Ambulance always returns home with each service; standard M/G/1 applies a But suppose we have an emergency repair vehicle that travels directly from one customer to the next?

Single Tree center problem G is a tree. e i=1. 2..m are the end vertices

There Are Three Things Important When Buying a House: Location Location Location

Lecture Outline A fundamental result for queuing networks State transition diagrams for Markovian queuing systems and networks: example Analysis of systems with dynamic demand and service rates Qualitative behavior of dynamic systems

Quiz #1: October 29 Open book, 85 minutes (start 10: 30) Chapter 4 coverage: Sections 4.1through 4.7 (inclusive); Section 4.9 (skim through 4.9.4) Review Problem Set 3 Review some old quizzes

Open book, 85 minutes(start 10: 30) Chapter 4 coverage: Sections 4.1through 4.7 (inclusive); Section 4.(skim through .9.4)[Up to lecture of 10/22] Review Problem Set 3 Review some old quizzes Prof. Barnett: Quiz review today

Lecture Outline Introduction to queuing systems Conceptual representation of queuing systems Codes for queuing models Terminology and notation Little's Law and basic relationships Birth-and-death processes The M/M/1 queuing system State transition diagrams Steady-state probabilities

two -Server- Hypercube” Queueing Model Distinguishable servers Different workloads(due to geography) Can appear with or without queueing With-- usually FCFS Without--usually means a backup contract service is in place

Outline Background and Definitions Shortest path Minimum spanning tree Introduction to Travelling Salesman Problem and Chinese Postman Problem

Consider a stick of length 1. Let XI and X2 be independent random variables denoting two points n the stick at which we break the stick into three pieces. We assume that X1 and X2 are uniformly distributed over the interval