Sec.1.2 Messages and Switching 15 E(t:)=1/入 Arrival Delivery E(X)=X Figure 1.5 Link utilization.The expected transmission time of a message is X.The expected interarrival period is 1/A.Thus,the link is used at most AX of the time. idle.It is intuitively plausible,since 1/A is the expected interarrival time and X is the expected busy time between arrivals,that the ratio of X to 1/A(i.e.,AX)is the fraction of time in which the portion of the link allocated to s is busy.This argument is made precise in Chapter 3.Our conclusion then is that if X1,session s's portion of the link is idle most of the time (i.e.,inefficiently utilized). To complete our argument about the inefficiency of circuit switching for data net- works,we must relate X to the allowable expected delay I'from message arrival at the source to delivery at the destination.Since X is the expected time until the last bit of the message has been sent on the first link,we must have X+P T,where P is the propagation delay through the network.Thus AX AT.If AT<1 (i.e.,the allowable delay is small relative to the message interarrival rate),the utilization AX for the session is correspondingly small.In summary,the bit rate rs allocated to a session must be large enough to allow message transmission within the required delay,and when AT<<1, this implies inefficient utilization of the link.Sessions for which AT<I are usually referred to as bursty sessions. For many of the interactive terminal sessions carried by data networks,AT is on the order of 0.01 or less.Thus,with circuit switching,that fraction of a link allocated to such sessions is utilized at most 1%of the time.The conclusion we draw from this is that if link costs are a dominant part of the cost of a network and if bursty sessions require a dominant fraction of link capacity using circuit switching,then circuit switching is an unattractive choice for data networks.Up to the present,both the assumptions above have been valid,and for this reason,data networks have not used circuit switching. The argument above has ignored propagation delays,switching delays in the nodes,and queueing delays.(Queueing delay arises when a message from session s arrives while another message from s is in transmission.)Since these delays must be added to the link transmission time X in meeting the delay requirement T,X must often be substantially smaller than T,making circuit switching even more inefficient.While propagation and switching delays are often negligible,queueing delay is not,as shown in Chapter 3, particularly when AT is close to or exceeds 1. In the future,it appears that link costs will become less important in the overall cost of a network.Also,with optical fiber,the marginal cost of link capacity is quite small, so that the wasted capacity of circuit switching will become less important.Finally,it appears that bursty interactive terminal traffic will grow considerably more slowly thanSec. 1.2 Messages and Switching Arrival E(t;) = l/A 15 1-+----t,---++---t2 --.-/----t3 ----I--! Delivery E(X;) =X Figure 1.5 Link utilization. The expected transmission time of a message is X. The expected interarrival period is 1/A. Thus, the link is used at most AX of the time. idle. It is intuitively plausible, since 1/A is the expected interarrival time and X is the expected busy time between arrivals, that the ratio of X to 1/A (i.e., AX) is the fraction of time in which the portion of the link allocated to 8 is busy. This argument is made precise in Chapter 3. Our conclusion then is that if AX « 1, session 8'S portion of the link is idle most of the time (i.e., inefficiently utilized). To complete our argument about the inefficiency of circuit switching for data net￾works, we must relate X to the allowable expected delay T from message arrival at the source to delivery at the destination. Since X is the expected time until the last bit of the message has been sent on the first link, we must have X + P ::; T, where P is the propagation delay through the network. Thus AX < AT. If AT « 1 (i.e., the allowable delay is small relative to the message interarrival rate), the utilization AX for the session is correspondingly small. In summary, the bit rate T" allocated to a session must be large enough to allow message transmission within the required delay, and when AT « 1, this implies inefficient utilization of the link. Sessions for which AT « 1 are usually referred to as bursty sessions. For many of the interactive terminal sessions carried by data networks, AT is on the order of 0.01 or less. Thus, with circuit switching, that fraction of a link allocated to such sessions is utilized at most 1% of the time. The conclusion we draw from this is that if link costs are a dominant part of the cost of a network and if bursty sessions require a dominant fraction of link capacity using circuit switching, then circuit switching is an unattractive choice for data networks. Up to the present, both the assumptions above have been valid, and for this reason, data networks have not used circuit switching. The argument above has ignored propagation delays, switching delays in the nodes, and queueing delays. (Queueing delay arises when a message from session 8 arrives while another message from 8 is in transmission.) Since these delays must be added to the link transmission time X in meeting the delay requirement T, X must often be substantially smaller than T, making circuit switching even more inefficient. While propagation and switching delays are often negligible, queueing delay is not, as shown in Chapter 3, particularly when AT is close to or exceeds 1. In the future, it appears that link costs will become less important in the overall cost of a network. Also, with optical fiber, the marginal cost of link capacity is quite small, so that the wasted capacity of circuit switching will become less important. Finally, it appears that bursty interactive terminal traffic will grow considerably more slowly than