Large buffer asymptotics for fluid queues with heterogeneous M/G/infinity Weibullian inputs
In this paper we consider a generalization of the so called M/G/infinity model where M types of sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G/infinity system with Weibullian G distributions. In particular we assume that a session of type i transmits r(i) cells per unit time and lasts for a random time tau with a Weibull distribution given by Pr(tau > x) similar to e(-gammaixalphai), 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 alpha(i) < 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.
asymptotics queues weibull distributions stationary tail distributions