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THE PROTOCOL STACK AND ITS MODULATING EFFECT
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ultimate realization as self-similar link traf c. Ef ciency dictates that le transmissions, including retransmission of lost packets, complete in a short amount of time. Subject to the limitations of congestion control in achieving optimally ef cient transfer [21], this has the effect of stretching out a large le or message transfer in time into an on-average, ``thin'' packet train. This also suggests why the linear on=off model may have been successful in modeling the output characteristics of a complicated nonlinear system, which real networks undoubtedly are. In some sense, the effect of the unaccounted-for nonlinearity is re ected back as a stretching-intime effect, thus conforming to the model's original suppositions. 14.4.7 Network Performance
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In this section, we present a summary of performance results evaluating the effects of self-similarity. A comprehensive study of the performance implications of selfsimilarity including quality-of-service (QoS) issues, resource trade-offs, and performance comparisons between TCP Reno, Tahoe, and Vegas can be found in Park et al. [20]. 14.4.7.1 Performance Evaluation Under Reliable Communication We evaluated network performance when both traf c self-similarity (a of Pareto le size distribution) and network resources (bottleneck bandwidth and buffer capacity) were varied. Figure 14.11(a) shows packet loss rate as a function of a for buffer sizes in the range 2 128 kB. We observe a gradual increase in the packet loss rate as a approaches 1, the atness of the curve increasing as buffer capacity is decreased. The latter is due to an overextension of buffer capacity whereby the burstiness associated with a 1:95 traf c is already high enough to cause signi cant packet drops. The added burstiness associated with highly self-similar traf c (a 1:05) bears little effect. The same gradual behavior is also observed for packet retransmission and throughput. Figure 14.11(b) shows mean queue length as a function of a for the same buffer range. In contrast to packet loss rate, queueing delay exhibits a superlinear dependence on self-similarity when buffer capacity is large. This is consistent
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Fig. 14.11 TCP run. (a) Packet loss rate and (b) mean queue length as a function of a; (c) queueing delay-packet loss trade-off curve.
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14.5 CONCLUSION
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with performance evaluation works [8, 15, 16] which show that queue length distribution decays more slowly for long-range dependent sources than for shortrange dependent sources. Figure 14.11(c) shows the queueing delay-packet loss trade-off curve for four levels of a. The individual performance points were obtained by varying buffer size while keeping bandwidth xed at the baseline value. The performance curves show that under highly self-similar traf c conditions, the negative effects of self-similarity are signi cantly ampli ed in the packet loss rate regime below 4%. A similar tradeoff relation exists for queueing delay and throughput. The effect of varying bandwidth to obtain the trade-off graphs and evaluation of the marginal bene t of network resources is shown in Figure 14.12. We observe that bandwidth affects a smooth, well-behaved performance curve with respect to self-similarity. It is, in part, due to this behavior that a ``small buffer capacity=large bandwidth'' resource provisioning policy is advocated. 14.4.7.2 Performance Evaluation Under Unreliable Communication Performance evaluations under unreliable, non- ow-controlled transport yield performance results that are signi cantly worse than their reliable, ow-controlled counterparts. In particular, the dependence of throughput-related measures such as effective throughput, packet loss, and packet retransmission is no longer gradual their shapes exhibit a superlinear dependence similar to the mean queue length relation in the reliable communication case. The superlinear dependence of queueing delay on the degree of self-similarity is further ampli ed, and so are trade-off relations between queueing delay and throughput. This is shown in Figure 14.13. 14.5 CONCLUSION
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In this chapter, we have shown that self-similarity in network traf c can arise due to a particularly simple cause: the reliable transfer of les drawn from heavy-tailed
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