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... both analytically and experimentally. In Section III-B, we present a mathematical model of the window control algorithm. We prove that FAST TCP has the same equilibrium properties as TCP Vegas [44], =-=[50]-=-. In particular, it does not penalize flows with large propagation delays and it achieves weighted proportional fairness [31]. For the special case of single bottleneck link with heterogeneous flows, ...

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...as . Otherwise, tedious but straightforward calculations yield where and a similar expression holds for . Related and more general results for FIFO queues have recently been derived by Mo and Walrand =-=[18]-=-. 2) Maximum Throughput: Theorem 1 relies on the fact that the scheduling policy is FIFO. However, when another policy is used instead, it turns out that an analogous result often holds, with a suitab...

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...ngestion control literature to model fairness, since with different utility functions the rate allocations that maximize the total system utility can be mapped to a range of fairness objectives [35], =-=[36]-=-. We assume that time is divided into slots. At each time slot, the scheduling policy will select a power assignment vector (or, equivalently, ), and select data to be forwarded on each link. Given a ...

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...of these flows. The Br must satisfy the capacity constraints: � xrBr ≤ Cl, for l ∈L. (11) r∋l The issue of what constitutes a fair bandwidth allocation has been discussed in a number of recent papers =-=[20, 26, 24]-=-. A significant range of fairness notions can be expressed as the solution to the following optimization problem [26]: Maximize � B 1−α r wrxr , subject to constraints (11), 1 − α r (12) where α �= 1 ...

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...ction), until recently this problem appeared to be well beyond the reach of analytical modeling and feedback control theory. Theoretical research on this topic (e.g., [1, 2, 3, 4, 5]) has dealt with simple scenarios (e.g., single bottleneck, per-flow queueing); see also recent survey in [6, 7]. Meanwhile the Internet community has turned to small-scale simulations to validate designs. All of these leave huge gaps in our understanding of real network behavior. In the last few years, however, large strides have been taken in bringing analytical models into Internet congestion control (see e.g., [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22] and references therein). Key to these advances has been to explicitly model the congestion measure that communicates back to data sources the information on congestion in network resources being used; more precisely, it is assumed that each network link measures its congestion by a scalar variable (termed price), and that sources have access to the aggregate price of links in their path. These assumptions are implicitly present in many variants of today’s TCP protocols; this framework exhibits the price signal being used in these protocols (e.g., loss probability, queueing delay). Also, it is...

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...wr log(·). From a resource allocation point of view, the resource allocation achieved under any concave and increasing utility functions can be achieved by a weighted proportionally-fair allocation 2 =-=[27]-=- through appropriate choice of weights {wr}. The objective is to maximize total utility in the network subject to the link and time constraints. In this paper, we develop congestion control mechanisms...