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21.3 OPEN PROBLEMS IN PERFORMANCE ANALYSIS
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timely manner [53, 54]. Otherwise, they are considered to be as useless as if they had been dropped by the network. It has been shown that correlated erasures stemming from queueing can signi cantly impede the ef cacy of packet-level FEC when compared to independent packet drops [2, 12 14]. Little is known, however, about performance analysis of packet-level FEC under self-similar burstiness either from the source traf c itself or interference from cross traf c and this looms as an important challenge. As in the general second-order performance measure case, a starting point is bufferless queueing under self-similar input where the packet loss process with respect to a block of n consecutive packets the packets belonging to a self-similar traf c stream are viewed as totally ordered is analyzed. For simplicity, n can be considered xed although, in general, n is variable. 21.3.3 Short-range Versus Long-range Correlation
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Related to re ned traf c modeling (see Section 21.2) is the issue of short-range versus long-range correlation in determining queueing behavior and performance in network systems. This book is meant, in part, to clarify some of the surrounding issues given the mixed and sometimes con icting messages and conclusions advanced in various works [16, 21, 28, 32, 52, 60]. It has been shown that buffer capacity and time scale, traf c intensity and bandwidth, marginals, payload type (e.g., aggregated data traf c, VBR video), and the performance measure of interest rst-order versus second-order statistics collectively determine what the relative import of short time scale and long time scale structure is on performance. Recent works along the line ``here is a traf c model with controllable short-range and long-range structure, and short-range or, alternatively, long-range structure is dominant in impacting performance'' oftentimes provide insuf cient comparative evaluation of related works yielding one-sided and, on the surface, contradictory conclusions. The reader may take away the message that there are few unconditional truths in performance evaluation with self-similar traf c, modeling of Internet traf c admits a large degree of freedom in choosing models (i.e., assumptions) and parameters, and queueing with self-similar input is but one albeit important facet of self-similar network traf c research. On the other hand, as a science with engineering applications to network design, resource provisioning and control, further clari cation efforts that focus on carefully quali ed comparative evaluations are needed to distill the facts, assumptions, and derived conclusions into a mutually consistent and coherent description unless the works contain technical errors, by de nition, this is possible where assumptions and opinions are delineated from scienti c facts. Without these efforts, ambiguities and resulting confusion may put forth avoidable barriers to effectively applying the lessons and knowledge learned from self-similar traf c research to networking practice. 21.3.4 Queueing Analysis of Feedback Control Systems
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Analysis of feedback-controlled queueing systems is a dif cult problem. Tractability is achieved by considering queueing systems with state-dependent arrival rates and
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admission control systems where arrivals are admitted=rejected according to a decision rule [33, 65]. In both cases, injection of control is carefully administered such that the Markov property is preserved. Since the bulk of current Internet traf c is governed by TCP a complicated feedback congestion control and its statedependent actions may in uence the very traf c being measured and analyzed, it is important that the in uence of feedback control on traf c characteristics and performance be ascertained. For example, in the multifractal characterization of network traf c [23], it is conjectured that multiplicative scaling observed in shortrange structure is in uenced by TCP's control actions. If so, why is this the case and what are the underlying mechanisms Park et al. [51] (see also 14) show that multiplexing of concurrent TCP connections at a bottleneck router transporting heavy-tailed les leads to self-similar burstiness, but the empirical slope of the Hurst parameter curve as a function of tail index is less than 1, the slope value implied by 2 the relation H 3 a =2 stemming from the on=off model where connections are assumed independent [70]. Does coupling among feedback-controlled connections sharing common resources lead to changes in traf c properties Does it matter whether the feedback congestion control is TCP, rate-based control, or adaptive FEC TCP, because of its idiosyncracies and historical evolution, is not an easy protocol to analyze. Tractable analysis of its dynamics, to date, is only achieved by making an independence assumption on the loss process [45, 50], which, in general, is a heavy price to pay for tractability. A more fundamental avenue of exploration is the analysis of feedback congestion controls including linear increase=exponential decrease controls a tractable exercise without injecting decoupling by assumption which have been investigated, principally, for in nite source models [9, 25, 47, 55, 63, 71]. For heavy-tailed workloads where most le transfers are small and a few very large, little is known about the consequent system behavior. For large le transfers, steady-state may be reached due to its approximation of an in nite source. For small transfers the bulk of connections analysis remains a challenge. In a similar vein, the impact of feedback on traf c properties when multiplexing a number of heavy-tailed sources has not been investigated suf ciently. The dynamics and effect of feedback congestion control have been studied with respect to fairness, stability, and synchronization issues; traf c properties represent another dimension to their multifaceted in uence on network performance. 21.3.5 Impact of Packet Scheduling
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In modern routers, ow protection and multiservice support are provided in the form of con gurable service classes per- ow or aggregate- ow over various scheduling disciplines including GPS, priority queues, and RED. From a performance analysis perspective, the question arises as to what impact self-similar burstiness has on packet scheduling, from subtle effects such as the in uence on resource sharing and performance across service classes due to work conservation, to more active design questions such as optimal scheduling with respect to target objective functions. A comparative evaluation of FCFS, PS, and LCFS-PR under heavy traf c conditions (see 6) provides insight into the role of scheduling with
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