Buffer Occupancy Asymptotics in Networks with Heterogeneous Long-tailed Inputs
نویسندگان
چکیده
In this paper, we consider a network in which sessions with long-tailed session lengths arrive as Poisson processes. In particular, we assume that a session of type n transmits rn cells per unit time and lasts for a random time τn with a generalized Pareto distribution given by IP(τn > x) ∼ αnx−(1+βn) for large x, where αn, βn > 0. The network is assumed to be loop-free with respect to source-destination routes. We characterize the order 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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