_pth)E peer(a), or a provide ute if first(rns-path)E provider(a). Two ASes may also have a A route registry can be used to verify the hierarchical rela- ilateral be fkyt agreement, as disc ussed in more detail in tionships. Each AS a supplies its set provider(a), updating Section 5.2. the registry upon adding or deleting a provider. The reg- istry can check for a cycle whene ver any As changes its set of The customer-provider and peer-to-peer agreements trans- providers. This could happen when an AS adds or remove late into several rules governing BGP export policies [1; 1: ider, or when an As changes its relationship with one of its neighbors; for example, a pair of ASes may transition from a customer-provider relat ionship to a peer-to-peer Exporting to a provider: In exchanging routing in- rangement. The algorit hm for checking whether there is an As t its takes O(N+ ED) time [w and the routes of its customers, but can not export whe is the number of edges and NI e num be of nodes of the directed were 6w7w ASes and 13895 AS interconnect tions known to Exporting to a customer: In exchanging routing globally-connected BGP systems[17]. BGP permits at most informat ion with a customer, an As can export its 216=65536 AS numbers and the number of as inter nections tends to grow linearly Exporting to a peer: In exchanging routing infor- conformity to the hierarchical relationships at all i ithr Therefore, it is possible to run the cycle-de tection algorithm henever an AS updates its list of t ation with a peer, an As can export its routes and t he routes of its customers, but can not export the If the provider-to-customer or customer-to-provider graph routes learned from ot her providers or peers has a cycle, the registry can e fficiently identify the sequence of ASes involved. If more detailed information is available bout the rout ing policies of these ASes, the registry could BGP speaker u check for possible ce problems. Although chec. and with a link i connect i for convergence is an NP-complete problem [10], the check E provider(a(u))u would be applied on the subgraph, which would involve peer(a(u)), then er_rport(l, u[[=& much fewer vertices and edges than the init ial As graph. Alternat ive ly, the registry could instruct the ASes in the cy 4.2 Hierarchy cle to coordinate amongst themselves to avoid policies that
d AS1 AS2 AS0 (0) (1,0) (0) (2,0) ✢ ✣ ✤ ✥ ✦ ✧ ✩ ✪ ✳ ✴ ✵ ✶ ✷ ✶ ✸ ✧ ✮ ✁ ✭ ✶ ✭ ✶ ✸ ✭ ✂ ✰ ✧ ✶ ✸ ✭ ✸ ✧ ✂ ✥ ✸ ✮ ✣ ✤ ✁ ✸ ✫ ✱ ✸ ✄ ✱ ✫ ☎ ✧ ✦ ✤ ✧ 4.1 Clients, Providers, and Peers ✖ ✗ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✠ ✝ ✙ ✒ ✄ ✛ ✝ ✆ ✕ ✍ ✆ ✓ ✡ ✝ ✠ ✍ ✡ ✒ ✡ ✂ ✠ ✡ ✞ ✄ ✮ ✓ ✄ ✡ ✂ ✄ ✘ ✝ ✙ ✍ ✙ ✓ ✜ ✕ ✆ ✞ ✄ ✎ ✠ ✓ ✞ ✡ ✂ ✄ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✆ ✛ ✡ ✝ ✠ ✭ ✍ ✣ ✫ ✓ ✠ ✛ ☞ ✟ ☎ ✝ ✌ ✁ ✝ ✡ ✝ ✆ ✕ ✁ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✥ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✙ ✒ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✠ ✒ ✕ ✠ ✎ ✎ ✄ ✝ ✖ ✗ ✡ ✂ ✠ ✡ ✘ ✠ ☞ ✒ ✠ ✎ ✠ ✝ ✜ ✄ ✝ ✖ ✗ ✛ ✆ ✝ ✠ ✍ ✍ ✄ ✒ ✒ ✡ ✆ ✡ ✂ ✄ ✝ ✄ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✣ ✁ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✕ ✠ ☞ ✥ ✙ ✓ ✡ ✔ ✝ ✓ ✥ ✢ ✄ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✆ ✛ ✠ ✓ ✄ ✚ ✄ ✓ ✎ ✠ ✝ ✜ ✄ ✝ ✖ ✗ ✣ ✫ ✓ ✠ ✡ ✁ ✁ ✝ ☎ ✝ ✝ ✡ ✁ ✁ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✥ ✡ ✂ ✄ ✡ ☛ ✆ ✘ ✄ ✄ ✝ ✒ ✠ ✝ ✄ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✆ ✛ ✍ ✆ ✕ ✘ ✠ ✝ ✠ ✢ ✎ ✄ ✒ ✙ ✲ ✄ ✠ ✓ ✞ ✮ ✓ ✞ ✙ ✡ ✕ ✔ ✡ ✔ ✠ ✎ ✎ ☞ ✠ ✞ ✚ ✠ ✓ ✡ ✠ ✜ ✄ ✆ ✔ ✒ ✡ ✆ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✝ ✠ ✭ ✍ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ✂ ✄ ✙ ✝ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✣ ✻ ✠ ✍ ✂ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✞ ✄ ✮ ✓ ✄ ✒ ✠ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ✂ ✄ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✙ ✡ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✒ ✣ ✖ ✎ ✡ ✂ ✆ ✔ ✜ ✂ ✡ ✂ ✄ ✝ ✄ ✕ ✙ ✜ ✂ ✡ ✢ ✄ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✄ ☎ ✟ ✌ ✒ ✄ ✒ ✒ ✙ ✆ ✓ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✥ ✡ ✂ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ✂ ✄ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✒ ✂ ✆ ✔ ✎ ✞ ✢ ✄ ✔ ✓ ✙ ✧ ✔ ✄ ✎ ☞ ✞ ✄ ✮ ✓ ✄ ✞ ✣ ✖ ✓ ✖ ✗ ✠ ✕ ✠ ☞ ✂ ✠ ✚ ✄ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✥ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✥ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✒ ✣ ✱ ✄ ✞ ✄ ✮ ✓ ✄ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✠ ✑ ✥ ✏ ✑ ✑ ✎ ✏ ✠ ✑ ✥ ✠ ✓ ✞ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✑ ✠ ✒ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✥ ✘ ✄ ✄ ✝ ✒ ✥ ✠ ✓ ✞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✛ ✠ ✥ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✎ ☞ ✣ ✱ ✄ ✎ ✄ ✡ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✖ ✗ ✙ ✓ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✣ ✖ ✝ ✆ ✔ ✡ ✄ ✎ ✙ ✒ ✍ ✎ ✠ ✒ ✒ ✙ ✮ ✄ ✞ ✠ ✒ ✠ ✍ ✔ ✒ ✩ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✆ ✛ ✠ ✙ ✛ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✠ ✑ ✥ ✠ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✛ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✑ ✑ ✎ ✏ ✠ ✑ ✥ ✆ ✝ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✛ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✑ ✣ ✁ ☛ ✆ ✖ ✗ ✄ ✒ ✕ ✠ ☞ ✠ ✎ ✒ ✆ ✂ ✠ ✚ ✄ ✠ ✢ ✙ ✎ ✠ ✡ ✄ ✝ ✠ ✎ ✁ ✄ ✛ ✆ ☞ ✡ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✥ ✠ ✒ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✄ ✞ ✙ ✓ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✺ ✣ ❃ ✣ ✁ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✒ ✡ ✝ ✠ ✓ ✒ ✩ ✎ ✠ ✡ ✄ ✙ ✓ ✡ ✆ ✒ ✄ ✚ ✄ ✝ ✠ ✎ ✝ ✔ ✎ ✄ ✒ ✜ ✆ ✚ ✄ ✝ ✓ ✙ ✓ ✜ ☎ ✟ ✌ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✿ ✽ ❀ ✽ ❃ ❁ ✡ ✝ ✞ ✬ ✯ ✱ ✦ ✸ ✣ ✫ ✤ ✸ ✱ ✭ ✯ ✦ ✱ ☎ ✣ ✟ ✧ ✦ ✩ ✫ ✓ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✩ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✠ ✓ ✖ ✗ ✍ ✠ ✓ ✄ ✪ ✘ ✆ ✝ ✡ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✛ ✙ ✡ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✥ ✢ ✔ ✡ ✍ ✠ ✓ ✓ ✆ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✆ ✡ ✂ ✄ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✝ ✘ ✄ ✄ ✝ ✒ ✣ ✝ ✞ ✬ ✯ ✱ ✦ ✸ ✣ ✫ ✤ ✸ ✱ ✭ ✄ ✥ ✶ ✸ ✱ ✮ ✧ ✦ ✩ ✫ ✓ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✥ ✠ ✓ ✖ ✗ ✍ ✠ ✓ ✄ ✪ ✘ ✆ ✝ ✡ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ✠ ✒ ☛ ✄ ✎ ✎ ✠ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✒ ✣ ✝ ✞ ✬ ✯ ✱ ✦ ✸ ✣ ✫ ✤ ✸ ✱ ✭ ✯ ✧ ✧ ✦ ✩ ✫ ✓ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✆ ✝ ✩ ✕ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✡ ✂ ✠ ✘ ✄ ✄ ✝ ✥ ✠ ✓ ✖ ✗ ✍ ✠ ✓ ✄ ✪ ✘ ✆ ✝ ✡ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✛ ✙ ✡ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✥ ✢ ✔ ✡ ✍ ✠ ✓ ✓ ✆ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✆ ✡ ✂ ✄ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✝ ✘ ✄ ✄ ✝ ✒ ✣ ✰ ✝ ✠ ☛ ✙ ✓ ✜ ✆ ✓ ✆ ✔ ✝ ✠ ✢ ✒ ✡ ✝ ✠ ✍ ✡ ✕ ✆ ✞ ✄ ✎ ✥ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✹ ✠ ✓ ✞ ☛ ✙ ✡ ✂ ✠ ✎ ✙ ✓ ✵ ✙ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✓ ✜ ✡ ✆ ✠ ✓ ✖ ✗ ✺ ☛ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✏ ✹ ✑ ✑ ✎ ✏ ✑ ✑ ✎ ✏ ✠ ✏ ✹ ✑ ✑ ✣ ✯ ✆ ✝ ✄ ✠ ✍ ✂ ✎ ✥ ✙ ✛ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✏ ✹ ✑ ✑ ✎ ✏ ✑ ✑ ✎ ✏ ✠ ✏ ✹ ✑ ✑ ✥ ✡ ✂ ✄ ✓ ✑ ✓ ✑ ✓ ✏ ✗ ✎ ✕ ✏ ✙ ✆ ✹ ✑ ✿ ✼ ✎ ✽ ❁ ✄ ✼ ✽ ✣ 4.2 Hierarchy provider-to-customer peer-to-peer backup link AS ✢ ✣ ✤ ✥ ✦ ✧ ✠ ✩ ✪ ✁ ✣ ✧ ✦ ✭ ✦ ✄ ✁ ✣ ✄ ✭ ✰ ✪ ✡ ✣ ✫ ✸ ✧ ✦ ✄ ✱ ✫ ✫ ✧ ✄ ✸ ✣ ✱ ✫ ✱ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✝ ✄ ✙ ✒ ✠ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✩ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✠ ✕ ✆ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ✁ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✠ ✝ ✙ ✒ ✄ ✒ ✢ ✄ ✩ ✍ ✠ ✔ ✒ ✄ ✠ ✓ ✖ ✗ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✔ ✒ ✄ ✒ ✠ ✓ ✖ ✗ ✆ ✛ ✎ ✠ ✝ ✜ ✄ ✝ ✒ ✙ ✲ ✄ ✠ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✖ ✓ ✖ ✗ ✹ ✒ ✄ ✝ ✚ ✙ ✓ ✜ ✠ ✕ ✄ ✡ ✝ ✆ ✘ ✆ ✎ ✙ ✡ ✠ ✓ ✠ ✝ ✄ ✠ ✙ ✒ ✎ ✙ ✵ ✄ ✎ ☞ ✡ ✆ ✂ ✠ ✚ ✄ ✠ ✝ ✄ ✩ ✜ ✙ ✆ ✓ ✠ ✎ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✺ ✥ ✠ ✓ ✞ ✠ ✝ ✄ ✜ ✙ ✆ ✓ ✠ ✎ ✖ ✗ ✺ ✙ ✒ ✎ ✙ ✵ ✄ ✎ ☞ ✡ ✆ ✂ ✠ ✚ ✄ ✠ ✓ ✠ ✡ ✙ ✆ ✓ ✠ ✎ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ☛ ❀ ✙ ✡ ✙ ✒ ✚ ✄ ✝ ☞ ✔ ✓ ✎ ✙ ✵ ✄ ✎ ☞ ✡ ✂ ✠ ✡ ✠ ✓ ✠ ✡ ✙ ✆ ✓ ☛ ✙ ✞ ✄ ✖ ✗ ☛ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✆ ✛ ✠ ✕ ✄ ✡ ✝ ✆ ✘ ✆ ✎ ✙ ✡ ✠ ✓ ✩ ✠ ✝ ✄ ✠ ✖ ✗ ✹ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ✙ ✛ ✹ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✺ ✑ ✠ ✓ ✞ ✺ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ☛ ✑ ✥ ✡ ✂ ✄ ✓ ☛ ☛✔ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✹ ✑ ✣ ✖ ✗ ✺ ✙ ✒ ✠ ✕ ✆ ✁ ✛ ☎ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✹ ✥ ☛ ✂ ✄ ✝ ✄ ✠ ✒ ✖ ✗ ☛ ✙ ✒ ✠ ✓ ✆ ✞ ✕ ✆ ✁ ✛ ☎ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ☛ ✣ ✖ ✓ ☞ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✹ ✍ ✠ ✓ ✓ ✆ ✡ ✢ ✄ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✆ ✛ ✹ ✣ ✁ ✆ ✒ ✙ ✕ ✘ ✎ ✙ ✛ ☞ ✡ ✂ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✩ ✒ ✙ ✆ ✓ ✥ ☛ ✄ ✞ ✄ ✮ ✓ ✄ ✡ ☛ ✆ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✜ ✝ ✠ ✘ ✂ ✒ ✛ ✆ ✝ ✕ ✄ ✞ ✢ ☞ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✫ ✓ ✡ ✂ ✄ ✡ ✝ ✆ ✕ ✁ ✝ ☎ ✝ ✝ ✛ ☞ ✟ ☎ ✝ ✌ ✁ ✢ ✄ ✡ ✠ ✥ ✡ ✂ ✄ ✄ ✞ ✜ ✄ ✒ ✠ ✝ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✛ ✝ ✆ ✕ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✡ ✆ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✣ ✁ ✂ ✄ ✝ ✄ ✩ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ✒ ✔ ✢ ✜ ✝ ✠ ✘ ✂ ✛ ✆ ✝ ✕ ✄ ✞ ✢ ☞ ✆ ✓ ✎ ☞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✩ ✒ ✂ ✙ ✘ ✒ ✒ ✂ ✆ ✔ ✎ ✞ ✢ ✄ ✠ ✕ ✆ ✁ ✛ ☎ ✁ ✕ ✄ ✛ ✍ ✛ ✂ ✆ ✛ ✢ ✄ ✡ ✠ ✏ ✰ ✖ ✟ ✑ ✥ ✠ ✒ ✒ ✂ ✆ ☛ ✓ ✙ ✓ ✡ ✂ ✄ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✙ ✓ ✯ ✙ ✜ ✔ ✝ ✄ ✾ ✣ ✫ ✓ ✡ ✂ ✄ ✛ ☞ ✟ ☎ ✝ ✌ ✁ ✝ ☎ ✝ ✝ ✡ ✝ ✆ ✕ ✁ ✢ ✄ ✡ ✠ ✥ ✡ ✂ ✄ ✄ ✞ ✜ ✄ ✒ ✠ ✝ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✛ ✝ ✆ ✕ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✡ ✆ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✖ ✝ ✆ ✔ ✡ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✠ ✓ ✢ ✄ ✔ ✒ ✄ ✞ ✡ ✆ ✚ ✄ ✝ ✙ ✛ ☞ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✝ ✄ ✎ ✠ ✩ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✻ ✠ ✍ ✂ ✖ ✗ ✠ ✒ ✔ ✘ ✘ ✎ ✙ ✄ ✒ ✙ ✡ ✒ ✒ ✄ ✡ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✑ ✥ ✔ ✘ ✞ ✠ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✔ ✘ ✆ ✓ ✠ ✞ ✞ ✙ ✓ ✜ ✆ ✝ ✞ ✄ ✎ ✄ ✡ ✙ ✓ ✜ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✁ ✂ ✄ ✝ ✄ ✜ ✩ ✙ ✒ ✡ ✝ ☞ ✍ ✠ ✓ ✍ ✂ ✄ ✍ ✵ ✛ ✆ ✝ ✠ ✍ ☞ ✍ ✎ ✄ ☛ ✂ ✄ ✓ ✄ ✚ ✄ ✝ ✠ ✓ ☞ ✖ ✗ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✒ ✄ ✡ ✆ ✛ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✁ ✂ ✙ ✒ ✍ ✆ ✔ ✎ ✞ ✂ ✠ ✘ ✘ ✄ ✓ ☛ ✂ ✄ ✓ ✠ ✓ ✖ ✗ ✠ ✞ ✞ ✒ ✆ ✝ ✝ ✄ ✕ ✆ ✚ ✄ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✆ ✝ ☛ ✂ ✄ ✓ ✠ ✓ ✖ ✗ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✆ ✓ ✄ ✆ ✛ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ❀ ✛ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✠ ✘ ✠ ✙ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✕ ✠ ☞ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✛ ✝ ✆ ✕ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✡ ✆ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✝ ✩ ✝ ✠ ✓ ✜ ✄ ✕ ✄ ✓ ✡ ✣ ✁ ✂ ✄ ✠ ✎ ✜ ✆ ✝ ✙ ✡ ✂ ✕ ✛ ✆ ✝ ✍ ✂ ✄ ✍ ✵ ✙ ✓ ✜ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✡ ✂ ✄ ✝ ✄ ✙ ✒ ✠ ✍ ☞ ✍ ✎ ✄ ✙ ✓ ✠ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✜ ✝ ✠ ✘ ✂ ✡ ✠ ✵ ✄ ✒ ☞ ✏ ✌ ☎ ✌ ✍ ✌ ✞ ✌ ✑ ✡ ✙ ✕ ✄ ✿ ☛ ❁ ✥ ☛ ✂ ✄ ✝ ✄ ✌ ✞ ✌ ✙ ✒ ✡ ✂ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✄ ✞ ✜ ✄ ✒ ✠ ✓ ✞ ✌ ☎ ✌ ✙ ✒ ✡ ✂ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✓ ✆ ✞ ✄ ✒ ✆ ✛ ✡ ✂ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✜ ✝ ✠ ✘ ✂ ✣ ✖ ✒ ✆ ✛ ✎ ✠ ✓ ✔ ✠ ✝ ☞ ❃ ❂ ❂ ❂ ✥ ✡ ✂ ✄ ✝ ✄ ☛ ✄ ✝ ✄ ❅ ☛ ✹ ☛ ✖ ✗ ✄ ✒ ✠ ✓ ✞ ✽ ✾ ✼ ✸ ✺ ✖ ✗ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✵ ✓ ✆ ☛ ✓ ✡ ✆ ✜ ✎ ✆ ✢ ✠ ✎ ✎ ☞ ✩ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✄ ✞ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✿ ✽ ✹ ❁ ✣ ☎ ✟ ✌ ✘ ✄ ✝ ✕ ✙ ✡ ✒ ✠ ✡ ✕ ✆ ✒ ✡ ❃ ✂ ✏ ✄ ❅ ✺ ✺ ✾ ❅ ✖ ✗ ✓ ✔ ✕ ✢ ✄ ✝ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✖ ✗ ✙ ✓ ✡ ✄ ✝ ✍ ✆ ✓ ✩ ✓ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✡ ✄ ✓ ✞ ✒ ✡ ✆ ✜ ✝ ✆ ☛ ✎ ✙ ✓ ✄ ✠ ✝ ✎ ☞ ✙ ✓ ✡ ✂ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✿ ✺ ❁ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ✙ ✡ ✙ ✒ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✡ ✆ ✝ ✔ ✓ ✡ ✂ ✄ ✍ ☞ ✍ ✎ ✄ ✩ ✞ ✄ ✡ ✄ ✍ ✡ ✙ ✆ ✓ ✠ ✎ ✜ ✆ ✝ ✙ ✡ ✂ ✕ ☛ ✂ ✄ ✓ ✄ ✚ ✄ ✝ ✠ ✓ ✖ ✗ ✔ ✘ ✞ ✠ ✡ ✄ ✒ ✙ ✡ ✒ ✎ ✙ ✒ ✡ ✆ ✛ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✡ ✆ ✄ ✓ ✒ ✔ ✝ ✄ ✡ ✂ ✄ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✙ ✡ ☞ ✡ ✆ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✠ ✡ ✠ ✎ ✎ ✡ ✙ ✕ ✄ ✒ ✣ ✫ ✛ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✆ ✝ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✜ ✝ ✠ ✘ ✂ ✂ ✠ ✒ ✠ ✍ ☞ ✍ ✎ ✄ ✥ ✡ ✂ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✠ ✓ ✄ ✭ ✍ ✙ ✄ ✓ ✡ ✎ ☞ ✙ ✞ ✄ ✓ ✡ ✙ ✛ ☞ ✡ ✂ ✄ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ✖ ✗ ✄ ✒ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✞ ✣ ✫ ✛ ✕ ✆ ✝ ✄ ✞ ✄ ✡ ✠ ✙ ✎ ✄ ✞ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✙ ✒ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✠ ✢ ✆ ✔ ✡ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✆ ✛ ✡ ✂ ✄ ✒ ✄ ✖ ✗ ✄ ✒ ✥ ✡ ✂ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✆ ✔ ✎ ✞ ✍ ✂ ✄ ✍ ✵ ✛ ✆ ✝ ✘ ✆ ✒ ✒ ✙ ✢ ✎ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✣ ✖ ✎ ✡ ✂ ✆ ✔ ✜ ✂ ✍ ✂ ✄ ✍ ✵ ✙ ✓ ✜ ✛ ✆ ✝ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✙ ✒ ✠ ✓ ✶ ✌ ✩ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✿ ✽ ❂ ❁ ✥ ✡ ✂ ✄ ✍ ✂ ✄ ✍ ✵ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✠ ✘ ✘ ✎ ✙ ✄ ✞ ✆ ✓ ✡ ✂ ✄ ✒ ✔ ✢ ✜ ✝ ✠ ✘ ✂ ✥ ☛ ✂ ✙ ✍ ✂ ☛ ✆ ✔ ✎ ✞ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✕ ✔ ✍ ✂ ✛ ✄ ☛ ✄ ✝ ✚ ✄ ✝ ✡ ✙ ✍ ✄ ✒ ✠ ✓ ✞ ✄ ✞ ✜ ✄ ✒ ✡ ✂ ✠ ✓ ✡ ✂ ✄ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ✣ ✖ ✎ ✡ ✄ ✝ ✓ ✠ ✡ ✙ ✚ ✄ ✎ ☞ ✥ ✡ ✂ ✄ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✆ ✔ ✎ ✞ ✙ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✍ ☞ ✩ ✍ ✎ ✄ ✡ ✆ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✄ ✠ ✕ ✆ ✓ ✜ ✒ ✡ ✡ ✂ ✄ ✕ ✒ ✄ ✎ ✚ ✄ ✒ ✡ ✆ ✠ ✚ ✆ ✙ ✞ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡
