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coupled system is stable. It is expected, however, that, by exploiting timescale separation between the two control modules, stability of the overall system can be achieved under fairly weak conditions. In particular, if TL , TS denote the time scales of the large and small time scale modules, respectively, TS ( TL (in a suitable sense), and the small time scale feedback control is assumed to converge fast (e.g., within a small factor of TS by exponential convergence), then the overall system may be shown to be stable (but not asymptotically stable) by the quasi-stationarity argument that the small time scale control converges ``well within'' TL a locally stationary regime from its perspective leading to a concatenation of locally wellbehaved trajectories (short transient followed by convergence), assuming the large time scale control itself is stable. The most challenging problem arises when suf cient separation between small and large time scales does not hold. Complicated dynamics can ensue and identi cation of suf ciency conditions for stability with relevant counterparts in networking looms as a challenging problem. Workload-sensitive Traf c Control Multiple time scale traf c control can be extended to workload-sensitive traf c control where traf c controls are made, to varying degrees, cognizant of workload properties in the broadest sense when this is deemed bene cial to do so. For example, when TCP is invoked by HTTP in the context of Web client=server interactions, the size of the le being transported known at the server may be conveyed or made accessible to protocols in the transport layer, including the selection of alternative protocols, for more effective data transport (see, e.g., Heddaya and Park [31] for a discussion of a speci c mechanism in the context of congestion control). For short les, which constitute the bulk of connection requests in heavy-tailed le size distributions of Web servers, elaborate feedback control geared toward steady-state ef ciency may be by-passed in favor of lightweight mechanisms in the spirit of optimistic control, which can, in some instances [39], result in improved ``effective bandwidth.'' Recently, the heavytailed characteristics of IP ow durations [23, 24] have been used to selectively perform routing table updates based on connection lifetime classi cation, where it is shown that desensitizing route updates triggered by short-lived ows can enhance routing stability [62]. Endowing workload sensitivity on traf c control need not be restricted to congestion control, error control, and routing (for that matter, closedloop control) and represents a broad area for future exploration facilitated by the recent discoveries and advancement in traf c characterization. Optimal Prediction of Long-range Correlation Structure Predicting the future traf c level from past observations is an important component to affecting traf c control under self-similar traf c conditions. s 17 and 18 provide heuristic approaches to estimating the future traf c level based on conditional expectation optimal with respect to mean square error but due to its nonlinearity, effective optimal prediction remains a technical challenge [6]. With long-range dependent time series and their slow convergence properties, it becomes dif cult to devise effective predictors that can rigorously be shown to have desirable properties. Traditional estimation theory achieves tractability through assumption of Markovian
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input (Kalman lters) or restriction on observation models (Wiener lters). On the positive side, the conditional expectation predictor E X m i jX m i 1 has proved effective in empirical evaluations with respect to yielding traf c level estimates that are close to the true traf c level. Furthermore, the performance gain obtained by engaging approximate information has been shown to approach the gain achievable when perfect information is available [67]. Thus there is room for further performance gain due to improved prediction, but its magnitude is expected to be incremental. On a related front, inference of network state through minimally intrusive actions is relevant for effectively incorporating the prediction mechanisms in network protocols. For example, in Tuan and Park [68] a TCP connection's interaction with other traf c ows at bottleneck routers and the consequent impact on its output behavior observable at the sender is used to infer the contention level at bottleneck routers. That is, no separate probing mechanism is engaged to estimate network state. The effectiveness of this minimally intrusive scheme is shown to be dependent on the tracking ability of the underlying feedback control [68]; state estimation suffers most heavily during the linear increase phase after backoff, which results in better tracking performance for TCP Vegas over TCP Reno. Inference can be performed by other means including arrival behavior of ACK packets, and further exploration of effective measurement schemes is of interest. When explicit probing is employed, the question arises as to how to perform accurate sampling and estimation of network state without signi cantly affecting Schrodin ger's cat in the process. Accurate sampling is made dif cult by the slow convergence properties of self-similar traf c, and trade-offs between accuracy and probing duration can bene t from further investigation (also relevant to measurementbased admission control [36]). 21.4.2 Open-loop Control and Resource Provisioning
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Resource Reservation and Admission Control The performance analysis techniques and issues discussed in Section 21.3 have direct bearing on the ability to compute performance bounds for routers fed with self-similar input, estimation of effective bandwidth and statistical multiplexing gain, bandwidth and buffer capacity dimensioning=provisioning, and admission control. 19 presents a speci c open-loop architecture based on per-VC framing, and 16 discusses design and performance evaluation considerations of open-loop architectures under selfsimilar traf c conditions. The same observations regarding the need for nitary analysis, incorporation of second-order performance measures, relative impact of short-range and long-range correlation structure, and in uence of scheduling advanced in Section 21.3 hold for the resource provisioning context. Similarly, the small buffer=large bandwidth resource provisioning strategy is expected to play a dominant role in facilitating guaranteed services deterministic or statistical in the context of open-loop control. Dynamic Admission Control In resource provisioning, admission control is exercised in a static manner, where the set of connections requesting service is
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