Buffer occupancy asymptotics in rate proportional sharing networks with heterogeneous long-tailed inputs

2014/11/11 by Ozturk, Oczan, Mazumdar, Ravi R., Likhanov, Nikolay B.
#90B18 #FOS: Computer and information sciences #Performance (cs.PF) #Primary 60J25 #Secondary 68M20

paper · doi:10.48550/arxiv.1411.2867

Abstract

In this paper, we consider a network of rate proportional processor sharing servers in which sessions with long-tailed duration arrive as Poisson processes. In particular, we assume that a session of type n transmits at a rate r_n bits per unit time and lasts for a random time τ_n with a generalized Pareto distribution given by P \τ_n > x\ ∼ α_n x^-(1+β_n) for large x, where α_n, β_n > 0. The weights are taken to be the rates of the flows. The network is assumed to be loop-free with respect to source-destination routes. We characterize the order O-asymptotics of the complementary buffer occupancy distribution at each node in terms of the input characteristics of the sessions. In particular, we show that the distributions obey a power law whose exponent can be calculated via solving a fixed point and deterministic knapsack problem. The paper concludes with some canonical examples.

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