convergence problems, or to force the use of LEMMA 5. 1. The BGP system has a stable state. a restrictive policy (such as shortest As path) that would guarantee convergence PROOF: We prove the lemma by construc ting an tion sequence a that leads to a stable st ate for any initial 5. BGP POLICY GUDELINES state. Let d denote the dest inat ion prefix and A sa denote This section nts policy guidelines that ensure that the the as that originates prefix d. Since the activation order BGP system is safe. To simplify the discussion, we initially among the BGP speakers within an as does not affect th onsider only customer-provider and peer-to-peer relation- best route selection of the bGP speakers, we ac tivate all ships. We then extend the guidelines to include backup re BGP speakers of an AS simult lationships. Since the route selection process for each d explanation, we use the activation of an as to represent the nation prefix is independent of other pre fixes, it is sufficient activation of all BGp st phase, a AS selects a customer kers in the as. We activate Ases to consider only one dest inat ion prefix d in describing and t he guideline route if one is available, following Guide line A. This is ac- complished by activating the ASes in an order that conforms 5.1 BGP Systems with no Backup Link to the partial order in the customer-to-provider DAG. In ti In this section, we present the policy configurat ion guidelines second phase, the A Ses that do not have a customer route for BGP systems that have only customer-provider and peer- after Phase 1 get provider or peer routes to-peer relationships. We first consider the guideline for the polished by ac tivating ASes in an order that conforms to case that any As pair can have a peer-to-peer agreement. partial order in the provider-to-customer DAG. Forma Then, we expand the set of local policies by imposing re we have a two-phase acti vation sequence a as follows. alistic rest ions on which As pairs can have peer-to-peer Phase 1: Activate A ses in a linear order that conforms to the partial order in the customer-to-provider DAG Phase 2: Activate Ases in a linear order that conforms to 5.1.1 Unconstrained Peer-to-Peer Agreements a cu the partial order in th vider-to-customer dag Our guide line requires an As to prefer a route via ave guide line A lor the e, provider or peer. Formally,we Lomer over a For the simplicity of the discussion, we partition the ASes to two classes; the first class consists of ASd and ASes as a: t hat select a customer route in Phase 1. The consists of the remaining A Ses. We call A class Phase-1 A Ses and A Ses in the second class Phase-2 Guideline a A Ses. Similarly, we call BGP speakers in a Phase-1 if (first(rI.as-pat ustomer(a))ar Phase-1 BGP speakers and BGP speakers in a Phase-2 AS Girst(r2as_path)E peer(a)U provider(a))) peakers on sequence res then ri_pref>r2 Loc-pre f stable st ate independent of the initial st ate. We prove that each Phase-1 BGP speaker reaches a stable state after its tivation in Phase 1 and each Phase-2 BGP speaker reaches Note that Guideline a does not restrict the preference among stable st ate after its acti vation in Phase 2. In other words ustomer routes or among provider or peer routes, which we prove the following two claims leaves ISPs with significant flexibility in selecting local poli cies. In addition, IsPs have a financial incentive to foll Claim 1: A Phase-1 BGP speaker reaches a stable state the guideline since an IsP does not have to pay its customer after its activation in Phase 1 o carry traffic. Guide line A allows a large number of possi ble configurations, much larger than policies based only on Proof: We prove by induct ion on the order AS-path length. To implement the guidelines, an AS could BG among allocate a range of locakpref values for each type of route Phase-1 BGP speakers, BGP speakers in ASd are the first (e. g, 86-100 for customer routes and 75-85 for peer and to be activated. BGP speakers in ASd reach a stable st ate as soon as ASa is activated. Let Phase-1 BGP speake belong to ASn. Suppose all Phase-1 BGP Guideline A ensures that the BGP system is safe. The proof belong to an As preceding ASn in Phase 1 reach a stable draws on how the localpref assignment affects how each state after their activation. BGP speaker i selects the best BGP speaker picks its best route route amongst its customer routes. All of the customers precede A Sn in the ac tivation sequence for Phase 1. Hence each customer has eit her reached a stable state (earlier in HEOREM 5.1. For a BGP systern thai Phase 1)or do route in Phase 1.Ar rovider and peer-lo-peer relationships, if all ASes follow cust omer that does not get a sideline A, then the bGP systen is safe not export its route to BGP speaker i according to export policy rule. Hence, those customers' routing decisions de not affect BGP speaker i. Therefore, BGP speaker i reaches We prove the theorem by two lemmas. The first lemma a stable state after its ac tivat ion in Phase 1 claims t hat the bgP system has a st able state. The second lemma claims that the BGP system converges to the st able A Phase-2 BGP speaker reaches a stable state state for any initial st ate and any fair ac tivat ion sequence after its act ivation in Phase
☛ ✆ ✔ ✎ ✞ ✍ ✠ ✔ ✒ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✥ ✆ ✝ ✡ ✆ ✛ ✆ ✝ ✍ ✄ ✡ ✂ ✄ ✔ ✒ ✄ ✆ ✛ ✠ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✙ ✚ ✄ ✘ ✆ ✎ ✙ ✍ ☞ ✏ ✒ ✔ ✍ ✂ ✠ ✒ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✖ ✗ ✘ ✠ ✡ ✂ ✑ ✡ ✂ ✠ ✡ ☛ ✆ ✔ ✎ ✞ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✣ 5. BGP POLICY GUIDELINES ✁ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✘ ✆ ✎ ✙ ✍ ☞ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✡ ✂ ✠ ✡ ✄ ✓ ✒ ✔ ✝ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✒ ✠ ✛ ✄ ✣ ✁ ✆ ✒ ✙ ✕ ✘ ✎ ✙ ✛ ☞ ✡ ✂ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✥ ☛ ✄ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✎ ☞ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✆ ✓ ✎ ☞ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✩ ✒ ✂ ✙ ✘ ✒ ✣ ✱ ✄ ✡ ✂ ✄ ✓ ✄ ✪ ✡ ✄ ✓ ✞ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✡ ✆ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✩ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✞ ✄ ✒ ✡ ✙ ✩ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✙ ✒ ✙ ✓ ✞ ✄ ✘ ✄ ✓ ✞ ✄ ✓ ✡ ✆ ✛ ✆ ✡ ✂ ✄ ✝ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✥ ✙ ✡ ✙ ✒ ✒ ✔ ✭ ✍ ✙ ✄ ✓ ✡ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✆ ✓ ✎ ☞ ✆ ✓ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✜ ✙ ✓ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✙ ✓ ✜ ✠ ✓ ✞ ✠ ✓ ✠ ✎ ☞ ✲ ✙ ✓ ✜ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✣ 5.1 BGP Systems with no Backup Link ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✡ ✂ ✄ ✘ ✆ ✎ ✙ ✍ ☞ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✛ ✆ ✝ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✆ ✓ ✎ ☞ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ ✱ ✄ ✮ ✝ ✒ ✡ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✛ ✆ ✝ ✡ ✂ ✄ ✍ ✠ ✒ ✄ ✡ ✂ ✠ ✡ ✠ ✓ ☞ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✣ ✁ ✂ ✄ ✓ ✥ ☛ ✄ ✄ ✪ ✘ ✠ ✓ ✞ ✡ ✂ ✄ ✒ ✄ ✡ ✆ ✛ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✢ ☞ ✙ ✕ ✘ ✆ ✒ ✙ ✓ ✜ ✝ ✄ ✩ ✠ ✎ ✙ ✒ ✡ ✙ ✍ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✙ ✆ ✓ ✒ ✆ ✓ ☛ ✂ ✙ ✍ ✂ ✖ ✗ ✘ ✠ ✙ ✝ ✒ ✍ ✠ ✓ ✂ ✠ ✚ ✄ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✣ 5.1.1 Unconstrained Peer-to-Peer Agreements ★ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✝ ✄ ✧ ✔ ✙ ✝ ✄ ✒ ✠ ✓ ✖ ✗ ✡ ✆ ✘ ✝ ✄ ✛ ✄ ✝ ✠ ✝ ✆ ✔ ✡ ✄ ✚ ✙ ✠ ✠ ✍ ✔ ✒ ✩ ✡ ✆ ✕ ✄ ✝ ✆ ✚ ✄ ✝ ✠ ✝ ✆ ✔ ✡ ✄ ✚ ✙ ✠ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✛ ✆ ✝ ✡ ✂ ✄ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✆ ✛ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✙ ✓ ✖ ✗ ✠ ✡ ✴ ✥ ✣ ✟ ✧ ✰ ✣ ✫ ✧ ✪ ✙ ✛ ✏ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✂ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✠ ✑ ✑ ✠ ✓ ✞ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✄ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✑ ✑ ✎ ✏ ✠ ✑ ✎ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✑ ✑ ✑ ✡ ✂ ✄ ✓ ✎ ✂ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✎ ✄ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✞ ✆ ✄ ✒ ✞ ✝ ☎ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✡ ✂ ✄ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✠ ✕ ✆ ✓ ✜ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✝ ✠ ✕ ✆ ✓ ✜ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ☛ ✂ ✙ ✍ ✂ ✎ ✄ ✠ ✚ ✄ ✒ ✫ ✗ ✌ ✒ ☛ ✙ ✡ ✂ ✒ ✙ ✜ ✓ ✙ ✮ ✍ ✠ ✓ ✡ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✓ ✜ ✎ ✆ ✍ ✠ ✎ ✘ ✆ ✎ ✙ ✩ ✍ ✙ ✄ ✒ ✣ ✫ ✓ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✥ ✫ ✗ ✌ ✒ ✂ ✠ ✚ ✄ ✠ ✮ ✓ ✠ ✓ ✍ ✙ ✠ ✎ ✙ ✓ ✍ ✄ ✓ ✡ ✙ ✚ ✄ ✡ ✆ ✛ ✆ ✎ ✎ ✆ ☛ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✙ ✓ ✍ ✄ ✠ ✓ ✫ ✗ ✌ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✡ ✆ ✘ ✠ ☞ ✙ ✡ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✡ ✆ ✍ ✠ ✝ ✝ ☞ ✡ ✝ ✠ ✭ ✍ ✣ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✠ ✎ ✎ ✆ ☛ ✒ ✠ ✎ ✠ ✝ ✜ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✘ ✆ ✒ ✒ ✙ ✩ ✢ ✎ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ✥ ✕ ✔ ✍ ✂ ✎ ✠ ✝ ✜ ✄ ✝ ✡ ✂ ✠ ✓ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✎ ☞ ✆ ✓ ✖ ✗ ✩ ✘ ✠ ✡ ✂ ✎ ✄ ✓ ✜ ✡ ✂ ✣ ✁ ✆ ✙ ✕ ✘ ✎ ✄ ✕ ✄ ✓ ✡ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✥ ✠ ✓ ✖ ✗ ✍ ✆ ✔ ✎ ✞ ✠ ✎ ✎ ✆ ✍ ✠ ✡ ✄ ✠ ✝ ✠ ✓ ✜ ✄ ✆ ✛ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✚ ✠ ✎ ✔ ✄ ✒ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✡ ☞ ✘ ✄ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✏ ✄ ✣ ✜ ✣ ✥ ✼ ❅ ✁ ✽ ❂ ❂ ✛ ✆ ✝ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✹ ✺ ✁ ✼ ✺ ✛ ✆ ✝ ✘ ✄ ✄ ✝ ✠ ✓ ✞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✑ ✣ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✄ ✓ ✒ ✔ ✝ ✄ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✒ ✠ ✛ ✄ ✣ ✁ ✂ ✄ ✘ ✝ ✆ ✆ ✛ ✞ ✝ ✠ ☛ ✒ ✆ ✓ ✂ ✆ ☛ ✡ ✂ ✄ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✠ ✒ ✒ ✙ ✜ ✓ ✕ ✄ ✓ ✡ ✠ ✳ ✄ ✍ ✡ ✒ ✂ ✆ ☛ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✘ ✙ ✍ ✵ ✒ ✙ ✡ ✒ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✣ ✂ ✄ ☎ ✆ ✝ ☎ ✞ ✺ ✣ ✽ ✣ ✟ ✝ ✄ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ☎ ✠ ✄ ☎ ✠ ✄ ✟ ✝ ✞ ✂ ✍ ✛ ☞ ✟ ☎ ✝ ✌ ✁ ✝ ✡ ✝ ✆ ✕ ✁ ✄ ✞ ✕ ✡ ✁ ✁ ✝ ☎ ✝ ✝ ✡ ✁ ✁ ✁ ✂ ✄ ☎ ✆ ✝ ✞ ✟ ✠ ✆ ✡ ✟ ✠ ✆ ✜ ✄ ✂ ✂ ✙ ✚ ✁ ✟ ✜ ✝ ✂ ✂ ✝ ✡ ✢ ☞ ✆ ✕ ✁ ✂ ✆ ✞ ✁ ✙ ✠ ☎ ✠ ✁ ✞ ☎ ✠ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✆ ✟ ✟ ✄ ✜ ✁ ☛ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✄ ✡ ✂ ✄ ✆ ✝ ✄ ✕ ✢ ☞ ✡ ☛ ✆ ✎ ✄ ✕ ✕ ✠ ✒ ✣ ✁ ✂ ✄ ✮ ✝ ✒ ✡ ✎ ✄ ✕ ✕ ✠ ✍ ✎ ✠ ✙ ✕ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✂ ✠ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✁ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✞ ✎ ✄ ✕ ✕ ✠ ✍ ✎ ✠ ✙ ✕ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✛ ✆ ✝ ✠ ✓ ☞ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✠ ✓ ✞ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ☞ ☎ ✞ ✞ ✌ ✺ ✣ ✽ ✣ ✍ ✠ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✠ ✄ ✟ ✄ ✟ ☎ ✄ ✁ ✂ ✁ ✟ ☎ ✄ ☎ ✁ ☛ ✎ ✝ ✆ ✆ ✏ ✡ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✄ ✎ ✄ ✕ ✕ ✠ ✢ ☞ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✙ ✓ ✜ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✩ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✑ ✡ ✂ ✠ ✡ ✎ ✄ ✠ ✞ ✒ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✛ ✆ ✝ ✠ ✓ ☞ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✣ ✟ ✄ ✡ ✜ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✠ ✓ ✞ ✾ ✁ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✡ ✂ ✠ ✡ ✆ ✝ ✙ ✜ ✙ ✓ ✠ ✡ ✄ ✒ ✘ ✝ ✄ ✮ ✪ ✜ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✆ ✝ ✞ ✄ ✝ ✠ ✕ ✆ ✓ ✜ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ☛ ✙ ✡ ✂ ✙ ✓ ✠ ✓ ✖ ✗ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✡ ✂ ✄ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ☛ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✆ ✛ ✠ ✓ ✖ ✗ ✒ ✙ ✕ ✔ ✎ ✡ ✠ ✓ ✄ ✆ ✔ ✒ ✎ ☞ ✣ ✯ ✆ ✝ ✒ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ☞ ✆ ✛ ✄ ✪ ✘ ✎ ✠ ✓ ✠ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✔ ✒ ✄ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✓ ✖ ✗ ✡ ✆ ✝ ✄ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✣ ✱ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ☛ ✆ ✘ ✂ ✠ ✒ ✄ ✒ ✣ ✫ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✘ ✂ ✠ ✒ ✄ ✥ ✠ ✖ ✗ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✛ ✆ ✓ ✄ ✙ ✒ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✥ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✁ ✂ ✙ ✒ ✙ ✒ ✠ ✍ ✩ ✍ ✆ ✕ ✘ ✎ ✙ ✒ ✂ ✄ ✞ ✢ ☞ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✓ ✜ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✓ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✣ ✫ ✓ ✡ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✞ ✘ ✂ ✠ ✒ ✄ ✥ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✞ ✆ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✌ ✂ ✠ ✒ ✄ ✽ ✜ ✄ ✡ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✁ ✂ ✙ ✒ ✙ ✒ ✠ ✍ ✍ ✆ ✕ ✩ ✘ ✎ ✙ ✒ ✂ ✄ ✞ ✢ ☞ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✓ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✠ ✡ ☛ ✆ ✩ ✘ ✂ ✠ ✒ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✑ ✠ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✣ ✵ ✁ ✭ ✶ ✧ ★ ✡ ✖ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✣ ✵ ✁ ✭ ✶ ✧ ✩ ✖ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✯ ✆ ✝ ✡ ✂ ✄ ✒ ✙ ✕ ✘ ✎ ✙ ✍ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✥ ☛ ✄ ✘ ✠ ✝ ✡ ✙ ✡ ✙ ✆ ✓ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✆ ✡ ☛ ✆ ✍ ✎ ✠ ✒ ✒ ✄ ✒ ❀ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✍ ✎ ✠ ✒ ✒ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✾ ✁ ✠ ✓ ✞ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✒ ✄ ✎ ✄ ✍ ✡ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✁ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✞ ✍ ✎ ✠ ✒ ✒ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✒ ✆ ✛ ✡ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ✱ ✄ ✍ ✠ ✎ ✎ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✍ ✎ ✠ ✒ ✒ ✘ ✠ ✄ ✟ ✁ ✝ ✒ ✙ ✚ ✁ ✟ ✠ ✓ ✞ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✞ ✍ ✎ ✠ ✒ ✒ ✘ ✠ ✄ ✟ ✁ ✝ ✓ ✙ ✚ ✁ ✟ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✎ ☞ ✥ ☛ ✄ ✍ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✘ ✠ ✄ ✟ ✁ ✝ ✒ ✖ ✗ ✘ ✟ ✡ ✁ ✄ ✆ ✁ ✟ ✠ ✓ ✞ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✘ ✠ ✄ ✟ ✁ ✝ ✓ ✖ ✗ ✘ ✟ ✡ ✁ ✄ ✆ ✁ ✟ ✣ ✁ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✙ ✓ ✞ ✄ ✘ ✄ ✓ ✞ ✄ ✓ ✡ ✆ ✛ ✡ ✂ ✄ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✣ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✄ ✠ ✍ ✂ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✠ ✓ ✞ ✄ ✠ ✍ ✂ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✫ ✓ ✆ ✡ ✂ ✄ ✝ ☛ ✆ ✝ ✞ ✒ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✄ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✡ ☛ ✆ ✍ ✎ ✠ ✙ ✕ ✒ ✣ ✔ ✰ ✭ ✣ ✮ ★ ✩ ✖ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✘ ✝ ✝ ✜ ✕ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✢ ☞ ✙ ✓ ✞ ✔ ✍ ✡ ✙ ✆ ✓ ✆ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✠ ✝ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✷ ✎ ✄ ✠ ✝ ✎ ☞ ✥ ✠ ✕ ✆ ✓ ✜ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✾ ✁ ✠ ✝ ✄ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ✆ ✢ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✾ ✁ ✝ ✄ ✠ ✍ ✂ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✒ ✒ ✆ ✆ ✓ ✠ ✒ ✾ ✁ ✙ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✟ ✄ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✢ ✄ ✎ ✆ ✓ ✜ ✡ ✆ ✾ ☎ ✣ ✗ ✔ ✘ ✘ ✆ ✒ ✄ ✠ ✎ ✎ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✢ ✄ ✎ ✆ ✓ ✜ ✡ ✆ ✠ ✓ ✖ ✗ ✘ ✝ ✄ ✍ ✄ ✞ ✙ ✓ ✜ ✾ ☎ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✝ ✄ ✠ ✍ ✂ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✡ ✂ ✄ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✡ ✂ ✄ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✠ ✕ ✆ ✓ ✜ ✒ ✡ ✙ ✡ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✖ ✎ ✎ ✆ ✛ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✘ ✝ ✄ ✍ ✄ ✞ ✄ ✾ ☎ ✙ ✓ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✛ ✆ ✝ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✄ ✠ ✍ ✂ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✂ ✠ ✒ ✄ ✙ ✡ ✂ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✄ ✞ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✏ ✄ ✠ ✝ ✎ ✙ ✄ ✝ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✑ ✆ ✝ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✜ ✄ ✡ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✖ ✓ ☞ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✡ ✂ ✠ ✡ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✜ ✄ ✡ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✠ ✍ ✍ ✆ ✝ ✞ ✙ ✓ ✜ ✡ ✆ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✝ ✔ ✎ ✄ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✡ ✂ ✆ ✒ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✬ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✒ ✞ ✆ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✔ ✰ ✭ ✣ ✮ ✩ ✖ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣
Proanf EB bi-jaa-i lI, C2 a-i 2 q BoA[: B (30) ABl2 U So k2-E((((+:-1:2E (10) -ik: 2E U So (10) JB U USoy-2人 (120) B1:20a412a22-E:1:UBUB1q∈0;(:f2(:S0'E 氵P20 Figure 4: A BGP system that violates Guideline A 12:1P-2nk丿h2;k2-1q2(;USn口 Wn k B B1:212-:12BB:BB1跑】A趴2 2-E C1 A 1,;2-8:12B:B题?(232BybE小:Ek时2B2)122B+E2B(:20 兵EE儿:y-;k:2 ABE)-:砖2 2-E a-:2-120(-220BqE 5.1.2 Constrained Peer-to-Peer Relationships kk品2B2)踢,2E:1:f((ajB B,(B124号:四km2Ak-1n12)331:B,2、N时 Eirik 2-B→ 2,2(FE jE 隐a22小(:E)1-;k:2 :12砖24B2I(ay-:A4-,C2Ca22--k:2E:;1」2 ((2B1 (2, B02(B 2xA团Bq(++2:C-k40a4(a,,a22 C;k(x:;nk丿2k2-1a412-2-2,nk丿h2k2 a22:B(aB1q2:C2:C:)A2E:B-成20)( 2 (, Eq4 B:,:2-BE,(: B,: Bt B) b2a k(k2亻 a22-:1-a22--2:BBCB1;(2;BE 0B(;-B0B(:∈a-;2-mM1-22-,,C2B(:1 u Ej to B2l::- Bo B2Lea-iR2-::(2 AU'Ea22-B7 W2 E aE ej I roo(i k B2(i(B (B; B E962((2 0, C2 a-2 q0 k:B(i(:12)A2EB:12-02--B2(q(1-1)A2E 4C20q(J12-2)AEC1229:11B-n(0J1-2 A2Ei-2 Assumption P: Gor any pair of ASes aI and ana there is 邮母(: BitB o Akaa;:1:nk provider of a, +1 for any 1<i< ilB: Bc oIlc 92: 12 fi-B (: B B g6S12B:20:(g2:④2.m1)“:Bt”;BE, B2qR2((2i(: B 2E,nk/ B2jk2-Bfi B24, j((: B2ETU q(kk品2B2) B一 Ba2jk2-E B v Sn-2 1 j Bjq B:2j: 2-gl teo d 12-2 : Br CE kE: i -2 x kkB2LR2 g2-i (: B BB: 12B (B B 2q&((20 Fi-,4, C2112 kkB2B2 n:-:12 2xalnB B ai: a: AG 2;(nk丿2;k2-B)Aat F24a-2B(:E(2x,a:3E::a:BE:1:B:2E 昂0是 2-:1 23: B B F farstir=as_pathe E peerage 卡团24B2成2q(a-22--83→;a-;2-- B1 forster1, as_path∈∈ customer∈(0 (ABi, 2--ik: 2 I'B)AOe d 1 AE n k I E B2, IE forster=as-athe∈ provider∈ E() A B BRY E2以 d1Ba-;E((i(:Bk2B02fB24a)E(:12-2x,a4 B2( B FH A:nkl耳
✘ ✝ ✝ ✜ ✕ ✯ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✠ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✢ ☞ ✙ ✓ ✞ ✔ ✍ ✡ ✙ ✆ ✓ ✆ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✠ ✝ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✟ ✄ ✡ ✾ ✞ ✢ ✄ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✡ ✂ ✠ ✡ ✙ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✷ ✎ ✄ ✠ ✝ ✎ ☞ ✥ ✾ ✞ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✠ ✓ ☞ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✗ ✙ ✓ ✍ ✄ ✾ ✞ ✬ ✒ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✠ ✝ ✄ ✓ ✆ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✥ ✡ ✂ ✄ ✒ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✍ ✠ ✓ ✆ ✓ ✎ ☞ ✜ ✄ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✛ ✝ ✆ ✕ ✾ ✞ ✬ ✒ ✘ ✄ ✄ ✝ ✒ ✠ ✓ ✞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✾ ✞ ✬ ✒ ✘ ✄ ✄ ✝ ✒ ✄ ✙ ✡ ✂ ✄ ✝ ✏ ✠ ✑ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✠ ✛ ✡ ✄ ✝ ✌ ✂ ✠ ✒ ✄ ✽ ✏ ✙ ✛ ✡ ✂ ✄ ✝ ✄ ✙ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✑ ✆ ✝ ✏ ✢ ✑ ✞ ✆ ✓ ✆ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✡ ✂ ✄ ✙ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✾ ✞ ✏ ✙ ✛ ✡ ✂ ✄ ✢ ✄ ✒ ✡ ✝ ✆ ✔ ✡ ✄ ✙ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✑ ✣ ✁ ✂ ✄ ✘ ✄ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✛ ✠ ✎ ✎ ✙ ✓ ✍ ✠ ✒ ✄ ✏ ✠ ✑ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✢ ✄ ✛ ✆ ✝ ✄ ✾ ✞ ✠ ✝ ✄ ✠ ✍ ✩ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✁ ✂ ✄ ✘ ✄ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✛ ✠ ✎ ✎ ✙ ✓ ✍ ✠ ✒ ✄ ✏ ✢ ✑ ✞ ✆ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✾ ✞ ✬ ✒ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✬ ✝ ✆ ✔ ✡ ✄ ✣ ✗ ✙ ✓ ✍ ✄ ✾ ✞ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✠ ✓ ☞ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✠ ✛ ✡ ✄ ✝ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✁ ✂ ✄ ✝ ✄ ✩ ✛ ✆ ✝ ✄ ✥ ✾ ✞ ✬ ✒ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✠ ✛ ✡ ✄ ✝ ✡ ✂ ✄ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✟ ✄ ✡ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✢ ✄ ✎ ✆ ✓ ✜ ✡ ✆ ✾ ☎ ✣ ✗ ✔ ✘ ✘ ✆ ✒ ✄ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✢ ✄ ✎ ✆ ✓ ✜ ✡ ✆ ✠ ✓ ✖ ✗ ✘ ✝ ✄ ✍ ✄ ✞ ✙ ✓ ✜ ✾ ☎ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✝ ✄ ✠ ✍ ✂ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✡ ✂ ✄ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✗ ✙ ✓ ✍ ✄ ✓ ✆ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ☛ ✠ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✥ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✕ ✔ ✒ ✡ ✒ ✄ ✎ ✄ ✍ ✡ ✠ ✝ ✆ ✔ ✡ ✄ ✛ ✝ ✆ ✕ ✆ ✓ ✄ ✆ ✛ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✝ ✘ ✄ ✄ ✝ ✒ ✣ ✻ ✠ ✍ ✂ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✂ ✠ ✒ ✠ ✎ ✝ ✄ ✠ ✞ ☞ ✝ ✄ ✠ ✍ ✂ ✄ ✞ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✏ ✄ ✙ ✡ ✂ ✄ ✝ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✥ ✆ ✝ ✄ ✠ ✝ ✎ ✙ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ✌ ✂ ✠ ✒ ✄ ❃ ✑ ✣ ✻ ✠ ✍ ✂ ✘ ✄ ✄ ✝ ✙ ✒ ✄ ✙ ✡ ✂ ✄ ✝ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✆ ✝ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✣ ✫ ✛ ✠ ✘ ✄ ✄ ✝ ✙ ✒ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✥ ✡ ✂ ✄ ✘ ✄ ✄ ✝ ✬ ✒ ✝ ✆ ✔ ✡ ✄ ✙ ✒ ✠ ✚ ✠ ✙ ✎ ✠ ✢ ✎ ✄ ✡ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ☛ ✂ ✄ ✓ ✙ ✡ ✙ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ✫ ✛ ✠ ✘ ✄ ✄ ✝ ✙ ✒ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✥ ✡ ✂ ✄ ✓ ✡ ✂ ✙ ✒ ✘ ✄ ✄ ✝ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✠ ✝ ✆ ✔ ✡ ✄ ✛ ✝ ✆ ✕ ✆ ✓ ✄ ✆ ✛ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✝ ✆ ✓ ✄ ✆ ✛ ✙ ✡ ✒ ✆ ✡ ✂ ✄ ✝ ✘ ✄ ✄ ✝ ✒ ✣ ✁ ✂ ✄ ✘ ✄ ✄ ✝ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✓ ✓ ✆ ✔ ✓ ✍ ✄ ✒ ✔ ✍ ✂ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✠ ✓ ✞ ✥ ✂ ✄ ✓ ✍ ✄ ✥ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✣ ☞ ☎ ✞ ✞ ✌ ✺ ✣ ❃ ✣ ✍ ✠ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✛ ✝ ✞ ✁ ✢ ✁ ✟ ☎ ✝ ☎ ✠ ✁ ✟ ☎ ✄ ✁ ✂ ✁ ✟ ☎ ✄ ☎ ✁ ✜ ✝ ✄ ✞ ✍ ✆ ✞ ✆ ☎ ✆ ✄ ✂ ✟ ☎ ✄ ☎ ✁ ✄ ✞ ✕ ✄ ✞ ✍ ✜ ✄ ✆ ✄ ✛ ☎ ✆ ✄ ☎ ✆ ✝ ✞ ✟ ✁ ✢ ☞ ✁ ✞ ✛ ✁ ☛ ✎ ✝ ✆ ✆ ✏ ✡ ✟ ✙ ✚ ✄ ✓ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✢ ☞ ✙ ✓ ✞ ✔ ✍ ✡ ✙ ✆ ✓ ✆ ✓ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✜ ✙ ✚ ✄ ✓ ✢ ☞ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✄ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✄ ✞ ✢ ☞ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✄ ✒ ☛ ✂ ✄ ✝ ✄ ✢ ✆ ✡ ✂ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✠ ✓ ✞ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✙ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✆ ✛ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✑ ✣ ✫ ✡ ✙ ✒ ✍ ✎ ✄ ✠ ✝ ✡ ✂ ✠ ✡ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✙ ✓ ✾ ✁ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✠ ✒ ✙ ✓ ✜ ✎ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✣ ✗ ✔ ✘ ✘ ✆ ✒ ✄ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✘ ✝ ✄ ✍ ✄ ✞ ✄ ✾ ☎ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✠ ✛ ✡ ✄ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✣ ✏ ✕ ✑ ✣ ✟ ✄ ✡ ✣ ✏ ✕ ✚ ✑ ✢ ✄ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✡ ✒ ✔ ✍ ✂ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✩ ✄ ✝ ✒ ✙ ✓ ✾ ☎ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✠ ✡ ✎ ✄ ✠ ✒ ✡ ✆ ✓ ✍ ✄ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✣ ✏ ✕ ✑ ✠ ✓ ✞ ✣ ✏ ✕ ✚ ✑ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ☛ ✄ ✍ ✠ ✓ ✮ ✓ ✞ ✕ ✚ ✒ ✙ ✓ ✍ ✄ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✒ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✙ ✓ ✮ ✓ ✙ ✡ ✄ ✎ ☞ ✕ ✠ ✓ ☞ ✡ ✙ ✕ ✄ ✒ ✣ ❆ ✒ ✩ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✠ ✒ ✠ ✢ ✆ ✚ ✄ ✥ ☛ ✄ ✍ ✠ ✓ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✾ ☎ ✝ ✄ ✠ ✍ ✂ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✣ ✏ ✕ ✚ ✑ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✛ ✡ ✄ ✝ ✠ ✮ ✓ ✙ ✡ ✄ ✓ ✔ ✕ ✩ ✢ ✄ ✝ ✆ ✛ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✙ ✓ ✡ ✂ ✄ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✯ ✙ ✜ ✔ ✝ ✄ ☛ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✒ ✠ ✓ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✆ ✛ ✠ ✒ ✄ ✡ ✆ ✛ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✒ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✁ ✂ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✄ ✞ ✄ ✞ ✜ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✜ ✝ ✠ ✘ ✂ ✙ ✓ ✞ ✙ ✍ ✠ ✡ ✄ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✛ ✄ ✠ ✍ ✂ ✖ ✗ ✠ ✝ ✄ ✎ ✙ ✒ ✡ ✄ ✞ ✙ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✆ ✛ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✣ ✖ ✗ ✾ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✙ ✓ ✍ ✄ ✢ ☞ ✘ ✝ ✄ ✛ ✄ ✝ ✝ ✙ ✓ ✜ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✏ ✚ ✙ ✠ ✖ ✗ ❃ ✑ ✆ ✚ ✄ ✝ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✏ ✚ ✙ ✠ ✖ ✗ ❂ ✑ ✣ ✁ ✂ ✙ ✒ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✓ ✆ ✡ ✒ ✠ ✛ ✄ ✣ ✻ ✠ ✍ ✂ ✖ ✗ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✎ ☞ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✏ ❂ ✑ ✠ ✓ ✞ ✡ ✂ ✄ ✓ ✞ ✄ ✍ ✙ ✞ ✄ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✆ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✙ ✡ ✒ ✍ ✆ ✔ ✓ ✡ ✄ ✝ ✍ ✎ ✆ ✍ ✵ ☛ ✙ ✒ ✄ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✣ ✁ ✂ ✙ ✒ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✍ ✠ ✓ ✍ ✆ ✓ ✡ ✙ ✓ ✔ ✄ ✙ ✓ ✞ ✄ ✮ ✓ ✙ ✡ ✄ ✎ ☞ ✣ ✖ ✒ ✠ ✓ ✆ ✡ ✂ ✄ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✜ ✙ ✚ ✄ ✓ ✙ ✓ ✯ ✙ ✜ ✔ ✝ ✄ ❃ ✣ ✖ ✗ ✽ ✠ ✓ ✞ ✖ ✗ 2 1 3 provider-to-customer (0) (2 0) (1 2 0) (1 0) d 0 (1 0) (0) (3 0) (2 3 0) (3 0) (0) (2 0) (1 3 0) ✢ ✣ ✤ ✥ ✦ ✧ ✩ ✪ ✳ ✴ ✵ ✶ ✷ ✶ ✸ ✧ ✮ ✸ ✁ ✭ ✸ ☎ ✣ ✱ ✰ ✭ ✸ ✧ ✶ ✴ ✥ ✣ ✟ ✧ ✰ ✣ ✫ ✧ ✪ ❃ ✠ ✝ ✄ ✘ ✄ ✄ ✝ ✒ ✠ ✓ ✞ ✢ ✆ ✡ ✂ ✠ ✝ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✆ ✛ ✖ ✗ ❂ ✣ ☎ ✆ ✡ ✂ ✖ ✗ ✽ ✠ ✓ ✞ ✖ ✗ ❃ ✘ ✝ ✄ ✛ ✄ ✝ ✡ ✂ ✄ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✆ ✚ ✄ ✝ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✥ ☛ ✂ ✙ ✍ ✂ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✒ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✁ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✓ ✆ ✡ ✒ ✠ ✛ ✄ ✣ 5.1.2 Constrained Peer-to-Peer Relationships ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✠ ✒ ✒ ✔ ✕ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✓ ☞ ✘ ✠ ✙ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✍ ✆ ✔ ✎ ✞ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✣ ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✕ ✠ ✵ ✄ ✒ ✆ ✕ ✄ ✝ ✄ ✩ ✠ ✎ ✙ ✒ ✡ ✙ ✍ ✠ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✒ ✠ ✢ ✆ ✔ ✡ ✘ ✄ ✄ ✝ ✙ ✓ ✜ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✒ ✒ ✆ ✠ ✒ ✡ ✆ ✝ ✄ ✎ ✠ ✪ ✡ ✂ ✄ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✣ ✫ ✓ ✘ ✠ ✝ ✡ ✙ ✍ ✔ ✎ ✠ ✝ ✥ ☛ ✄ ✠ ✎ ✎ ✆ ☛ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✂ ✠ ✚ ✄ ✡ ✂ ✄ ✟ ✄ ✌ ✁ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✠ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✥ ✡ ✆ ✜ ✙ ✚ ✄ ✫ ✗ ✌ ✒ ✜ ✝ ✄ ✠ ✡ ✄ ✝ ✦ ✄ ✪ ✙ ✢ ✙ ✎ ✙ ✡ ☞ ✙ ✓ ✢ ✠ ✎ ✠ ✓ ✍ ✙ ✓ ✜ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✎ ✆ ✠ ✞ ✣ ✁ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✥ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✙ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✆ ✛ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✒ ✙ ✲ ✄ ✣ ✖ ✓ ✖ ✗ ✙ ✒ ✔ ✓ ✎ ✙ ✵ ✄ ✎ ☞ ✡ ✆ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✆ ✓ ✄ ✆ ✛ ✙ ✡ ✒ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✏ ✆ ✝ ✄ ✜ ✄ ✓ ✄ ✝ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✒ ✠ ☞ ✡ ✂ ✠ ✡ ✖ ✗ ✹ ✙ ✒ ✠ ✡ ✁ ✁ ✝ ✡ ✝ ✆ ✕ ✁ ✆ ✛ ✺ ✙ ✛ ✡ ✂ ✄ ✝ ✄ ✄ ✪ ✙ ✒ ✡ ✒ ✠ ✓ ✖ ✗ ☛ ☛ ✏ ✑ ✑ ✎ ✏ ✺ ✑ ✒ ✔ ✍ ✂ ✡ ✂ ✠ ✡ ✹ ✙ ✒ ✠ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ☛ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ✹ ✙ ✒ ✠ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✆ ✓ ✄ ✆ ✛ ✺ ✬ ✒ ✘ ✄ ✄ ✝ ✒ ✣ ✱ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✒ ✠ ✡ ✙ ✒ ✛ ☞ ✡ ✂ ✄ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✍ ✆ ✓ ✞ ✙ ✡ ✙ ✆ ✓ ✡ ✪ ✶ ✶ ✥ ✮ ✯ ✸ ✣ ✱ ✫ ✵ ✩ ✟ ✝ ✄ ✞ ✍ ✡ ✄ ✆ ✝ ✜ ✙ ✚ ✁ ✟ ✠ ✂ ✄ ✞ ✕ ✠ ☎ ✠ ☎ ✠ ✁ ✁ ✆ ✟ ✞ ✝ ✟ ✁ ✢ ☞ ✁ ✞ ✛ ✁ ✝ ✜ ✙ ✚ ✁ ✟ ✠ ✄ ✆ ✠ ✁ ✆ ✓ ✓ ✓ ✆ ✠ ☎ ✂ ✂ ✟ ☞ ✛ ✠ ☎ ✠ ✄ ☎ ✠ ✆ ✆ ✟ ✄ ✡ ✁ ✁ ✝ ✡ ✝ ✆ ✕ ✁ ✝ ✜ ✠ ✆ ✄ ✂ ✜ ✝ ✄ ✞ ✍ ✽ ☎ ✡ ✆ ✔ ☛ ✖ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✠ ✓ ✍ ✂ ✄ ✍ ✵ ✛ ✆ ✝ ✚ ✙ ✆ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✆ ✛ ✖ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✌ ✠ ✓ ✞ ✓ ✆ ✡ ✙ ✛ ☞ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✞ ✥ ✆ ✝ ✛ ✆ ✝ ✍ ✄ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✡ ✆ ✠ ✢ ✙ ✞ ✄ ✢ ☞ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✖ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✌ ✠ ✎ ✎ ✆ ☛ ✒ ✔ ✒ ✡ ✆ ✝ ✄ ✎ ✠ ✪ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✡ ✆ ✠ ✎ ✎ ✆ ☛ ✠ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✂ ✠ ✚ ✄ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✠ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ☎ ✛ ✆ ✝ ✡ ✂ ✄ ✄ ✪ ✘ ✎ ✙ ✍ ✙ ✡ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✆ ✛ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✙ ✓ ✖ ✗ ✠ ✡ ✴ ✥ ✣ ✟ ✧ ✰ ✣ ✫ ✧ ✳ ✙ ✛ ✏ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✂ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✠ ✑ ✑ ✠ ✓ ✞ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✄ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✑ ✑ ✎ ✏ ✠ ✑ ✑ ✡ ✂ ✄ ✓ ✎ ✂ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✝ ✎ ✄ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✙ ✛ ✏ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✂ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✚ ✹ ✘ ✕ ✗ ✛ ✑ ✎ ✏ ✠ ✑ ✑ ✠ ✓ ✞ ✏ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✄ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ☛ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✠ ✑ ✑ ✡ ✂ ✄ ✓ ✎ ✂ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✎ ✄ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✖ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✌ ✙ ✒ ✄ ✒ ✒ ✄ ✓ ✡ ✙ ✠ ✎ ✛ ✆ ✝ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✣
(3450) wolH p, Ra, P ORMR i2 ulH TOxO HR- tR-PROWiMR DAF. WTE wilH p, Rr, PORMR, HO 1: ORH ul, 2 OeH AS uo bH, Tiv, uHM 2Hxu, Tiav, td, 2 As. TOIH PHIR T, vH, P bH, Tiv, uHM bRh kieg aH, biuR, RHL. WTHe, IPO tOTH ASHIT, vH, w Ft fw (10),(450) OeH pHRul, wT, 1 2Ow bhIe, Tiniv, uHM, Triv, uh, 2 As Oel if IPol toTHAT, fF1 ICID: IRf o iud pHRI T, vhb, Tiiv, uHM I:d粗t,2 OH ICT As IKilul,liv,ilAs.TT了 (50) oH ITORH As P, wil,: Og iu !CIO: IR ROGi E i2i: C Feguil,: Og, IPp, ul FL, R2HM IRO: qUo HRT provider-to-customer PTase 2: ATu v, uH ASH 12, F2H R OFMR il, w TbefoR 1 o dIH p, Rr, PORMR i2 tlH pROwiMIRt IR-1CuO HR DAF til, W. H T, VH wTH 1,: H AT, 1H 2, 1 12 OCk pRoO C wilH Iuy bilI of AT, IHF2 ASHI foIRO 1 wilH 1,:H @e AT, lIF1 ASHI. 12 Figure r: A BGP system tTat oheys GuiGeline B AT,IH 1, Hi: pOlH, MMtoe, PORMR o2 ASH 1o ul;w, 2 AS sumption i1, Tiiv, tdM OeFL if, IPaf itd pHIR, RH luy bF OR tilH POGd of iud Celu bH pHIR. doM 2Ow, HHliw wlH ROGa2g Mli line TH ORMR TeroR 1 tR wlH Fegwif d wlH fIORdw 1OnOr IR 2A2AS1,2说mpm,pHaA53.宽C如5m,pRm2T1,如myRP旺2 AppHLi2g FGMHi2H B, AS 3, Ifig2I H C PpRHHRH TH I wlH uOr HRROGHH. iwl, laoutbu as p, uil. HHTH ulil, Mui@, P ROGrH FlkD wilRoCgT'iud phR, 2M ulH HOCH FEk5k0tilhoCT RHf uRi Tnoe oe, Tiiv, tioe ORMR ICH uil, w, AT, 1H1 AS if ud I@uOr H AS3 C:, tfL f, VOR ilHROGrH Flk0. iuiTwlH Iu bHI, fuR iud, Tiiv, tioe, folIa i2g, li: iPR, RgC Hew, 1 i2 ITORIR AS P, wiT. HQ IHR, AS 1 pRHHRI wilH ICIO: HR OGH dH::,5.1. NHxu. H pROH bL Tbeur, MTiioe uil,w,IPASHI E2A0· OvHR iu MRHlin ROGH FO°,2MAS2 pRHIR wiTH ROGIH FH, Tiiv, uHM i2 A T, IH 1 3k6A0· IRoGTiud 1CO HR OvHR lHR和mhcT tI pRONIMR. AlIC H uil, W i2it, IFL 2OeH df wlH ASHI T, vh AlIC H il, w u it, EMRHTin OR i2MRHlW pROwiMR O AS,,2M ROGH o d. AfR AS 5, 2M AS E T,vH bHe, Tav, ulM, 2HvHR bHT: H HligibH foR, Ti, uioe i2 AT, NH 1.-TH2, H C Hl, W ASH 1, 2,, 2M3, RH, P, L1, Tiniv, tIM HOgHDliR. will O2H of u'lTCuO: HRd, 1 20, Tiv, uHM OR O2H dulL IH fiRIw, Tiniv, u@e hl M ASH 1, 2,, 2M 3 uD IHfHlio raHall 1Cuo: HRf Cf u'I pHRf., 1 2Ow, Tav, uhM WitiloGn Fof d FO, F,, 2M FEk5k0, RHlpHliivHL. O2 tilH 2Hxw, Tiiv, tioe, gH2HR, Fil, IIC Huil, wuT; 1, IOuo HRu ul, wil, EMRHli DIHL 1. iuTT I F2K0", BhEk5h0,, 2M F1k0,, 2M wilH pROTHl1 CR i2MRHTi pROwiMR of ASd uf, w., 1 2Ow, Tiiv, uM Si: i- RIpH, w i2Mi2itiL-Ti1 ILluH: aaM bH 1, H if iu faQ I P RlL, u HwIIRT, 1, ICuC Hair, w, 1 20, Tiv, tIM CRO2H FGM2H l bL RIK GE R2g as 3 I f, VOR wilH /CuOr HR ROGh of wilH IQuOr Hf of uI'1 pHRf, 1 20v, Tiv, ulM WiuiloGr KA· OwHR wlH PHR ROGIH FIk0° FOlI o gHI li,, 1IC Huil, wuI T 1, pHR. iuT, 1QuO IR 1 20w, Tiiv, uHM -Til pRoTH1 1, 22Ow RIH w 12 2nO-nM 5.2. Fov a h o s lyltbm laat aaLonly mllombux MieiuHlL. iuiloGn ITOCeuHR2g Io H As, w lupI i, 2M J u:,12TH Asd t, 1, fi2iuh 2c bhR of FMRHIiD OR i up 2it bu ant i bbuLo-i bbv blationlai Lant rirlounl to l l, i2MRHflii pROviMR. Ha IHR, iif it,702uRMTioe,1i2TH Lum tion s, wd all I cbldollo: guit blint h, tabn tab h os i i: plit ui, w AIIC price A T, 1 bH vioR wHIM-TIRHOFHL AT, IH 1, Triv, tH, P ASd 1 EMRHIiw OR i2MRH/in pROwiMR1 U.OOF: WH PRONH olH ollRH bl M: oeI d, ui2g wl, w wlH E FA ILI T,I, I bI Iuy uh, 2M lOvHRgH uo ulH Iu bl Iu: uH foR, 2L i2i, P lu uH, 2M, 2L f, iR, Tiv, tioe 1H@rTH 5. 2 BGP Systems with Backup Links Si2TH ilH tHoM p, Rvif Ii: iP R to-THORH 5.1,. H 1O2TIe- CCIA: HR-pROwiMR, 2M pHIRtIO-PHIR, RH olH u o: ofwlOr uR, uh Oe ppoi2g wl, wiTH E FA ILI T,1, Iuy bIH 1u tL oe Re noefTipl bHn H W O ASH. HQ HvIR,, 2 AS:, L HOT, vH, b, IkG RHP uoefTip. iot, 2Hig TboRi2g As.H, 1H CrTH ui, w H M to, Iuy bI Ivy uH. WH, Tiv, uH, IPASHI, 2 AS T, 1 R: itHM 1022HIuniviuL uo toTH RHIw af wIH 2uIR F2H R OMR al, w 1oeroR 1 uo wlH p, Rr, PCRMR 12 2H FOR Hx, PHL ASHI A, 2ME TOCM Huy bRIT, biP uR P ICID: HR-RO-pROwiMR DAF 12 AT, IH 1. WH i: POlH, MM b, IkGp, gRHI Iw fOR pROwiM2g wlH 1O22Hlio2 I wilH 2uIR to, P1oeI R i2d Oe wilH ORMR of As, Tiv, toe1 i2 AT, IH 2Hv i2 wlH T, IH uil, w OeH As l2k to pROiMRI L if1. AsCi 1 b, HM Oe tilH pHIR-oO-pHR RHP uoefTip 1, 2M wlH AS-P, ul PROWIMRC AS A, 2MAS D il, pROwiMRC AS E ASHf C egil.-IRHfoRH, E FA Ipl, kiRI gHo wHR ICuO IR, 2M 2MDT, VH, PHIR-uO-pHR, gRHH Hu -LpiT, HL, A RH TTH HR ROGH i2 AT, TH 1. -TH E FA IpH kH wl, w M 2Ow OlIRt vi, C, 2ME RH, TTHf ODIHR vi, D If wlH l2k bH He gHo, BOGH i2 AT, TH 1 wIe IHHio, PoGa IRO, pHIR OR A, 2MC FORE, 2MD" f, ill, thb, IkG liek bH H A, 2ME OROVIMGR IHRHORIH 12 AT, IH 2, ASH, RH, Tv, tdM 12 if CHM fOR A FOR E"tD 1022HliD uo ulH I2uHReH I2i, HL 2 ORMR ti, w 1beroR I tD ulH P, Ra, P ORMR givE i2 wlH 11C Huil, u, 2 As p, iRT, 22OuT, vH boiT, b, IkG RHP toe Cuo HR DAF. FaR HL.H PT, IH ITip 2M, 1QuOr HR-pROwiMR OR PHRIR-PHIR, I, 2gH: Heup Tuv, uoe IcRt o, 1 folRa I H RHP x wlif, 11c poe i2 SHine 6.2. PTase 1: ATiv, uH ASHf i2, I2H R ORMR ui, w loefOR 1 t E, IkG lek1, Rh 2Ow: H 2w to bH OHM CIlI, f, i CRH
