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SAC (e Determination) 1. Let l L1 St . P 2. Compute H E L2 jL1 l 8H 1 l H PrfL2 l H jL1 lg. l l 3. Set E E H . l Thus, the current traf c level St is normalized and mapped to the index l L1 St , which is then used to calculate the expectation of L2 conditioned on l H ; H . The latter l is then nally used to index into a table E H is called the aggressiveness schedule. l The intuition behind the aggressiveness schedule E is that if the expected future contention level is low (i.e., H close to 1) then it is likely that applying a high level of l aggressiveness will pay off. Conversely, if the expected future contention level is high (i.e., H near 8) then applying a low level of aggressiveness is called for. One l schedule that we use is the inverse schedule, E H 1=H : l l Other schedules of interest include the threshold schedule with threshold y P 1; 8 and aggressiveness factor y*, where E y* if H y, and 0 otherwise. l Table 18.1 shows the CondProb table for two runs corresponding to a 1:05 (top) and a 1:95 (bottom) traf c conditions. The column containing hl has been omitted and the entries show actual relative frequencies rather than hlH counts for illustrative purposes. Clearly, the conditional probability densities are skewed diagonally for a 1:05 traf c, whereas they are roughly invariant for a 1:95 traf c. The expected future contention level H E L2 jL1 l and aggressiveness l schedule (inverse) are shown as separate columns. For a 1:05 traf c, the expected future contention level E L2 j varies over a wide range, which is a direct consequence of the predictability that is, skewedness present in the correlation structure. For a 1:95 traf c, however, E L2 j is fairly `` at,'' indicating that conditioning on the present does not aid signi cantly in predicting the future.
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We use the LBNL Network Simulator, ns (version 2), as the basis of our simulation environment. ns is an event-driven simulator derived from Keshav's REAL network simulator supporting several avors of TCP and router packet scheduling algorithms. We have modi ed ns in order to model a bottleneck network environment where several concurrent connections are multiplexed over a shared bottleneck link. A UDP-based unreliable transport protocol was added to the existing protocol suite, and our congestion control and predictive control were implemented on top of it. An important feature of the setup is the mechanism whereby self-similar traf c conditions are induced in the network. One possibility is to have a host inject self-
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TABLE 18.1 Snapshot of CondProb 10,000 s After Connection Has Been Established (Top, a 1:05; Bottom, a 1:95) L1 1 2 3 4 5 6 7 8 L1 1 2 3 4 5 6 7 8 L2 L2 1 0.667 0.003 0 0 0 0 0 0 1 0.155 0.043 0.023 0.020 0.012 0.017 0.008 0 2 0.333 0.568 0.126 0.035 0.003 0 0 0 2 0.116 0.058 0.049 0.058 0.039 0.058 0.042 0 3 0 0.306 0.468 0.205 0.078 0.012 0.018 0 3 0.155 0.179 0.132 0.135 0.134 0.141 0.126 0.167 4 0 0.093 0.262 0.368 0.296 0.099 0.079 0 4 0.233 0.272 0.306 0.274 0.273 0.243 0.211 0.233 5 0 0.027 0.116 0.305 0.356 0.285 0.245 0.333 5 0.165 0.257 0.273 0.286 0.307 0.325 0.322 0.233 6 0 0.003 0.023 0.077 0.205 0.418 0.443 0 6 0.078 0.128 0.161 0.167 0.183 0.166 0.195 0.300 7 0 0 0.003 0.201 0.060 0.182 0.213 0.500 7 0.087 0.054 0.054 0.055 0.044 0.044 0.088 0.067 8 0 0 0 0 0.002 0.003 0.003 0.167 8 0.097 0.008 0.003 0.004 0.008 0.007 0.008 0 E L2 j 1.3 2.6 3.4 4.2 4.9 5.7 5.8 6.5 E L2 j 3.8 4.3 4.5 4.5 4.6 4.5 4.8 4.8 E 0.769 0.384 0.294 0.238 0.204 0.175 0.172 0.153 E 0.263 0.232 0.222 0.222 0.217 0.222 0.208 0.208
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similar time series into the network. We follow a different approach based on the notion of structural causality (see Section 18.2.2) whereby we make use of the fact that a networked client=server environment, with clients interactively accessing les or objects with heavy-tailed sizes from servers across the network, leads to aggregate traf c that is self-similar [33]. Most importantly, this mechanism is robust and holds when the le transfers are mediated by transport layer protocols executing reliable ow-controlled transport (e.g., TCP) or unreliable ow-controlled transport. The separation and isolation of ``self-similar causality'' to the highest layer of the protocol stack allows us to interject different congestion control protocols in the transport layer, discern their in uence, and study their impact on network performance. This is illustrated in Fig. 18.7. Figure 18.8 shows a 2-server, n-client n ! 33 network con guration with a bottleneck link connecting gateways G1 and G2 . The link bandwidths were set at 10 Mb=s and the latency of each link was set to 5 ms. The maximum segment size was xed at 1 kB for all runs. Some of the clients engage in interactive transport of les with heavy-tailed sizes across the bottleneck link to the servers (i.e., the nomenclature of ``client'' and ``server'' are reversed here), sleeping for an exponential time between successive transfers. Others act as in nite sources (i.e., they have always data to send) executing the generic linear increase=exponential decrease feeback congestion control with and without SAC in the protocol stack trying to
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