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...be asymptotically optimal as β ↓ 0in[3, 21]. Ifs404 STOLYAR we remove all commodity flows (so that we are not concerned about any utility), the GPD algorithm becomes a “MaxWeight”-type algorithm (cf. =-=[4,20,22,23]-=-), “greedily” pursuing minimization of Lyapunov function � N p(1/2)Q2n (t), and known to ensure stability of queueing networks if such is feasible at all. (Cf. [4] for recent results and review of pre...

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...t the back-pressure policy with fixed routing (with α = 1) stabilizes the system for any arrival rate satisfying the preceding condition. It can be shown using the fluid model techniques developed in =-=[3]-=- and [18] that the above policy with (α > 0) is stable whenever the arrival processes satisfy a strong-law-of-large numbers assumption and the flow rate vector g ∈ C. III. DERIVING LOWER BOUNDS ON AVE...

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...ht scheduling policy of Tassiulas and Ephremides [28], in the diffusion (or heavy traffic) limit. Whereas previous works on switched networks and stochastic processing networks in the diffusion limit =-=[6, 7, 27]-=- have assumed the “complete resource pooling” condition, which roughly means that there is a single bottleneck cut constraint, we do not make this assumption. Section 3 discusses further the related w...

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...fluid model by [28, Proposition 11] (the myopic policies defined with respect to V or V p are identical when p > 0.) The resulting feedback law f V is a special case of the maximum pressure policy of =-=[7]-=-, which is a generalization of the MaxWeight and related policies considered in [36, 11, 34, 25]. The main results of [36, 7] imply that f V is a stabilizing policy for a stochastic network under very...

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...atic function, h(x) = 12x TDx, x ∈ Rℓ, (1) with D > 0 a diagonal matrix. Stability theory for this and similar classes of policies has been extended in multiple directions over the past fifteen years =-=[20, 51, 47, 17, 13]-=-, and in particular these policies are known to be approximately optimal in heavy traffic under certain conditions on the network — see [54, 48, 33], and the recent comprehensive results by Dai and Li...

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...t appears to have received little attention. Recently, Bambos and Michialidis [8] examined the problem of allocating a single resource (bandwidth) to maximize throughput in a system of parallel queues operating in a random environment (see also the references in [8] for related work on such models). Rather than considering a single server model, we examine a very general network structure, and by dealing specifically with failures, provide extensive structural results. Here, we use fluid limits to design server assignment policies, as in [7]. In addition to [7], 3 a recent work by Dai and Lin [18] shows that for a class of stochastic processing networks (which include an instance of the class studied in [7]), maximum pressure policies may be used to maximize network capacity. A little less closely related, but still in the spirit of our approach, is a body of work that uses diffusion approximations to design policies that minimize the long-run discounted holding cost in flexible server systems (Williams and coauthors [11, 12, 14], Harrison and co-authors [23, 24, 25], Laws [30], and Mandelbaum and Stolyar [31]). In these works, the notion of heavy traffic is defined through an LP simil...