(3 4 5 0) ... (0) (2 0) 3 0 4 5 (0) provider-to-customer peer-to-peer (1 0), (4 5 0) ... ... 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✂ ✠ ✚ ✄ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✜ ✣ ✖ ✛ ✡ ✄ ✝ ✖ ✗ ✺ ✠ ✓ ✞ ✖ ✗ ☛ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✥ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✖ ✗ ✄ ✒ ✽ ✥ ❃ ✥ ✠ ✓ ✞ ✾ ✠ ✝ ✄ ✠ ✎ ☛ ✠ ☞ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✡ ✆ ✜ ✄ ✡ ✂ ✄ ✝ ✣ ✁ ✂ ✄ ✮ ✝ ✒ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✎ ✄ ✠ ✞ ✒ ✖ ✗ ✄ ✒ ✽ ✥ ❃ ✥ ✠ ✓ ✞ ✾ ✡ ✆ ✒ ✄ ✎ ✄ ✍ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✏ ❂ ✑ ✥ ✏ ❂ ✑ ✥ ✠ ✓ ✞ ✏ ☛ ✆ ✺ ✆ ❂ ✑ ✥ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✎ ☞ ✣ ★ ✓ ✡ ✂ ✄ ✓ ✄ ✪ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✥ ✡ ✂ ✄ ☞ ✒ ☛ ✙ ✡ ✍ ✂ ✡ ✆ ✏ ❃ ✆ ❂ ✑ ✥ ✏ ✾ ✆ ☛ ✆ ✺ ✆ ❂ ✑ ✥ ✠ ✓ ✞ ✏ ✽ ✆ ❂ ✑ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✝ ✄ ✘ ✄ ✠ ✡ ✙ ✓ ✞ ✄ ✮ ✓ ✙ ✡ ✄ ✎ ☞ ✣ ✁ ✂ ✙ ✒ ✒ ☞ ✒ ✡ ✄ ✕ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✒ ✠ ✛ ✄ ✙ ✛ ✙ ✡ ✛ ✆ ✎ ✎ ✆ ☛ ✄ ✞ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✙ ✢ ☞ ✝ ✄ ✧ ✔ ✙ ✝ ✙ ✓ ✜ ✖ ✗ ✾ ✡ ✆ ✛ ✠ ✚ ✆ ✝ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✏ ☛ ✆ ✺ ✆ ❂ ✑ ✆ ✚ ✄ ✝ ✡ ✂ ✄ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✏ ✽ ✆ ❂ ✑ ✣ ✂ ✄ ☎ ✆ ✝ ☎ ✞ ✺ ✣ ❃ ✣ ✟ ✝ ✄ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ☎ ✠ ✄ ☎ ✠ ✄ ✟ ✝ ✞ ✂ ✍ ✛ ☞ ✟ ☎ ✝ ✌ ✁ ✝ ✡ ✝ ✆ ✕ ✁ ✄ ✞ ✕ ✡ ✁ ✁ ✝ ☎ ✝ ✝ ✡ ✁ ✁ ✁ ✂ ✄ ☎ ✆ ✝ ✞ ✟ ✠ ✆ ✡ ✟ ✄ ✞ ✕ ✛ ✝ ✞ ✜ ✝ ✌ ✟ ☎ ✝ ✙ ✟ ✝ ✟ ☞ ✌ ✡ ☎ ✆ ✝ ✞ ✘ ✠ ✆ ✜ ✄ ✂ ✂ ✙ ✚ ✁ ✟ ✜ ✝ ✂ ✂ ✝ ✡ ✢ ☞ ✆ ✕ ✁ ✂ ✆ ✞ ✁ ✖ ✠ ☎ ✠ ✁ ✞ ☎ ✠ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✆ ✟ ✟ ✄ ✜ ✁ ☛ ✎ ✝ ✆ ✆ ✏ ✡ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✄ ✡ ✂ ✄ ✆ ✝ ✄ ✕ ✢ ☞ ✞ ✄ ✕ ✆ ✓ ✒ ✡ ✝ ✠ ✡ ✙ ✓ ✜ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✂ ✠ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✠ ✓ ✞ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✛ ✆ ✝ ✠ ✓ ☞ ✙ ✓ ✙ ✡ ✙ ✠ ✎ ✒ ✡ ✠ ✡ ✄ ✠ ✓ ✞ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✒ ✄ ✍ ✆ ✓ ✞ ✘ ✠ ✝ ✡ ✙ ✒ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✡ ✆ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✥ ☛ ✄ ✍ ✆ ✓ ✍ ✄ ✓ ✩ ✡ ✝ ✠ ✡ ✄ ✆ ✓ ✘ ✝ ✆ ✚ ✙ ✓ ✜ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✂ ✠ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✡ ✆ ✟ ✄ ✕ ✕ ✠ ✺ ✣ ✽ ✥ ☛ ✄ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✠ ✡ ☛ ✆ ✩ ✘ ✂ ✠ ✒ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✡ ✂ ✠ ✡ ✎ ✄ ✠ ✞ ✒ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✱ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✠ ✎ ✎ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✱ ✄ ✙ ✕ ✘ ✆ ✒ ✄ ✠ ✞ ✞ ✙ ✩ ✡ ✙ ✆ ✓ ✠ ✎ ✍ ✆ ✓ ✒ ✡ ✝ ✠ ✙ ✓ ✡ ✒ ✆ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✆ ✛ ✖ ✗ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ✡ ✂ ✄ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✖ ✗ ✩ ✘ ✠ ✡ ✂ ✎ ✄ ✓ ✜ ✡ ✂ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✜ ✄ ✡ ✡ ✂ ✄ ✙ ✝ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✁ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✡ ✂ ✠ ✡ ✞ ✆ ✓ ✆ ✡ ✜ ✄ ✡ ✠ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✡ ✂ ✄ ✓ ✒ ✄ ✎ ✄ ✍ ✡ ✠ ✝ ✆ ✔ ✡ ✄ ✛ ✝ ✆ ✕ ✠ ✘ ✄ ✄ ✝ ✆ ✝ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ❃ ✥ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✠ ✓ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✜ ✙ ✚ ✄ ✓ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✠ ✡ ☛ ✆ ✩ ✘ ✂ ✠ ✒ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✑ ✠ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✣ ✵ ✁ ✭ ✶ ✧ ★ ✡ ✖ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✣ ✱ ✂ ✄ ✓ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✠ ✎ ✎ ✆ ☛ ✒ ✕ ✆ ✝ ✄ ✡ ✂ ✠ ✓ ✆ ✓ ✄ ✖ ✗ ✡ ✆ ✢ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✓ ✄ ✪ ✡ ✥ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✠ ✓ ✖ ✗ ☛ ✂ ✆ ✒ ✄ ✘ ✄ ✄ ✝ ✒ ✂ ✠ ✚ ✄ ✠ ✎ ✎ ✢ ✄ ✄ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✥ ✢ ✝ ✄ ✠ ✵ ✙ ✓ ✜ ✡ ✙ ✄ ✒ ✠ ✝ ✢ ✙ ✡ ✝ ✠ ✝ ✙ ✎ ☞ ✣ ✱ ✂ ✄ ✓ ✠ ✎ ✎ ✆ ✛ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✂ ✠ ✚ ✄ ✠ ✡ ✎ ✄ ✠ ✒ ✡ ✆ ✓ ✄ ✘ ✄ ✄ ✝ ✡ ✂ ✠ ✡ ✂ ✠ ✒ ✓ ✆ ✡ ✢ ✄ ✄ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✥ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✠ ✓ ✖ ✗ ✆ ✓ ✎ ☞ ✙ ✛ ✠ ✎ ✎ ✆ ✛ ✡ ✂ ✄ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✆ ✛ ✙ ✡ ✒ ✘ ✄ ✄ ✝ ✒ ✂ ✠ ✚ ✄ ✢ ✄ ✄ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✫ ✛ ✕ ✆ ✝ ✄ ✡ ✂ ✠ ✓ ✆ ✓ ✄ ✒ ✔ ✍ ✂ ✖ ✗ ✄ ✪ ✙ ✒ ✡ ✒ ✥ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ☛ ✂ ✆ ✂ ✠ ✒ ✡ ✂ ✄ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✖ ✗ ✘ ✠ ✡ ✂ ✠ ✕ ✆ ✓ ✜ ✙ ✡ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✏ ✕ ✙ ✓ ✙ ✕ ✔ ✕ ✎ ✄ ✓ ✜ ✡ ✂ ✠ ✕ ✆ ✓ ✜ ✠ ✎ ✎ ✘ ✠ ✡ ✂ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✑ ✣ ✵ ✁ ✭ ✶ ✧ ✩ ✖ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ☛ ✄ ✂ ✠ ✚ ✄ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✌ ✂ ✠ ✒ ✄ ❃ ✠ ✒ ✙ ✓ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✣ ★ ✔ ✝ ✘ ✝ ✆ ✆ ✛ ✆ ✛ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✌ ✂ ✠ ✒ ✄ ✩ ❃ ✖ ✗ ✄ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✒ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ☛ ✄ ✍ ✆ ✓ ✍ ✄ ✓ ✡ ✝ ✠ ✡ ✄ ✆ ✓ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✄ ✒ ✣ ✫ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✥ ☛ ✄ ✙ ✕ ✘ ✆ ✒ ✄ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✆ ✓ ✖ ✗ ✄ ✒ ✒ ✆ ✡ ✂ ✠ ✡ ✠ ✓ ✖ ✗ ✙ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✆ ✓ ✎ ☞ ✙ ✛ ✠ ✎ ✎ ✆ ✛ ✙ ✡ ✒ ✘ ✄ ✄ ✝ ✒ ✠ ✝ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✆ ✝ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✛ ✙ ✡ ✒ ✔ ✓ ✒ ✡ ✠ ✢ ✎ ✄ ✘ ✄ ✄ ✝ ✒ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✣ ✁ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✎ ✄ ✓ ✜ ✡ ✂ ✆ ✛ ✡ ✂ ✄ ✒ ✂ ✆ ✝ ✡ ✄ ✒ ✡ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✣ ✗ ✙ ✓ ✍ ✄ ✠ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✓ ✄ ✚ ✄ ✝ ✂ ✠ ✒ ✠ ✂ ✄ ✢ ✁ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✡ ✂ ✠ ✓ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✥ ✠ ✓ ✖ ✗ ✓ ✄ ✚ ✄ ✝ ✒ ✄ ✎ ✄ ✍ ✡ ✒ ✠ ✘ ✄ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✆ ✚ ✄ ✝ ✠ ✍ ✔ ✒ ✩ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ☛ ✙ ✡ ✂ ✠ ✟ ✠ ✝ ☎ ✁ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✡ ✂ ✙ ✒ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✙ ✆ ✓ ✆ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✆ ✝ ✞ ✄ ✝ ✄ ✓ ✒ ✔ ✝ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✌ ✂ ✠ ✒ ✄ ✩ ✽ ✖ ✗ ✙ ✒ ✒ ✡ ✠ ✢ ✎ ✄ ✠ ✛ ✡ ✄ ✝ ✙ ✡ ✒ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✥ ✛ ✆ ✎ ✎ ✆ ☛ ✙ ✓ ✜ ✠ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✠ ✒ ✙ ✓ ✟ ✄ ✕ ✕ ✠ ✺ ✣ ✽ ✣ ✶ ✄ ✪ ✡ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✢ ☞ ✍ ✆ ✓ ✡ ✝ ✠ ✞ ✙ ✍ ✡ ✙ ✆ ✓ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✖ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✹ ✙ ✒ ✠ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✾ ✁ ✠ ✓ ✞ ✓ ✄ ✚ ✄ ✝ ✢ ✄ ✍ ✠ ✕ ✄ ✄ ✎ ✙ ✜ ✙ ✢ ✎ ✄ ✛ ✆ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✽ ✣ ✁ ✂ ✄ ✓ ✥ ✄ ✙ ✩ ✡ ✂ ✄ ✝ ✆ ✓ ✄ ✆ ✛ ✹ ✬ ✒ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✥ ✆ ✝ ✆ ✓ ✄ ✆ ✛ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✆ ✛ ✹ ✬ ✒ ✘ ✄ ✄ ✝ ✒ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✱ ✙ ✡ ✂ ✆ ✔ ✡ ✎ ✆ ✒ ✒ ✆ ✛ ✜ ✄ ✓ ✄ ✝ ✠ ✎ ✙ ✡ ☞ ✥ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✹ ✂ ✠ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✹ ✂ ✡ ✂ ✠ ✡ ✙ ✒ ✠ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✾ ✁ ✡ ✂ ✠ ✡ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✗ ✙ ✕ ✙ ✩ ✎ ✠ ✝ ✎ ☞ ✥ ✹ ✂ ✄ ✙ ✡ ✂ ✄ ✝ ✂ ✠ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✡ ✂ ✠ ✡ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✥ ✆ ✝ ✆ ✓ ✄ ✆ ✛ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✆ ✛ ✹ ✂ ✬ ✒ ✘ ✄ ✄ ✝ ✒ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✱ ✙ ✡ ✂ ✆ ✔ ✡ ✎ ✆ ✒ ✒ ✆ ✛ ✜ ✄ ✓ ✄ ✝ ✠ ✎ ✙ ✡ ☞ ✥ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✹ ✂ ✂ ✠ ✒ ✠ ✘ ✄ ✄ ✝ ☛ ✙ ✡ ✂ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✹ ✄ ✡ ✂ ✠ ✡ ☛ ✠ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✣ ✁ ✂ ✙ ✒ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✍ ✠ ✓ ✓ ✆ ✡ ✝ ✄ ✘ ✄ ✠ ✡ ✙ ✓ ✩ ✞ ✄ ✮ ✓ ✙ ✡ ✄ ✎ ☞ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✄ ✓ ✍ ✆ ✔ ✓ ✡ ✄ ✝ ✙ ✓ ✜ ✒ ✆ ✕ ✄ ✖ ✗ ✠ ✡ ✒ ✡ ✄ ✘ ✒ ✡ ✠ ✓ ✞ ☞ ✏ ✙ ✣ ✄ ✣ ✥ ✹ ✆ ✄ ✹ ✠ ✑ ✥ ✒ ✙ ✓ ✍ ✄ ✾ ✁ ✂ ✠ ✒ ✠ ✮ ✓ ✙ ✡ ✄ ✓ ✔ ✕ ✢ ✄ ✝ ✆ ✛ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✡ ✂ ✙ ✒ ✙ ✒ ✠ ✍ ✆ ✓ ✡ ✝ ✠ ✞ ✙ ✍ ✡ ✙ ✆ ✓ ✥ ✒ ✙ ✓ ✍ ✄ ✙ ✡ ✙ ✕ ✘ ✎ ✙ ✄ ✒ ✡ ✂ ✠ ✡ ✖ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✌ ✂ ✠ ✒ ✢ ✄ ✄ ✓ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✞ ✣ ✁ ✂ ✄ ✝ ✄ ✛ ✆ ✝ ✄ ✥ ✌ ✂ ✠ ✒ ✄ ✽ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✒ ✠ ✎ ✎ ✾ ✁ ✬ ✒ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✆ ✝ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ 5.2 BGP Systems with Backup Links ✷ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✝ ✄ ✡ ✂ ✄ ✡ ☛ ✆ ✕ ✆ ✒ ✡ ✍ ✆ ✕ ✩ ✕ ✆ ✓ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✠ ✓ ✖ ✗ ✕ ✠ ☞ ✠ ✎ ✒ ✆ ✂ ✠ ✚ ✄ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✣ ✤ ✠ ✚ ✩ ✙ ✓ ✜ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✠ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✡ ☛ ✂ ✄ ✓ ✠ ✓ ✖ ✗ ✂ ✠ ✒ ✎ ✙ ✕ ✙ ✡ ✄ ✞ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✡ ✆ ✡ ✂ ✄ ✝ ✄ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✩ ✓ ✄ ✡ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✖ ✗ ✄ ✒ ✖ ✠ ✓ ✞ ☎ ✍ ✆ ✔ ✎ ✞ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✠ ✢ ✙ ✎ ✠ ✡ ✄ ✝ ✠ ✎ ✢ ✠ ✍ ✵ ✔ ✘ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✛ ✆ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✙ ✓ ✜ ✡ ✂ ✄ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✆ ✓ ✡ ✆ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✩ ✓ ✄ ✡ ✙ ✓ ✡ ✂ ✄ ✍ ✠ ✒ ✄ ✡ ✂ ✠ ✡ ✆ ✓ ✄ ✖ ✗ ✬ ✎ ✙ ✓ ✵ ✡ ✆ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✛ ✠ ✙ ✎ ✒ ✣ ✖ ✗ ✷ ✙ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✖ ✗ ✖ ✠ ✓ ✞ ✖ ✗ ✰ ✙ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✛ ✖ ✗ ☎ ✣ ✖ ✗ ✄ ✒ ✷ ✠ ✓ ✞ ✰ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✜ ✝ ✄ ✄ ✕ ✄ ✓ ✡ ✣ ✁ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✥ ✖ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✆ ✡ ✂ ✄ ✝ ✒ ✚ ✙ ✠ ✷ ✠ ✓ ✞ ☎ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✆ ✡ ✂ ✄ ✝ ✒ ✚ ✙ ✠ ✰ ✣ ✫ ✛ ✡ ✂ ✄ ✎ ✙ ✓ ✵ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✠ ✓ ✞ ✷ ✏ ✆ ✝ ☎ ✠ ✓ ✞ ✰ ✑ ✛ ✠ ✙ ✎ ✒ ✥ ✡ ✂ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✠ ✓ ✞ ☎ ✙ ✒ ✔ ✒ ✄ ✞ ✛ ✆ ✝ ✖ ✏ ✆ ✝ ☎ ✑ ✡ ✆ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✡ ✆ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✣ ✫ ✓ ✙ ✡ ✙ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✢ ✆ ✡ ✂ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✩ ✒ ✂ ✙ ✘ ✠ ✓ ✞ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✝ ✝ ✠ ✓ ✜ ✄ ✕ ✄ ✓ ✡ ❀ ☛ ✄ ✝ ✄ ✎ ✠ ✪ ✡ ✂ ✙ ✒ ✠ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ❅ ✣ ❃ ✣ ☎ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✠ ✝ ✄ ✓ ✆ ✡ ✕ ✄ ✠ ✓ ✡ ✡ ✆ ✢ ✄ ✔ ✒ ✄ ✞ ✔ ✓ ✎ ✄ ✒ ✒ ✠ ✛ ✠ ✙ ✎ ✔ ✝ ✄
occu-so H2nc2, -Or: 2s invoving b, ckup Links Si alM 1, v g in: 1 2 fi-S To]- pI, $2S, nMI, V2, b, ckup -inko Sinc2: 12$2 lo ph2 loc, up-2f 1, n a12--Ql: 2s0 Na2 AS2s M na p-OwiM - nsi: 82-viC2,: 1 2y I-oug, b, ckup Link is,-oul Ins on2 O- m ycM-σ ks i I Cpa Fo-m, V,, 21, v2 FuiMLin2 C To- 2, CI n FP sp2, k2-t Using: 1 2 S, m2,-gum2n og. 1:1 ar: using, b, ckup Linko Simiy-Ly, in P1, S23,nM 4,,山AS FR MOns no con:, in, b nM1, v2,-o:2 vi, 2 3Tb, ckup Link -2, cI, S:, by S:,:20 fola FuiMLin2 A O n: O, ssign PiSv-FPI Fin, y, in P1, $2 5,: 1 2-2m, ining AS2 f FFPca:, ins, b, ckup Link",nM Ⅵ, spc:iv2 b, ckup ink g2:: o, s:, by s:, 2G AUd FR M2s no co:, in, b, ckup Link :1 282C, n b2 p-Ow2n by inMIc: ion,, s in d 1 20-2m 5do PhISyfp No d1202m -in2,-O-M-o ASso Using 1 2 S, m2, -gum C, n D=ov No2: 1,: un -ik2 FuiMLin2 AO n, 2nfocing FuiM-in2 C qui-2s cOOp2-,: ion b2: 22n AS2so An AS c, n no: 2U.1 ic 2 n FP sys 2 m conv2-g2s: 0: 12, bl s:,: 2 fo, ny D: 2s invd-v2 b, ckup Links b2: 22n a1 2-AS P, i-so Hanc FP, M2-: is2m2n:s mus iMn: ify: 1 282 -Q1: 2so d I is is: ypic, Ly, C1 12v2M using 1 2 cOmmuni:y, -ibu: 2 FN-P: a 6. PRACTICAL IMPLICATIONS P-OwiM-S, nMcus: Om2-S, g-22 On, cOmmun:y numb In 1 is s2c: ion,,2 Mscuss: 12, ppic, bi liy of a]- guiM- inMic,: 2s, I icI -Q: 2s incLtiMs, b, ckup Link [3]o W1 2n Cin2s: OMv2-S2, nMCI, nging n2: Ok: Cpdogi2s, nM-ou: ing cus: Om2-$2nMS:1 2 P. ckup-Ql: 2, 1:, ssigr m2: 1 ology communI b2-:o:12-O b2, ppLi2 M: O mo-2 cOmpLlx-24: iOns ips b [2]fo Mesc-ib21a, n AS p, i-C, n: - ns:iOn: O, n2.