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self-similar input. Performance analysis of EDF, xed priority schemes, and related scheduling algorithms under self-similar input remain to be investigated. Re ned analysis of work conservation and its impact on GPS with respect to providing inter ow (in general, inter-service class) protection under self-similar workloads looms as a challenging problem. On a broader level, the in uence of self-similarity and heavy-tailedness on scheduling need not be restricted to routers. Empirical evidence of heavy-tailedness across UNIX process life time distribution [35, 51], UNIX le size distribution [35, 51], and Web document size distribution [3, 15] points toward CPU scheduling policies that make active use of the heavy-tailed property. For example, given the empirical observation that most tasks require short service times whereas a few require very long service times, a shortest job rst (SJF) scheduling policy known to be optimal with respect to average waiting time is expected to yield ampli ed performance gain vis-a-vis FCFS and other workload-insensitive schedulers. The technical challenge lies in achieving tractable analysis of relevant performance measures such as waiting time under heavy-tailed workloads when using SJF or other workload-sensitive schedulers. The service time of a task may be known a priori for example, if related to the size of documents at Web servers or it may be estimated on-line. Heavy tailedness implies predictability if a task has been active for some time, then it is likely to persist into the future (see 1, Section 1.4) which can be used to perform on-line identi cation of long-running tasks.
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21.4 21.4.1
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Multiple Time Scale Traf c Control Self-similarity and long-range dependence imply predictability structure at large time scales that may be exploitable for traf c control purposes. Most feedback traf c controls are impervious to this information, principally, due to the fact that the time scale of the feedback loop that is, roundtrip time is an order of magnitude (or more) smaller than the time scale at which ``long-range'' correlation structure, in practice, manifests itself: millisecond versus second range. The multiple time scale traf c control framework was introduced by Tuan and Park [67] and shown to be effective at yielding signi cant performance improvement when large time scale correlation is exploited for traf c control. In Tuan and Park [67] (see also 18), large time scale correlation structure was on-line estimated and utilized to modulate the bandwidth consumption behavior of linear increase=exponential decrease rate-based congestion control for throughput maximization. In Tuan and Park [68], the approach was adapted to window-based congestion control and reliable transport using TCP (e.g., Reno and Vegas) with similar performance gains. In Tuan and Park [69], multiple time scale traf c control was extended to adaptive redundancy control where adaptive packet-level FEC is used for end-to-end QoS control of real-time traf c [8, 54]. An important bene t of multiple time scale traf c control is the mitigation of performance cost of reactive
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controls in broadband wide area networks with a large delay bandwidth product due to outdated feedback. The mechanism for exploiting large time scale structure employed by Tuan and Park [67 69] couples the feedback traf c control (i.e., short time scale module) with the large time scale module via a well-de ned modular interface, and is called selective aggressiveness control (SAC). Two methods are distinguished: selective slope control and selective level control. In selective slope control used in rate-based and window-based TCP congestion control the slope of the linear increase phase is varied as a function of expected contention level during large time intervals (e.g., 2 seconds), increasing the slope if the contention level is predicted to be low (thereby amplifying aggressiveness), and vice versa if the oppositive is true. In selective level control used in adaptive redundancy control a ``DC'' level, which is held constant during a large time scale interval, is shifted from high to low (and vice versa) across successive time intervals as a function of predicted contention level. This is depicted in Fig. 21.2. Selective aggressiveness control is but one approach to engaging large time scale predictability structure for traf c control. There may be other approaches and mechanisms, equally or perhaps even more effective, which can be used to harness long-term predictability for traf c control. Their identi cation and evaluation is a subject for continued exploration. We note that there are four challenges to be overcome in this endeavor: (1) correlation structure is dispersed over large distances in time, (2) information is probabilistic, (3) the mechanism should be implementable over existing traf c controls, and (4) it should not ``harm'' the underlying traf c control (if not help it) with respect to performance. Multilayered Feedback Control Multiple time scale traf c control, by coupling short time scale and large time scale control modules, leads to a multilayered feedback control. The large time scale module dynamically estimates the optimal slope and level values to use for particular network contention levels, which are then used to modulate the small time scale feedback control module. Even if the underlying small time scale feedback control (e.g., linear increase=exponential decrease rate-based control, TCP, or AFEC) is stable, this does not imply that the
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Fig. 21.2 Left: Selective slope control that is, slope shift during linear increase phase for high- and low-contention periods. Right: Selective level control that is, ``DC'' level shift between high- and low-contention periods.
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