have various propagation delays. The actual values of the propagation delays are not important to the discussion here, and thus are not listed.

Note that both traffic B and E share the same link between S4 and S5, and the source of E is closer to the link than that of B. This is analogous to a parking lot scenario in which E starts from a position closer to the exit than B. In a normal, real-world parking lot, E would have an unfair advantage over B by being able to move itself in front of B and get out first. However, in a good ATM network with separate virtual circuits for B and E, they ought to share fairly the bandwidth of the link, as long as they are not bottlenecked elsewhere in the network.

With this fairness objective in mind, we naturally consider the performance criterion described below, which is sometimes called "max-min" fairness [3, 4, 6] in the literature. First, the VCs on the most congested link will share the link bandwidth equally, and this determines the rates to be set for these VCs. Then, apply the procedure to the other VCs with the remaining bandwidth of the network. Continue repeating the procedure until rates for all the VCs have been assigned. Table 1 shows the resulting rates assigned to individual VC groups.

Translating the above mathematical rate-setting procedure into an efficient and robust implementation is a major challenge. First, with highly bursty ABR traffic, because load changes rapidly, there would be no static rate-setting that could be ideal for any significant period of time. When traffic changes, "optimal" rates to be assigned to the affected VCs must change accordingly.

For this reason, adaptive rate-setting is necessary for bursty traffic and has been the subject of intensive research for many years. The Enhanced Proportional Rate-Control Algorithm (EPRCA) [18], one of the schemes considered at the 1994 ATM Forum, represents the kind of adaptive rate-setting schemes this paper assumes.

Rate adaptation cannot be so precise that the newly derived rates will be exactly right with respect to current load, for at least two reasons. First, information and measurements based on which particular adaptation is performed cannot be totally complete or up to date due to various cost and implementation constraints. Second, the feedback control time that the adaptation takes to inform sources can vary because of disparities in propagation delay and link speed, congestion conditions, scheduling policies, and many other factors.

More interesting, perhaps, is that rate adaptation should not be precise either. To achieve high utilization with bursty traffic, it is necessary that the total assigned rate for all the VCs over a link be higher than the peak link rate. Consider the simple scenario shown in Figure 13 involving only two VCs, A and B. Assume that the two VCs share the same switch output link

TABLE 1

Expected Rates for VC Groups in Generic Fairness Configuration (GFC) of Figure 12

Group

Bandwidth

Bottleneck Link

A

1/27 = 0.037

S1-S2

B

2/27 = 0.074

S4-S5

C

2/9 = 0.222

S3-S4

D

1/27 = 0.037

S1-S2

E

2/27 = 0.074

S4-S5

F

1/3 = 0.333

S2-S3



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