-24: ions ip 1 2 cOnfigu-, iOn spzcifi2M using Rou: ing Pdicy Sp2 cific 1:1 Q1: Ms-up: ing sys: 2m s:, biliya on F, ngu, g2 FRPSF o Na,.2 p-Ow2: 1,: FuimLin2 C 1 nFP sys: 2m is s, f2 6.1 Robustness of the guidelines k apdogy nm-an: ing pd-iciz I ation 5Bo l =l A SIr dollop Fjklknh C hn dtthnF in: OM s-, piMy g-a ing In: 2-n2: a Rou: 2-, nMLi'nk f, ilt ni thhf2i olkckhcthIn thh bgp dohrn hd ch nM:12 Mploym2n: a, MM: ion, Un2: ok 2quipm2n:, -2sul in [-2qu2n: cI, ngs: 0: 1 2 unMe-Lying: opdogyo ISPs o : 2n Poi iFt W2 p-Ow2 1 2: 1 20-2m To:12 C, S2: 1 iOns: O, M p:: o b, ckup-O: 2s fdla FuiMLin2 Aod 1 2 sim gurman: fdJ Men, nM, nM Cl, ngs In LUb, ckup -o: 2s fda FuiM in2 n o nMcOnn2c: ions: O nig bo-ing AS2so In, MM: ion, AS2s p2- F2: 23 TM na 2: 1 2 AS DIgin,:2 iOn p-2f oMC moving go W2 cOn8-uc iv: iOn $ qu2 nc2: 1,: M: 1 2 n FP cus Om2-S, P22S, O- P-oiM-so Ou- guiM-in2s 2nsu-2:12 ys:2m:o, 8, bl s:, 20 W2: 1 2n p-Ow2: 1, : 1 2 sys: 2m, U bili:y o FP sys 2m 2v2n in: 1 is Mn, mic 2 nvi-On b d n? p22-inks,, nM: 1 2n p-Cp, g,: 2s-Ou: 2s using b, ckup links n2. -ou: ing Mcisions, 1 2 p, 1, Uo-M-ing, mong-ar2s: O 2, C1 MS In,: IOn 2nsu-2S 2 svS.2 n d 120-2m 5d,: 12: 1 i-M, nM fou-1 pI, S2 p-gp, g,:2S s:,:20 AU2-ny"oming, C1 2ck on: 12: podgy, nMpe ca . g C1 28[9] us223Ts b, ckup link,, nM: 1 2 fif 2 AS?s v2 na ga: 2n,-ou: 2, nM 1, v2, b, ckup icy configu-,: ions. oulM1, v2: 0-2cOnfi-m 1 2$2 P-Op2-: 12S, Linko Fom, y,, 2 cOs: -uc:,n, C: Iv,: IOn $2 qu2 nc n2.n FP sys: 2m. aulD b2 s, f2g 4, M:O, s:, bu s:, 20 d 12, c: iv,: ion $2qu2nc2, c: iv,: 2s 12 n FP sp2, ki-s in 2, CI AS simul, n2ouslya Simiy-:O, -Li2-.ok on n FP camv2-g2 nc2 p-Cp2-: i2s 9 10; 20], o- guiM Lin2s forus On: 1 2, ppIc,: ion d oc, Up-af k b an a Inform o p-2f2-som2-o: 2s Ow2-, 2-n,: iv2s 12 P,-1,00M-gIv2n In m2: O-p-OwiM- DAFU W2 i od/s, bo: k ban u-, c: iv, 2 AS2s in,in2,-OM 2-2suling n FP sys 2m, i: is impo:,n::O 1 2 p,:i, o-M- givan in p-OviM--: O-cus: Om2- DAFo cOnsiM-: 1 2 imp, c: of a1 2-n FP,: : -ibu: 2s, nM: 1 2 possi- 1, v2, b, ckup Link. 1 bili:y d FP sp2, s k2-s0 d 1 2 mOMU 23T,nM1,V2 na ga: 2n,-Qu: 2 in 12 fi- S2c: ion 3,, n ua 2 2n FP k2-SO Sp2, k- 2-s. I in 1 2 S, m2 AS M no n2 C2 SS, -ily ci P-OwiM- DAFo o:20d 1 2 uim, 2-Qu: ing M cision m, y, so M p2nMOn As k ban a, c: i 2 AS2s 1, V2 na go: 2n a1: 2 P, I Lng: 1 FincLIMng P, 1 s. i: 1 AS p-2P2nMing', mulipy 1-22p1,s28in:12OM confo-m 2 XI: MSC-lmIn, :O-S, m,: 10n I-Om p-OM№= ocus om k b an 5-, c: iv,: 2: 1 2 AS2s: 1 V2 na g sibu: 2s =h2, pplying Oc, Up-2f: 0: 1 2-O: 2s L,-n2Mf-Ox
✆ ✍ ✍ ✔ ✝ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✝ ✆ ✔ ✡ ✄ ✒ ✙ ✓ ✚ ✆ ✎ ✚ ✙ ✓ ✜ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✒ ✂ ✆ ✔ ✎ ✞ ✂ ✠ ✚ ✄ ✠ ✂ ✝ ✡ ✁ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✡ ✂ ✠ ✓ ✆ ✡ ✂ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✙ ✒ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✒ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✣ ✡ ✂ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✞ ✆ ✄ ✒ ✞ ✝ ☎ ✂ ✠ ✚ ✄ ✡ ✆ ✢ ✄ ✮ ✝ ✒ ✡ ✂ ✆ ✘ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✂ ✠ ✚ ✄ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✷ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✴ ✥ ✣ ✟ ✧ ✰ ✣ ✫ ✧ ✔ ✙ ✛ ✏ ✏ ✎ ✂ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✑ ✠ ✓ ✞ ✏ ✎ ✄ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✑ ✑ ✛ ✆ ✎ ✎ ✆ ☛ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✆ ✝ ☎ ✡ ✆ ✠ ✒ ✒ ✙ ✜ ✓ ✎ ✂ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✙ ✛ ✏ ✏ ✎ ✂ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✒ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✑ ✠ ✓ ✞ ✏ ✎ ✄ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✍ ✆ ✓ ✡ ✠ ✙ ✓ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✑ ✑ ✎ ✂ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✆ ✎ ✄ ✓ ✙ ✗ ✚ ✏ ✎ ✑ ✒ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✥ ✔ ✓ ✎ ✙ ✵ ✄ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✆ ✝ ☎ ✥ ✄ ✓ ✛ ✆ ✝ ✍ ✙ ✓ ✜ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✷ ✝ ✄ ✩ ✧ ✔ ✙ ✝ ✄ ✒ ✍ ✆ ✆ ✘ ✄ ✝ ✠ ✡ ✙ ✆ ✓ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ ✖ ✓ ✖ ✗ ✍ ✠ ✓ ✓ ✆ ✡ ✡ ✄ ✎ ✎ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✙ ✓ ✚ ✆ ✎ ✚ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✆ ✡ ✂ ✄ ✝ ✖ ✗ ✘ ✠ ✙ ✝ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✡ ✂ ✄ ☎ ✟ ✌ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✕ ✄ ✓ ✡ ✒ ✕ ✔ ✒ ✡ ✙ ✞ ✄ ✓ ✡ ✙ ✛ ☞ ✡ ✂ ✄ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✁ ✂ ✙ ✒ ✙ ✒ ✡ ☞ ✘ ✙ ✍ ✠ ✎ ✎ ☞ ✠ ✍ ✂ ✙ ✄ ✚ ✄ ✞ ✔ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✏ ✚ ✘ ✑ ✕ ✑ ✣ ✌ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✓ ✞ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✠ ✜ ✝ ✄ ✄ ✆ ✓ ✠ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✓ ✔ ✕ ✢ ✄ ✝ ✡ ✂ ✠ ✡ ✙ ✓ ✞ ✙ ✍ ✠ ✡ ✄ ✒ ☛ ✂ ✙ ✍ ✂ ✝ ✆ ✔ ✡ ✄ ✒ ✙ ✓ ✍ ✎ ✔ ✞ ✄ ✒ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✿ ✾ ❁ ✣ ✱ ✂ ✄ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✄ ✓ ✞ ✒ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✆ ✔ ✡ ✄ ✥ ✙ ✡ ✠ ✒ ✒ ✙ ✜ ✓ ✒ ✡ ✂ ✄ ✍ ✆ ✕ ✕ ✔ ✓ ✙ ✡ ☞ ✓ ✔ ✕ ✢ ✄ ✝ ✡ ✆ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✍ ✠ ✓ ✠ ✒ ✒ ✙ ✜ ✓ ✠ ✓ ✠ ✘ ✘ ✝ ✆ ✘ ✝ ✙ ✠ ✡ ✄ ✎ ✆ ✍ ✘ ✝ ✄ ✛ ✣ ✗ ✄ ✄ ✿ ❃ ❁ ✛ ✆ ✝ ✠ ✓ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✆ ✛ ✡ ✂ ✄ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ✘ ✄ ✍ ✙ ✮ ✄ ✞ ✔ ✒ ✙ ✓ ✜ ✴ ✆ ✔ ✡ ✙ ✓ ✜ ✌ ✆ ✎ ✙ ✍ ☞ ✗ ✘ ✄ ✍ ✙ ✮ ✍ ✠ ✩ ✡ ✙ ✆ ✓ ✟ ✠ ✓ ✜ ✔ ✠ ✜ ✄ ✏ ✴ ✌ ✗ ✟ ✑ ✣ ✶ ✆ ☛ ✥ ☛ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✷ ✄ ✓ ✒ ✔ ✝ ✄ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✙ ✒ ✒ ✠ ✛ ✄ ✣ ✂ ✄ ☎ ✆ ✝ ☎ ✞ ✺ ✣ ✾ ✣ ✜ ✄ ✂ ✂ ✙ ✚ ✁ ✟ ✜ ✝ ✂ ✂ ✝ ✡ ✢ ☞ ✆ ✕ ✁ ✂ ✆ ✞ ✁ ✁ ✆ ✞ ✟ ✁ ☎ ☎ ✆ ✞ ✢ ☞ ✡ ☎ ✠ ✁ ✆ ✡ ✝ ✂ ✆ ✛ ✆ ✁ ✟ ✠ ☎ ✠ ✁ ✞ ☎ ✠ ✁ ✖ ✗ ✘ ✟ ✍ ✟ ☎ ✁ ✌ ✆ ✟ ✟ ✄ ✜ ✁ ☛ ✎ ✝ ✆ ✆ ✏ ✡ ✱ ✄ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✄ ✡ ✂ ✄ ✆ ✝ ✄ ✕ ✛ ✆ ✝ ✡ ✂ ✄ ✍ ✠ ✒ ✄ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ✓ ✆ ✓ ✩ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✆ ✔ ✡ ✄ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✁ ✂ ✄ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✛ ✆ ✎ ✩ ✎ ✆ ☛ ✒ ✛ ✆ ✝ ✡ ✂ ✄ ✍ ✠ ✒ ✄ ✡ ✂ ✠ ✡ ✠ ✎ ✎ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✆ ✔ ✡ ✄ ✒ ✛ ✆ ✎ ✎ ✆ ☛ ✟ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ☎ ✣ ✟ ✄ ✡ ✾ ✁ ✞ ✄ ✓ ✆ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✡ ✂ ✠ ✡ ✆ ✝ ✙ ✜ ✙ ✓ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✜ ✣ ✱ ✄ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✡ ✂ ✠ ✡ ✎ ✄ ✠ ✞ ✒ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✱ ✄ ✡ ✂ ✄ ✓ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✠ ✎ ✩ ☛ ✠ ☞ ✒ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✁ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✮ ✝ ✒ ✡ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✔ ✒ ✙ ✓ ✜ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✎ ✙ ✓ ✵ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✓ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✔ ✒ ✙ ✓ ✜ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✒ ✣ ✁ ✂ ✄ ✝ ✄ ✠ ✝ ✄ ✮ ✚ ✄ ✘ ✂ ✠ ✒ ✄ ✒ ❀ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ☛ ✆ ✘ ✂ ✠ ✒ ✄ ✒ ✠ ✝ ✄ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✠ ✒ ✙ ✓ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✥ ✡ ✂ ✄ ✡ ✂ ✙ ✝ ✞ ✠ ✓ ✞ ✛ ✆ ✔ ✝ ✡ ✂ ✘ ✂ ✠ ✒ ✄ ✘ ✝ ✆ ✘ ✠ ✜ ✠ ✡ ✄ ✒ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✂ ✠ ✡ ✔ ✒ ✄ ✾ ✁ ✬ ✒ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✮ ✛ ✡ ✂ ✘ ✂ ✠ ✒ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✓ ✆ ✡ ✜ ✆ ✡ ✡ ✄ ✓ ✠ ✝ ✆ ✔ ✡ ✄ ✠ ✓ ✞ ✂ ✠ ✚ ✄ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✣ ✯ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ☛ ✄ ✍ ✆ ✓ ✒ ✡ ✝ ✔ ✍ ✡ ✠ ✓ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ ✑ ✡ ✂ ✠ ✡ ✎ ✄ ✠ ✞ ✒ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✁ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✒ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✙ ✓ ✄ ✠ ✍ ✂ ✖ ✗ ✒ ✙ ✕ ✔ ✎ ✡ ✠ ✓ ✄ ✆ ✔ ✒ ✎ ☞ ✣ ✵ ✁ ✭ ✶ ✧ ★ ✡ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✜ ✙ ✚ ✄ ✓ ✙ ✓ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✣ ✵ ✁ ✭ ✶ ✧ ✩ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✖ ✗ ✄ ✒ ✙ ✓ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✜ ✙ ✚ ✄ ✓ ✙ ✓ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✵ ✁ ✭ ✶ ✧ ✠ ✩ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ☛ ✙ ✡ ✂ ✾ ✁ ✠ ✓ ✞ ✂ ✠ ✚ ✄ ✓ ✆ ✡ ✜ ✆ ✡ ✡ ✄ ✓ ✠ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ☛ ✆ ✘ ✂ ✠ ✒ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✒ ✄ ✖ ✗ ✄ ✒ ✬ ✏ ✞ ✙ ✝ ✄ ✍ ✡ ✠ ✓ ✞ ✙ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✑ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✁ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✰ ✖ ✟ ✣ ✵ ✁ ✭ ✶ ✧ ✩ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✓ ✆ ✡ ✜ ✆ ✡ ✡ ✄ ✓ ✠ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ✂ ✝ ✄ ✄ ✘ ✂ ✠ ✒ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✆ ✝ ✞ ✄ ✝ ✡ ✂ ✠ ✡ ✍ ✆ ✓ ✛ ✆ ✝ ✕ ✒ ✡ ✆ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✰ ✖ ✟ ✣ ✵ ✁ ✭ ✶ ✧ ✩ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✡ ✂ ✄ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✓ ✆ ✡ ✜ ✆ ✡ ✡ ✄ ✓ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✜ ✙ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✛ ✆ ✔ ✝ ✘ ✂ ✠ ✒ ✄ ✒ ✠ ✓ ✞ ✂ ✠ ✚ ✄ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✒ ✄ ✖ ✗ ✄ ✒ ✞ ✆ ✓ ✆ ✡ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✒ ✄ ✝ ✚ ✙ ✍ ✄ ✥ ✡ ✂ ✄ ☞ ✍ ✠ ✓ ✢ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✄ ✞ ✙ ✓ ✠ ✓ ✠ ✝ ✢ ✙ ✡ ✝ ✠ ✝ ☞ ✆ ✝ ✞ ✄ ✝ ✣ ❆ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✠ ✒ ✙ ✓ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✥ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ☛ ✆ ✘ ✂ ✠ ✒ ✄ ✒ ✄ ✓ ✒ ✔ ✝ ✄ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✛ ✆ ✝ ✠ ✎ ✎ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✠ ✝ ✆ ✔ ✡ ✄ ✡ ✆ ✜ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✔ ✒ ✙ ✓ ✜ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✎ ☞ ✥ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✾ ✠ ✓ ✞ ☛ ✥ ✠ ✎ ✎ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✞ ✆ ✓ ✆ ✡ ✜ ✄ ✡ ✠ ✝ ✆ ✔ ✡ ✄ ✙ ✓ ✡ ✂ ✄ ✮ ✝ ✒ ✡ ✡ ☛ ✆ ✘ ✂ ✠ ✒ ✄ ✒ ✠ ✓ ✞ ✂ ✠ ✚ ✄ ✠ ✝ ✆ ✔ ✡ ✄ ✚ ✙ ✠ ✾ ✁ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✝ ✄ ✠ ✍ ✂ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✯ ✙ ✓ ✠ ✎ ✎ ☞ ✥ ✙ ✓ ✌ ✂ ✠ ✒ ✄ ✺ ✥ ✡ ✂ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ✂ ✠ ✚ ✄ ✠ ✝ ✆ ✔ ✡ ✄ ✚ ✙ ✠ ✡ ✂ ✄ ✙ ✝ ✝ ✄ ✒ ✘ ✄ ✍ ✡ ✙ ✚ ✄ ✢ ✠ ✍ ✵ ✔ ✘ ✎ ✙ ✓ ✵ ✜ ✄ ✡ ✡ ✆ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✖ ✎ ✎ ✆ ✛ ✡ ✂ ✄ ✒ ✄ ✍ ✠ ✓ ✢ ✄ ✘ ✝ ✆ ✚ ✄ ✓ ✢ ☞ ✙ ✓ ✞ ✔ ✍ ✡ ✙ ✆ ✓ ✥ ✠ ✒ ✙ ✓ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✣ ✶ ✆ ✡ ✄ ✡ ✂ ✠ ✡ ✙ ✓ ✁ ✂ ✄ ✆ ✝ ✄ ✕ ✺ ✣ ✽ ✥ ✡ ✂ ✄ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✜ ✙ ✚ ✄ ✒ ✠ ✎ ✙ ✓ ✄ ✠ ✝ ✆ ✝ ✞ ✄ ✝ ✆ ✛ ✖ ✗ ✄ ✒ ✣ ❆ ✒ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✥ ☛ ✄ ✍ ✠ ✓ ✘ ✝ ✆ ✚ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✛ ✆ ✝ ✠ ✓ ☞ ✛ ✠ ✙ ✝ ✠ ✍ ✡ ✙ ✚ ✠ ✡ ✙ ✆ ✓ ✒ ✄ ✧ ✔ ✄ ✓ ✍ ✄ ✣ 6. PRACTICAL IMPLICATIONS ✫ ✓ ✡ ✂ ✙ ✒ ✒ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ☛ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✡ ✂ ✄ ✠ ✘ ✘ ✎ ✙ ✍ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✩ ✎ ✙ ✓ ✄ ✒ ✡ ✆ ✞ ✙ ✚ ✄ ✝ ✒ ✄ ✠ ✓ ✞ ✍ ✂ ✠ ✓ ✜ ✙ ✓ ✜ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ✙ ✄ ✒ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✁ ✂ ✄ ✓ ✥ ☛ ✄ ✞ ✄ ✕ ✆ ✓ ✒ ✡ ✝ ✠ ✡ ✄ ✂ ✆ ☛ ✆ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✆ ✎ ✆ ✜ ☞ ✍ ✠ ✓ ✢ ✄ ✠ ✘ ✘ ✎ ✙ ✄ ✞ ✡ ✆ ✕ ✆ ✝ ✄ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✥ ✠ ✓ ✞ ✞ ✄ ✒ ✍ ✝ ✙ ✢ ✄ ✂ ✆ ☛ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✡ ✆ ✠ ✓ ✄ ☛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✆ ✔ ✡ ✞ ✙ ✒ ✝ ✔ ✘ ✡ ✙ ✓ ✜ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ 6.1 Robustness of the Guidelines ✁ ✂ ✄ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✠ ✝ ✄ ✚ ✄ ✝ ☞ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✙ ✓ ✡ ✆ ✞ ✠ ☞ ✬ ✒ ✝ ✠ ✘ ✙ ✞ ✎ ☞ ✜ ✝ ✆ ☛ ✙ ✓ ✜ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✣ ✴ ✆ ✔ ✡ ✄ ✝ ✠ ✓ ✞ ✎ ✙ ✓ ✵ ✛ ✠ ✙ ✎ ✔ ✝ ✄ ✒ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✞ ✄ ✘ ✎ ✆ ☞ ✕ ✄ ✓ ✡ ✆ ✛ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✓ ✄ ✡ ☛ ✆ ✝ ✵ ✄ ✧ ✔ ✙ ✘ ✕ ✄ ✓ ✡ ✥ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✛ ✝ ✄ ✧ ✔ ✄ ✓ ✡ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✆ ✡ ✂ ✄ ✔ ✓ ✞ ✄ ✝ ✎ ☞ ✙ ✓ ✜ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✣ ✫ ✗ ✌ ✒ ✆ ✛ ✡ ✄ ✓ ✮ ✓ ✄ ✩ ✡ ✔ ✓ ✄ ✡ ✂ ✄ ✙ ✝ ✘ ✆ ✎ ✙ ✍ ☞ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ✡ ✆ ✠ ✞ ✠ ✘ ✡ ✡ ✆ ✦ ✔ ✍ ✡ ✔ ✠ ✡ ✙ ✆ ✓ ✒ ✙ ✓ ✡ ✝ ✠ ✭ ✍ ✞ ✄ ✕ ✠ ✓ ✞ ✒ ✠ ✓ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✓ ✡ ✂ ✄ ✙ ✝ ✙ ✓ ✡ ✄ ✝ ✓ ✠ ✎ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✡ ✆ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ✫ ✓ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✥ ✖ ✗ ✄ ✒ ✘ ✄ ✩ ✝ ✙ ✆ ✞ ✙ ✍ ✠ ✎ ✎ ☞ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✙ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ☞ ✠ ✞ ✞ ✙ ✓ ✜ ✆ ✝ ✝ ✄ ✕ ✆ ✚ ✙ ✓ ✜ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✥ ✘ ✄ ✄ ✝ ✒ ✥ ✆ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ★ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✄ ✓ ✒ ✔ ✝ ✄ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✄ ✚ ✄ ✓ ✙ ✓ ✡ ✂ ✙ ✒ ✞ ☞ ✓ ✠ ✕ ✙ ✍ ✄ ✓ ✚ ✙ ✝ ✆ ✓ ✩ ✕ ✄ ✓ ✡ ✣ ✖ ✎ ✡ ✂ ✆ ✔ ✜ ✂ ✡ ✂ ✄ ✒ ✄ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✕ ✠ ☞ ✡ ✝ ✙ ✜ ✜ ✄ ✝ ✡ ✂ ✄ ✄ ✪ ✍ ✂ ✠ ✓ ✜ ✄ ✆ ✛ ✓ ✄ ☛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✥ ✠ ✓ ✞ ✕ ✠ ☞ ✔ ✎ ✡ ✙ ✕ ✠ ✡ ✄ ✎ ☞ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✓ ✄ ☛ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✒ ✥ ✡ ✂ ✄ ✘ ✠ ✝ ✡ ✙ ✠ ✎ ✆ ✝ ✞ ✄ ✝ ✙ ✓ ✜ ✠ ✕ ✆ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✄ ✠ ✍ ✂ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✄ ✓ ✒ ✔ ✝ ✄ ✒ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✒ ☞ ✒ ✡ ✄ ✕ ✝ ✄ ✠ ✍ ✂ ✄ ✒ ✠ ✒ ✡ ✠ ✢ ✎ ✄ ✒ ✡ ✠ ✡ ✄ ✣ ✖ ✎ ✡ ✄ ✝ ✓ ✠ ✡ ✄ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✄ ✒ ✿ ✸ ❁ ✡ ✂ ✠ ✡ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✢ ☞ ✘ ✄ ✝ ✛ ✆ ✝ ✕ ✙ ✓ ✜ ✠ ✍ ✂ ✄ ✍ ✵ ✆ ✓ ✡ ✂ ✄ ✡ ✆ ✘ ✆ ✎ ✆ ✜ ☞ ✠ ✓ ✞ ✘ ✆ ✎ ✩ ✙ ✍ ☞ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✒ ☛ ✆ ✔ ✎ ✞ ✂ ✠ ✚ ✄ ✡ ✆ ✝ ✄ ✍ ✆ ✓ ✮ ✝ ✕ ✡ ✂ ✄ ✒ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✥ ☛ ✙ ✡ ✂ ✓ ✆ ✜ ✔ ✠ ✝ ✠ ✓ ✡ ✄ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✓ ✄ ☛ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✒ ✠ ✛ ✄ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✡ ✆ ✄ ✠ ✝ ✎ ✙ ✄ ✝ ☛ ✆ ✝ ✵ ✆ ✓ ☎ ✟ ✌ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✘ ✄ ✝ ✡ ✙ ✄ ✒ ✿ ✸ ❀ ✽ ❂ ❀ ❃ ❂ ❁ ✥ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✛ ✆ ✍ ✔ ✒ ✆ ✓ ✡ ✂ ✄ ✠ ✘ ✘ ✎ ✙ ✍ ✠ ✡ ✙ ✆ ✓ ✆ ✛ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✡ ✆ ✘ ✝ ✄ ✛ ✄ ✝ ✒ ✆ ✕ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✆ ✚ ✄ ✝ ✠ ✎ ✡ ✄ ✝ ✓ ✠ ✡ ✙ ✚ ✄ ✒ ☛ ✙ ✡ ✂ ✠ ✒ ✂ ✆ ✝ ✡ ✄ ✝ ✖ ✗ ✘ ✠ ✡ ✂ ✣ ✗ ✙ ✓ ✍ ✄ ✆ ✔ ✝ ☛ ✆ ✝ ✵ ✠ ✙ ✕ ✒ ✡ ✆ ✘ ✝ ✆ ✚ ✄ ✡ ✝ ✟ ✆ ☎ ✆ ✁ ✝ ✄ ✒ ✔ ✎ ✡ ✒ ✠ ✢ ✆ ✔ ✡ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✥ ✙ ✡ ✙ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✡ ✡ ✆ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ✂ ✄ ✙ ✕ ✘ ✠ ✍ ✡ ✆ ✛ ✆ ✡ ✂ ✄ ✝ ☎ ✟ ✌ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✆ ✒ ✒ ✙ ✩ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✠ ✓ ✖ ✗ ✂ ✠ ✚ ✙ ✓ ✜ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✣ ✁ ✂ ✄ ✕ ✆ ✞ ✄ ✎ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✾ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✘ ✝ ✆ ✆ ✛ ✒ ✆ ✛ ✡ ✂ ✄ ✡ ✂ ✄ ✆ ✝ ✄ ✕ ✒ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ✺ ✥ ✠ ✎ ✎ ✆ ☛ ✄ ✠ ✍ ✂ ✖ ✗ ✡ ✆ ✂ ✠ ✚ ✄ ✆ ✓ ✄ ✆ ✝ ✕ ✆ ✝ ✄ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✣ ✗ ✘ ✄ ✠ ✵ ✩ ✄ ✝ ✒ ☛ ✙ ✡ ✂ ✙ ✓ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✖ ✗ ✞ ✆ ✓ ✆ ✡ ✓ ✄ ✍ ✄ ✒ ✒ ✠ ✝ ✙ ✎ ☞ ✍ ✂ ✆ ✆ ✒ ✄ ✡ ✂ ✄ ✒ ✠ ✕ ✄ ✝ ✆ ✔ ✡ ✄ ✣ ✁ ✂ ✄ ✔ ✎ ✡ ✙ ✕ ✠ ✡ ✄ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✞ ✄ ✍ ✙ ✒ ✙ ✆ ✓ ✕ ✠ ☞ ✠ ✎ ✒ ✆ ✞ ✄ ✘ ✄ ✓ ✞ ✆ ✓ ✖ ✗ ✘ ✠ ✡ ✂ ✎ ✄ ✓ ✜ ✡ ✂ ✏ ✙ ✓ ✍ ✎ ✔ ✞ ✙ ✓ ✜ ✘ ✠ ✡ ✂ ✒ ☛ ✙ ✡ ✂ ✖ ✗ ✘ ✝ ✄ ✘ ✄ ✓ ✞ ✙ ✓ ✜ ✑ ✥ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✄ ✪ ✙ ✡ ✞ ✙ ✒ ✍ ✝ ✙ ✕ ✙ ✓ ✠ ✡ ✆ ✝ ✒ ✥ ✠ ✓ ✞ ✍ ✆ ✒ ✡ ✙ ✓ ✛ ✆ ✝ ✕ ✠ ✡ ✙ ✆ ✓ ✛ ✝ ✆ ✕ ✡ ✂ ✄ ✙ ✓ ✡ ✝ ✠ ✞ ✆ ✩ ✕ ✠ ✙ ✓ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✘ ✝ ✆ ✡ ✆ ✍ ✆ ✎ ✣ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✒ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ✂ ✄ ✒ ✄ ✠ ✡ ✩ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✄ ✜ ☎ ✁ ✠ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✡ ✆ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕
neighboring A Ses. As such, these additional attributes only figuration first. We focus the discussion on a BGP system impact se lec tion of routes i khIn a preference class. For that obeys guideline A Similar arguments apply under xample, As path length may determine i hkh customer ot her guideline route is chosen but would not cause a BGP speaker to pick a provider route over a customer route For example, consider a customer u and a provider v that transi tion to a peer-to-peer relat ionship. Each As may change olicitly assumes that an As pair has a customer-provider or doese ration while remaining consistent with guideline 6.2 Complex As relationships s presented in Section 4, the hierarchical relationships ap- v remains in FRufp(u)UF"Ru. Similarly, guideline A oly at the level of As he discussion in not require u to change its import policies. AS u may peer-to-peer relationship for =I destinat ion prefixes. Since in fact modify its local-pref value for routes learned from v, the path selection process proceeds independently for each but differences in local-pref wit hin a preference class do not fix, this restrict ion is not actually necessary. In fact, ah affect system stability. AS u does not need to coordinate lowing an As pair to have their relat ionship depend on the with v in making these changes. In contrast, AS needs to destination prefix is important for expressing more complex change its import and export policies. AS v stops exporting ies. For example, two ASe have both routes le arned from its providers and peers. In addition, the to-peer and a backup relat ionship, where each AS provides import policy must apply a smaller local-pref to treat u as a ckup connectivity to the rest of the Internet in the event peer,rather than a customer. This removes an edge in the f a failure. This arrangement does not violate our guide provider-to-customer h. Since removing lines, since the relat ionship is still uniquely defined for each introduce a cycle, the resulting graph is still a DAG destination prefix. The ASes have a peer-to-peer relat ion- ship for any prefixes belonging to either AS, and a backup Next, we consider a change in the opposite direction, from a relationship for all other prefixes. The ASes would need to eer-to-peer to a customer-provider relationship, where u is se different ranges of local-pref values based on whe the the customer and v is the provider. We assume that the final the routes were learned from customers or from providers customer-provider configurat ion does not violate the hierar and ot her peers chy in the as graph; that is, the final customer-to-provide d provider-to graphs are DAGs. As in the pre Similarly, an AS may act as an intermediary between two vious example, As u does not need to change its import Ses that would like to establish a peer-to-peer relationship For example, consider two ASes u and. that would like to e a peer-to-peer arrangement. Suppose that u and. do learned from ot her providers and its peers. In addition, not have dedicated connections to each other but t hat the changes its import policies to apply a higher local prefere ach have a peer-to-peer relationship with AS U. Normally, to routes learned from u. Since the changes are isolated to n As would not advertise routes learned from one peer to AS U, the BGP system remains safe. Stability problems another peer. But, AS agree to export routes learned may arise if multiple ASes transition from peer-Lo-peer to from u to.(and routes learned from. to u). That is, routes customer-provider relat ionships, if the resulting AS graph P with fPPRXPhP-FhdB)a u would be exported to. and does not retain its hierarchical st ruct ure. A routing regi routes with fpPRxPhP-FhdBy a. would be exported to could be consulted as each provider changes its configura S u would not export these routes to any of its other peers tion, and can flag proposed changes that would violate th or providers. This arrange ment obeys our guidelines. AS v hierarchical struct ure cts as a provider for u for routes to and from. (and as a ovider for. for routes to and from u), and as a peer for all Ion Is nore com ther routes. Hence, guideline A ensures the stability of the relat ionship changes to a provider-customer relationship. This result ing BGP system. We believe that a similar approach situation is ext remely unlikely to hap ppen in prac an be used to analyze ot her potential re lat ionships between could be handled by performing two separate transition ASes from customer-provider to peer-to-peer, and from peer-to peer to provider-customer. But, for the sake of complete 6.3 Changing As Relationships ness, we show how the As pair can direct ly transition from customer-provider to provider-customer with its neighbors. For example, a cus tomer may grow large enough to renegotiate its relationship with a provider, and t he final configural does not violate our assumpt ions of the As pair may transition to a peer-to-peer relationshi a hierarchical relationship bet ween ASes. We also assum that at most one As pair changes its relat ionship at a time As part of evolving to a new relat ionship, the two ASes Applying our methodology, we can show that the provider ay need to change their import and export policies. Ide ally, these changes would U should y practice, each As configures its routers independent ly of ose that u changes its configurat ion first. Then, during tI the other. As a result, the BGP system may go through trar d, der and u sees transition period where one As has changed its configura- provider. This introduces t oble First. there is a ion and the other has not. Since these changes occur on cycle in the provider-to-customer graph. Second, both ASes ht important to care fully study the xport all routes to each other. The resulting BGP system influence of the transition period on system stability. Our may not be safe. For example, the two ASes are vulnerable met hodology can be used to identify potential convergence to the scenario in Figure 2 problems, and to determine which As should change its con
✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✙ ✓ ✜ ✖ ✗ ✄ ✒ ✣ ✖ ✒ ✒ ✔ ✍ ✂ ✥ ✡ ✂ ✄ ✒ ✄ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✠ ✎ ✠ ✡ ✡ ✝ ✙ ✢ ✔ ✡ ✄ ✒ ✆ ✓ ✎ ☞ ✙ ✕ ✘ ✠ ✍ ✡ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✆ ✛ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ☎ ✠ ✆ ✞ ✠ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✍ ✎ ✠ ✒ ✒ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✖ ✗ ✘ ✠ ✡ ✂ ✎ ✄ ✓ ✜ ✡ ✂ ✕ ✠ ☞ ✞ ✄ ✡ ✄ ✝ ✕ ✙ ✓ ✄ ✡ ✠ ✆ ✛ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✙ ✒ ✍ ✂ ✆ ✒ ✄ ✓ ✢ ✔ ✡ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✍ ✠ ✔ ✒ ✄ ✠ ☎ ✟ ✌ ✒ ✘ ✄ ✠ ✵ ✄ ✝ ✡ ✆ ✘ ✙ ✍ ✵ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✆ ✚ ✄ ✝ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✣ 6.2 Complex AS Relationships ✖ ✒ ✘ ✝ ✄ ✒ ✄ ✓ ✡ ✄ ✞ ✙ ✓ ✗ ✄ ✍ ✡ ✙ ✆ ✓ ☛ ✥ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✠ ✘ ✩ ✘ ✎ ☞ ✠ ✡ ✡ ✂ ✄ ✎ ✄ ✚ ✄ ✎ ✆ ✛ ✖ ✗ ✘ ✠ ✙ ✝ ✒ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ✡ ✂ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✙ ✕ ✩ ✘ ✎ ✙ ✍ ✙ ✡ ✎ ☞ ✠ ✒ ✒ ✔ ✕ ✄ ✒ ✡ ✂ ✠ ✡ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✂ ✠ ✒ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✆ ✝ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✛ ✆ ✝ ✄ ✂ ✂ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✘ ✠ ✡ ✂ ✒ ✄ ✎ ✄ ✍ ✡ ✙ ✆ ✓ ✘ ✝ ✆ ✍ ✄ ✒ ✒ ✘ ✝ ✆ ✍ ✄ ✄ ✞ ✒ ✙ ✓ ✞ ✄ ✘ ✄ ✓ ✞ ✄ ✓ ✡ ✎ ☞ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✘ ✝ ✄ ✮ ✪ ✥ ✡ ✂ ✙ ✒ ✝ ✄ ✒ ✡ ✝ ✙ ✍ ✡ ✙ ✆ ✓ ✙ ✒ ✓ ✆ ✡ ✠ ✍ ✡ ✔ ✠ ✎ ✎ ☞ ✓ ✄ ✍ ✄ ✒ ✒ ✠ ✝ ☞ ✣ ✫ ✓ ✛ ✠ ✍ ✡ ✥ ✠ ✎ ✩ ✎ ✆ ☛ ✙ ✓ ✜ ✠ ✓ ✖ ✗ ✘ ✠ ✙ ✝ ✡ ✆ ✂ ✠ ✚ ✄ ✡ ✂ ✄ ✙ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✞ ✄ ✘ ✄ ✓ ✞ ✆ ✓ ✡ ✂ ✄ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✙ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✡ ✛ ✆ ✝ ✄ ✪ ✘ ✝ ✄ ✒ ✒ ✙ ✓ ✜ ✕ ✆ ✝ ✄ ✍ ✆ ✕ ✘ ✎ ✄ ✪ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✕ ✠ ☞ ✂ ✠ ✚ ✄ ✢ ✆ ✡ ✂ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✓ ✞ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✥ ☛ ✂ ✄ ✝ ✄ ✄ ✠ ✍ ✂ ✖ ✗ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✒ ✢ ✠ ✍ ✵ ✔ ✘ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✚ ✙ ✡ ☞ ✡ ✆ ✡ ✂ ✄ ✝ ✄ ✒ ✡ ✆ ✛ ✡ ✂ ✄ ✫ ✓ ✡ ✄ ✝ ✓ ✄ ✡ ✙ ✓ ✡ ✂ ✄ ✄ ✚ ✄ ✓ ✡ ✆ ✛ ✠ ✛ ✠ ✙ ✎ ✔ ✝ ✄ ✣ ✁ ✂ ✙ ✒ ✠ ✝ ✝ ✠ ✓ ✜ ✄ ✕ ✄ ✓ ✡ ✞ ✆ ✄ ✒ ✞ ✝ ☎ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✩ ✎ ✙ ✓ ✄ ✒ ✥ ✒ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✙ ✒ ✒ ✡ ✙ ✎ ✎ ✔ ✓ ✙ ✧ ✔ ✄ ✎ ☞ ✞ ✄ ✮ ✓ ✄ ✞ ✛ ✆ ✝ ✄ ✠ ✍ ✂ ✞ ✄ ✒ ✡ ✙ ✓ ✠ ✡ ✙ ✆ ✓ ✘ ✝ ✄ ✮ ✪ ✣ ✁ ✂ ✄ ✖ ✗ ✄ ✒ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✩ ✒ ✂ ✙ ✘ ✛ ✆ ✝ ✠ ✓ ☞ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✢ ✄ ✎ ✆ ✓ ✜ ✙ ✓ ✜ ✡ ✆ ✄ ✙ ✡ ✂ ✄ ✝ ✖ ✗ ✥ ✠ ✓ ✞ ✠ ✢ ✠ ✍ ✵ ✔ ✘ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✛ ✆ ✝ ✠ ✎ ✎ ✆ ✡ ✂ ✄ ✝ ✘ ✝ ✄ ✮ ✪ ✄ ✒ ✣ ✁ ✂ ✄ ✖ ✗ ✄ ✒ ☛ ✆ ✔ ✎ ✞ ✓ ✄ ✄ ✞ ✡ ✆ ✔ ✒ ✄ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✡ ✝ ✠ ✓ ✜ ✄ ✒ ✆ ✛ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✚ ✠ ✎ ✔ ✄ ✒ ✢ ✠ ✒ ✄ ✞ ✆ ✓ ☛ ✂ ✄ ✡ ✂ ✄ ✝ ✡ ✂ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ☛ ✄ ✝ ✄ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✒ ✆ ✝ ✛ ✝ ✆ ✕ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✓ ✞ ✆ ✡ ✂ ✄ ✝ ✘ ✄ ✄ ✝ ✒ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✎ ☞ ✥ ✠ ✓ ✖ ✗ ✕ ✠ ☞ ✠ ✍ ✡ ✠ ✒ ✠ ✓ ✙ ✓ ✡ ✄ ✝ ✕ ✄ ✞ ✙ ✠ ✝ ☞ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✡ ✂ ✠ ✡ ☛ ✆ ✔ ✎ ✞ ✎ ✙ ✵ ✄ ✡ ✆ ✄ ✒ ✡ ✠ ✢ ✎ ✙ ✒ ✂ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✹ ✠ ✓ ✞ ☛ ✡ ✂ ✠ ✡ ☛ ✆ ✔ ✎ ✞ ✎ ✙ ✵ ✄ ✡ ✆ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✠ ✝ ✝ ✠ ✓ ✜ ✄ ✕ ✄ ✓ ✡ ✣ ✗ ✔ ✘ ✘ ✆ ✒ ✄ ✡ ✂ ✠ ✡ ✹ ✠ ✓ ✞ ☛ ✞ ✆ ✓ ✆ ✡ ✂ ✠ ✚ ✄ ✞ ✄ ✞ ✙ ✍ ✠ ✡ ✄ ✞ ✍ ✆ ✓ ✓ ✄ ✍ ✡ ✙ ✆ ✓ ✒ ✡ ✆ ✄ ✠ ✍ ✂ ✆ ✡ ✂ ✄ ✝ ✥ ✢ ✔ ✡ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ☞ ✄ ✠ ✍ ✂ ✂ ✠ ✚ ✄ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✖ ✗ ✺ ✣ ✶ ✆ ✝ ✕ ✠ ✎ ✎ ☞ ✥ ✠ ✓ ✖ ✗ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✆ ✓ ✄ ✘ ✄ ✄ ✝ ✡ ✆ ✠ ✓ ✆ ✡ ✂ ✄ ✝ ✘ ✄ ✄ ✝ ✣ ☎ ✔ ✡ ✥ ✖ ✗ ✺ ✍ ✠ ✓ ✠ ✜ ✝ ✄ ✄ ✡ ✆ ✄ ✪ ✘ ✆ ✝ ✡ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✹ ✡ ✆ ☛ ✏ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ☛ ✡ ✆ ✹ ✑ ✣ ✁ ✂ ✠ ✡ ✙ ✒ ✥ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ☛ ✙ ✡ ✂ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ✄ ✹ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✄ ✪ ✘ ✆ ✝ ✡ ✄ ✞ ✡ ✆ ☛ ✥ ✠ ✓ ✞ ✝ ✆ ✔ ✡ ✄ ✒ ☛ ✙ ✡ ✂ ✒ ✡ ✎ ✘ ✕ ✏ ✎ ✓ ✠ ✘ ✏ ✠ ✕ ✖ ✑ ✄ ☛ ☛ ✆ ✔ ✎ ✞ ✢ ✄ ✄ ✪ ✘ ✆ ✝ ✡ ✄ ✞ ✡ ✆ ✹ ✣ ✖ ✗ ✺ ☛ ✆ ✔ ✎ ✞ ✓ ✆ ✡ ✄ ✪ ✘ ✆ ✝ ✡ ✡ ✂ ✄ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✓ ☞ ✆ ✛ ✙ ✡ ✒ ✆ ✡ ✂ ✄ ✝ ✘ ✄ ✄ ✝ ✒ ✆ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✣ ✁ ✂ ✙ ✒ ✠ ✝ ✝ ✠ ✓ ✜ ✄ ✕ ✄ ✓ ✡ ✆ ✢ ✄ ☞ ✒ ✆ ✔ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✣ ✖ ✗ ✺ ✠ ✍ ✡ ✒ ✠ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✛ ✆ ✝ ✹ ✛ ✆ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✓ ✞ ✛ ✝ ✆ ✕ ☛ ✏ ✠ ✓ ✞ ✠ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✛ ✆ ✝ ☛ ✛ ✆ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✠ ✓ ✞ ✛ ✝ ✆ ✕ ✹ ✑ ✥ ✠ ✓ ✞ ✠ ✒ ✠ ✘ ✄ ✄ ✝ ✛ ✆ ✝ ✠ ✎ ✎ ✆ ✡ ✂ ✄ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✄ ✓ ✒ ✔ ✝ ✄ ✒ ✡ ✂ ✄ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✆ ✛ ✡ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✣ ✱ ✄ ✢ ✄ ✎ ✙ ✄ ✚ ✄ ✡ ✂ ✠ ✡ ✠ ✒ ✙ ✕ ✙ ✎ ✠ ✝ ✠ ✘ ✘ ✝ ✆ ✠ ✍ ✂ ✍ ✠ ✓ ✢ ✄ ✔ ✒ ✄ ✞ ✡ ✆ ✠ ✓ ✠ ✎ ☞ ✲ ✄ ✆ ✡ ✂ ✄ ✝ ✘ ✆ ✡ ✄ ✓ ✡ ✙ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ 6.3 Changing AS Relationships ★ ✚ ✄ ✝ ✡ ✙ ✕ ✄ ✥ ✠ ✓ ✖ ✗ ✕ ✠ ☞ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✓ ✠ ✡ ✔ ✝ ✄ ✆ ✛ ✙ ✡ ✒ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ☛ ✙ ✡ ✂ ✙ ✡ ✒ ✓ ✄ ✙ ✜ ✂ ✢ ✆ ✝ ✒ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✕ ✠ ☞ ✜ ✝ ✆ ☛ ✎ ✠ ✝ ✜ ✄ ✄ ✓ ✆ ✔ ✜ ✂ ✡ ✆ ✝ ✄ ✓ ✄ ✜ ✆ ✡ ✙ ✠ ✡ ✄ ✙ ✡ ✒ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ☛ ✙ ✡ ✂ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✥ ✠ ✓ ✞ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✙ ✝ ✕ ✠ ☞ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✡ ✆ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✣ ✖ ✒ ✘ ✠ ✝ ✡ ✆ ✛ ✄ ✚ ✆ ✎ ✚ ✙ ✓ ✜ ✡ ✆ ✠ ✓ ✄ ☛ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✥ ✡ ✂ ✄ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✕ ✠ ☞ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✡ ✂ ✄ ✙ ✝ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✞ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✫ ✞ ✄ ✩ ✠ ✎ ✎ ☞ ✥ ✡ ✂ ✄ ✒ ✄ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ☛ ✆ ✔ ✎ ✞ ✆ ✍ ✍ ✔ ✝ ✒ ✙ ✕ ✔ ✎ ✡ ✠ ✓ ✄ ✆ ✔ ✒ ✎ ☞ ✣ ✤ ✆ ☛ ✄ ✚ ✄ ✝ ✥ ✙ ✓ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✥ ✄ ✠ ✍ ✂ ✖ ✗ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✄ ✒ ✙ ✡ ✒ ✝ ✆ ✔ ✡ ✄ ✝ ✒ ✙ ✓ ✞ ✄ ✘ ✄ ✓ ✞ ✄ ✓ ✡ ✎ ☞ ✆ ✛ ✡ ✂ ✄ ✆ ✡ ✂ ✄ ✝ ✣ ✖ ✒ ✠ ✝ ✄ ✒ ✔ ✎ ✡ ✥ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✕ ✠ ☞ ✜ ✆ ✡ ✂ ✝ ✆ ✔ ✜ ✂ ✠ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✘ ✄ ✝ ✙ ✆ ✞ ☛ ✂ ✄ ✝ ✄ ✆ ✓ ✄ ✖ ✗ ✂ ✠ ✒ ✍ ✂ ✠ ✓ ✜ ✄ ✞ ✙ ✡ ✒ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✩ ✡ ✙ ✆ ✓ ✠ ✓ ✞ ✡ ✂ ✄ ✆ ✡ ✂ ✄ ✝ ✂ ✠ ✒ ✓ ✆ ✡ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✒ ✄ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✆ ✍ ✍ ✔ ✝ ✆ ✓ ✠ ✂ ✔ ✕ ✠ ✓ ✡ ✙ ✕ ✄ ✒ ✍ ✠ ✎ ✄ ✥ ✙ ✡ ✙ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✡ ✡ ✆ ✍ ✠ ✝ ✄ ✛ ✔ ✎ ✎ ☞ ✒ ✡ ✔ ✞ ☞ ✡ ✂ ✄ ✙ ✓ ✦ ✔ ✄ ✓ ✍ ✄ ✆ ✛ ✡ ✂ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✘ ✄ ✝ ✙ ✆ ✞ ✆ ✓ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ★ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✆ ✎ ✆ ✜ ☞ ✍ ✠ ✓ ✢ ✄ ✔ ✒ ✄ ✞ ✡ ✆ ✙ ✞ ✄ ✓ ✡ ✙ ✛ ☞ ✘ ✆ ✡ ✄ ✓ ✡ ✙ ✠ ✎ ✍ ✆ ✓ ✚ ✄ ✝ ✜ ✄ ✓ ✍ ✄ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✥ ✠ ✓ ✞ ✡ ✆ ✞ ✄ ✡ ✄ ✝ ✕ ✙ ✓ ✄ ☛ ✂ ✙ ✍ ✂ ✖ ✗ ✒ ✂ ✆ ✔ ✎ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✍ ✆ ✓ ✩ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✮ ✝ ✒ ✡ ✣ ✱ ✄ ✛ ✆ ✍ ✔ ✒ ✡ ✂ ✄ ✞ ✙ ✒ ✍ ✔ ✒ ✒ ✙ ✆ ✓ ✆ ✓ ✠ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✡ ✂ ✠ ✡ ✆ ✢ ✄ ☞ ✒ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✠ ✝ ✜ ✔ ✕ ✄ ✓ ✡ ✒ ✠ ✘ ✘ ✎ ☞ ✔ ✓ ✞ ✄ ✝ ✡ ✂ ✄ ✆ ✡ ✂ ✄ ✝ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✒ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✹ ✠ ✓ ✞ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✺ ✡ ✂ ✠ ✡ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✡ ✆ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✣ ✻ ✠ ✍ ✂ ✖ ✗ ✕ ✠ ☞ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ☛ ✂ ✙ ✎ ✄ ✝ ✄ ✕ ✠ ✙ ✓ ✙ ✓ ✜ ✍ ✆ ✓ ✒ ✙ ✒ ✡ ✄ ✓ ✡ ☛ ✙ ✡ ✂ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✣ ✖ ✗ ✹ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✒ ✙ ✓ ✍ ✄ ✺ ✝ ✄ ✕ ✠ ✙ ✓ ✒ ✙ ✓ ✏ ✎ ✗ ✺ ✡ ✜ ✑ ✎ ✏ ✹ ✑ ✎ ✏ ✑ ✑ ✎ ✏ ✹ ✑ ✣ ✗ ✙ ✕ ✙ ✎ ✠ ✝ ✎ ☞ ✥ ✜ ✔ ✙ ✞ ✄ ✎ ✙ ✓ ✄ ✖ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✝ ✄ ✧ ✔ ✙ ✝ ✄ ✹ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✖ ✗ ✹ ✕ ✠ ☞ ✙ ✓ ✛ ✠ ✍ ✡ ✕ ✆ ✞ ✙ ✛ ☞ ✙ ✡ ✒ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✚ ✠ ✎ ✔ ✄ ✛ ✆ ✝ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✺ ✥ ✢ ✔ ✡ ✞ ✙ ✳ ✄ ✝ ✄ ✓ ✍ ✄ ✒ ✙ ✓ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ☛ ✙ ✡ ✂ ✙ ✓ ✠ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✍ ✎ ✠ ✒ ✒ ✞ ✆ ✓ ✆ ✡ ✠ ✳ ✄ ✍ ✡ ✒ ☞ ✒ ✡ ✄ ✕ ✒ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✣ ✖ ✗ ✹ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✄ ☛ ✙ ✡ ✂ ✺ ✙ ✓ ✕ ✠ ✵ ✙ ✓ ✜ ✡ ✂ ✄ ✒ ✄ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✣ ✫ ✓ ✍ ✆ ✓ ✡ ✝ ✠ ✒ ✡ ✥ ✖ ✗ ✺ ✓ ✄ ✄ ✞ ✒ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✞ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✖ ✗ ✺ ✒ ✡ ✆ ✘ ✒ ✄ ✪ ✘ ✆ ✝ ✡ ✙ ✓ ✜ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✙ ✡ ✒ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✓ ✞ ✘ ✄ ✄ ✝ ✒ ✣ ✫ ✓ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✥ ✡ ✂ ✄ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ☞ ✕ ✔ ✒ ✡ ✠ ✘ ✘ ✎ ☞ ✠ ✒ ✕ ✠ ✎ ✎ ✄ ✝ ✎ ✆ ✍ ✠ ✎ ✩ ✘ ✝ ✄ ✛ ✡ ✆ ✡ ✝ ✄ ✠ ✡ ✹ ✠ ✒ ✠ ✘ ✄ ✄ ✝ ✥ ✝ ✠ ✡ ✂ ✄ ✝ ✡ ✂ ✠ ✓ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✣ ✁ ✂ ✙ ✒ ✝ ✄ ✕ ✆ ✚ ✄ ✒ ✠ ✓ ✄ ✞ ✜ ✄ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✜ ✝ ✠ ✘ ✂ ✣ ✗ ✙ ✓ ✍ ✄ ✝ ✄ ✕ ✆ ✚ ✙ ✓ ✜ ✠ ✓ ✄ ✞ ✜ ✄ ✍ ✠ ✓ ✓ ✆ ✡ ✙ ✓ ✡ ✝ ✆ ✞ ✔ ✍ ✄ ✠ ✍ ☞ ✍ ✎ ✄ ✥ ✡ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ✜ ✝ ✠ ✘ ✂ ✙ ✒ ✒ ✡ ✙ ✎ ✎ ✠ ✰ ✖ ✟ ✣ ✶ ✄ ✪ ✡ ✥ ☛ ✄ ✍ ✆ ✓ ✒ ✙ ✞ ✄ ✝ ✠ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✓ ✡ ✂ ✄ ✆ ✘ ✘ ✆ ✒ ✙ ✡ ✄ ✞ ✙ ✝ ✄ ✍ ✡ ✙ ✆ ✓ ✥ ✛ ✝ ✆ ✕ ✠ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✡ ✆ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✥ ☛ ✂ ✄ ✝ ✄ ✹ ✙ ✒ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✠ ✓ ✞ ✺ ✙ ✒ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✱ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✮ ✓ ✠ ✎ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✩ ✍ ✂ ☞ ✙ ✓ ✡ ✂ ✄ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ❀ ✡ ✂ ✠ ✡ ✙ ✒ ✥ ✡ ✂ ✄ ✮ ✓ ✠ ✎ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✜ ✝ ✠ ✘ ✂ ✒ ✠ ✝ ✄ ✰ ✖ ✟ ✒ ✣ ✖ ✒ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✄ ✩ ✚ ✙ ✆ ✔ ✒ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✖ ✗ ✹ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✠ ✓ ✞ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✣ ✤ ✄ ✓ ✍ ✄ ✥ ✹ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✓ ✄ ✄ ✞ ✡ ✆ ✍ ✆ ✆ ✝ ✞ ✙ ✓ ✠ ✡ ✄ ☛ ✙ ✡ ✂ ✺ ✣ ✖ ✗ ✺ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✄ ✪ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✠ ✞ ✚ ✄ ✝ ✡ ✙ ✒ ✄ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✆ ✡ ✂ ✄ ✝ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✒ ✠ ✓ ✞ ✙ ✡ ✒ ✘ ✄ ✄ ✝ ✒ ✣ ✫ ✓ ✠ ✞ ✞ ✙ ✡ ✙ ✆ ✓ ✥ ✺ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✙ ✕ ✘ ✆ ✝ ✡ ✘ ✆ ✎ ✙ ✍ ✙ ✄ ✒ ✡ ✆ ✠ ✘ ✘ ✎ ☞ ✠ ✂ ✙ ✜ ✂ ✄ ✝ ✎ ✆ ✍ ✠ ✎ ✘ ✝ ✄ ✛ ✄ ✝ ✄ ✓ ✍ ✄ ✡ ✆ ✝ ✆ ✔ ✡ ✄ ✒ ✎ ✄ ✠ ✝ ✓ ✄ ✞ ✛ ✝ ✆ ✕ ✹ ✣ ✗ ✙ ✓ ✍ ✄ ✡ ✂ ✄ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✠ ✝ ✄ ✙ ✒ ✆ ✎ ✠ ✡ ✄ ✞ ✡ ✆ ✖ ✗ ✺ ✥ ✡ ✂ ✄ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✝ ✄ ✕ ✠ ✙ ✓ ✒ ✒ ✠ ✛ ✄ ✣ ✗ ✡ ✠ ✢ ✙ ✎ ✙ ✡ ☞ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✕ ✠ ☞ ✠ ✝ ✙ ✒ ✄ ✙ ✛ ✕ ✔ ✎ ✡ ✙ ✘ ✎ ✄ ✖ ✗ ✄ ✒ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✛ ✝ ✆ ✕ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✡ ✆ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✒ ✥ ✙ ✛ ✡ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ✖ ✗ ✜ ✝ ✠ ✘ ✂ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✝ ✄ ✡ ✠ ✙ ✓ ✙ ✡ ✒ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✣ ✖ ✝ ✆ ✔ ✡ ✙ ✓ ✜ ✝ ✄ ✜ ✙ ✒ ✡ ✝ ☞ ✍ ✆ ✔ ✎ ✞ ✢ ✄ ✍ ✆ ✓ ✒ ✔ ✎ ✡ ✄ ✞ ✠ ✒ ✄ ✠ ✍ ✂ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✩ ✡ ✙ ✆ ✓ ✥ ✠ ✓ ✞ ✍ ✠ ✓ ✦ ✠ ✜ ✘ ✝ ✆ ✘ ✆ ✒ ✄ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✂ ✠ ✡ ☛ ✆ ✔ ✎ ✞ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✡ ✂ ✄ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✒ ✡ ✝ ✔ ✍ ✡ ✔ ✝ ✄ ✣ ✁ ✂ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✙ ✒ ✕ ✆ ✝ ✄ ✍ ✆ ✕ ✘ ✎ ✙ ✍ ✠ ✡ ✄ ✞ ☛ ✂ ✄ ✓ ✠ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✡ ✆ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✣ ✁ ✂ ✙ ✒ ✒ ✙ ✡ ✔ ✠ ✡ ✙ ✆ ✓ ✙ ✒ ✄ ✪ ✡ ✝ ✄ ✕ ✄ ✎ ☞ ✔ ✓ ✎ ✙ ✵ ✄ ✎ ☞ ✡ ✆ ✂ ✠ ✘ ✘ ✄ ✓ ✙ ✓ ✘ ✝ ✠ ✍ ✡ ✙ ✍ ✄ ✥ ✠ ✓ ✞ ✍ ✆ ✔ ✎ ✞ ✢ ✄ ✂ ✠ ✓ ✞ ✎ ✄ ✞ ✢ ☞ ✘ ✄ ✝ ✛ ✆ ✝ ✕ ✙ ✓ ✜ ✡ ☛ ✆ ✒ ✄ ✘ ✠ ✝ ✠ ✡ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✒ ✛ ✝ ✆ ✕ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✡ ✆ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✥ ✠ ✓ ✞ ✛ ✝ ✆ ✕ ✘ ✄ ✄ ✝ ✩ ✡ ✆ ✩ ✘ ✄ ✄ ✝ ✡ ✆ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✣ ☎ ✔ ✡ ✥ ✛ ✆ ✝ ✡ ✂ ✄ ✒ ✠ ✵ ✄ ✆ ✛ ✍ ✆ ✕ ✘ ✎ ✄ ✡ ✄ ✩ ✓ ✄ ✒ ✒ ✥ ☛ ✄ ✒ ✂ ✆ ☛ ✂ ✆ ☛ ✡ ✂ ✄ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✠ ✓ ✞ ✙ ✝ ✄ ✍ ✡ ✎ ☞ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✛ ✝ ✆ ✕ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✩ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✡ ✆ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✣ ✫ ✓ ✙ ✡ ✙ ✠ ✎ ✎ ☞ ✥ ✹ ✙ ✒ ✡ ✂ ✄ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✠ ✓ ✞ ✺ ✙ ✒ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✖ ✜ ✠ ✙ ✓ ✥ ☛ ✄ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✮ ✓ ✠ ✎ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✞ ✆ ✄ ✒ ✓ ✆ ✡ ✚ ✙ ✆ ✎ ✠ ✡ ✄ ✆ ✔ ✝ ✠ ✒ ✒ ✔ ✕ ✘ ✡ ✙ ✆ ✓ ✒ ✆ ✛ ✠ ✂ ✙ ✄ ✝ ✠ ✝ ✍ ✂ ✙ ✍ ✠ ✎ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✢ ✄ ✡ ☛ ✄ ✄ ✓ ✖ ✗ ✄ ✒ ✣ ✱ ✄ ✠ ✎ ✒ ✆ ✠ ✒ ✒ ✔ ✕ ✄ ✡ ✂ ✠ ✡ ✠ ✡ ✕ ✆ ✒ ✡ ✆ ✓ ✄ ✖ ✗ ✘ ✠ ✙ ✝ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✝ ✄ ✎ ✠ ✡ ✙ ✆ ✓ ✒ ✂ ✙ ✘ ✠ ✡ ✠ ✡ ✙ ✕ ✄ ✣ ✖ ✘ ✘ ✎ ☞ ✙ ✓ ✜ ✆ ✔ ✝ ✕ ✄ ✡ ✂ ✆ ✞ ✆ ✎ ✆ ✜ ☞ ✥ ☛ ✄ ✍ ✠ ✓ ✒ ✂ ✆ ☛ ✡ ✂ ✠ ✡ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✺ ✒ ✂ ✆ ✔ ✎ ✞ ✍ ✂ ✠ ✓ ✜ ✄ ✙ ✡ ✒ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✮ ✝ ✒ ✡ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✒ ✔ ✘ ✩ ✘ ✆ ✒ ✄ ✡ ✂ ✠ ✡ ✹ ✍ ✂ ✠ ✓ ✜ ✄ ✒ ✙ ✡ ✒ ✍ ✆ ✓ ✮ ✜ ✔ ✝ ✠ ✡ ✙ ✆ ✓ ✮ ✝ ✒ ✡ ✣ ✁ ✂ ✄ ✓ ✥ ✞ ✔ ✝ ✙ ✓ ✜ ✡ ✂ ✄ ✡ ✝ ✠ ✓ ✒ ✙ ✡ ✙ ✆ ✓ ✘ ✄ ✝ ✙ ✆ ✞ ✥ ✹ ✒ ✄ ✄ ✒ ✺ ✠ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✠ ✓ ✞ ✺ ✒ ✄ ✄ ✒ ✹ ✠ ✒ ✠ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✣ ✁ ✂ ✙ ✒ ✙ ✓ ✡ ✝ ✆ ✞ ✔ ✍ ✄ ✒ ✡ ☛ ✆ ✘ ✝ ✆ ✢ ✎ ✄ ✕ ✒ ✣ ✯ ✙ ✝ ✒ ✡ ✥ ✡ ✂ ✄ ✝ ✄ ✙ ✒ ✠ ✍ ☞ ✍ ✎ ✄ ✙ ✓ ✡ ✂ ✄ ✘ ✝ ✆ ✚ ✙ ✞ ✄ ✝ ✩ ✡ ✆ ✩ ✍ ✔ ✒ ✡ ✆ ✕ ✄ ✝ ✜ ✝ ✠ ✘ ✂ ✣ ✗ ✄ ✍ ✆ ✓ ✞ ✥ ✢ ✆ ✡ ✂ ✖ ✗ ✄ ✒ ✄ ✪ ✘ ✆ ✝ ✡ ✠ ✎ ✎ ✝ ✆ ✔ ✡ ✄ ✒ ✡ ✆ ✄ ✠ ✍ ✂ ✆ ✡ ✂ ✄ ✝ ✣ ✁ ✂ ✄ ✝ ✄ ✒ ✔ ✎ ✡ ✙ ✓ ✜ ☎ ✟ ✌ ✒ ☞ ✒ ✡ ✄ ✕ ✕ ✠ ☞ ✓ ✆ ✡ ✢ ✄ ✒ ✠ ✛ ✄ ✣ ✯ ✆ ✝ ✄ ✪ ✠ ✕ ✘ ✎ ✄ ✥ ✡ ✂ ✄ ✡ ☛ ✆ ✖ ✗ ✄ ✒ ✠ ✝ ✄ ✚ ✔ ✎ ✓ ✄ ✝ ✠ ✢ ✎ ✄ ✡ ✆ ✡ ✂ ✄ ✒ ✍ ✄ ✓ ✠ ✝ ✙ ✆ ✙ ✓ ✯ ✙ ✜ ✔ ✝ ✄ ❃ ✣
