Abstract
In Stolyar (Queueing Systems 50 (2005) 401–457) a dynamic control strategy, called greedy primal-dual (GPD) algorithm, was introduced for the problem of maximizing queueing network utility subject to stability of the queues, and was proved to be (asymptotically) optimal. (The network utility is a concave function of the average rates at which the network generates several “commodities.”) Underlying the control problem of Stolyar (Queueing Systems 50 (2005) 401–457) is a convex optimization problem subject to a set of linear constraints.
In this paper we introduce a generalized GPD algorithm, which applies to the network control problem with additional convex (possibly non-linear) constraints on the average commodity rates. The underlying optimization problem in this case is a convex problem subject to convex constraints. We prove asymptotic optimality of the generalized GPD algorithm. We illustrate key features and applications of the algorithm on simple examples.
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AMS Subject Classifications: 90B15 · 90C25 · 60K25 · 68M12
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Stolyar, A.L. Greedy primal-dual algorithm for dynamic resource allocation in complex networks. Queueing Syst 54, 203–220 (2006). https://doi.org/10.1007/s11134-006-0067-2
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DOI: https://doi.org/10.1007/s11134-006-0067-2