Large Buffer Asymptotics for Fluid Queues with Heterogeneous M/G/ Weibullian Inputs

Abstract

In this paper we consider a generalization of the so called M/G/∞ model where M types of sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G/∞ system with Weibullian G distributions. In particular we assume that a session of type i transmits ri cells per unit time and lasts for a random time τ with a Weibull distribution given by Pr (τ>x)∼e−γixαi, where 0 0. We show that the complementary buffer occupancy distribution for large buffer size is Weibullian whose parameters can be determined as the solution of a deterministic nonlinear knapsack problem. For αi<0.5, upper and lower bound factors are determined. When specialized to the homogeneous case, i.e., when all the sessions are identical, the result coincides with a lower bound reported in the literature.