Tail asymptotics for monotone-separable networks

Details Tail asymptotics for monotone-separable networks Tail asymptotics for monotone-separable networks

2005-10-06

arxiv.org/abs/math/0510117v4

Mathematics

Probability

15 pages, shortened version, case of (max,plus)-networks handled in a separate paper

Scientific paper

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with i.i.d. driving sequences and the $GI /GI /1/1$ queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

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