Tails for (max,plus) Recursions under Subexponentiality

We study the stationary solution to a (max, plus)-linear recursion. Under subexponentiality assumptions on the input to the recursion, we obtain the tail asymptotics of certain (max, plus)-linear functionals of this solution.

(Max, plus)-linear recursions arise in FIFO queueing networks; more speci.cally, in stochastic event graphs. In the event graph setting, two special cases of our results are of particular interest and have already been investigated in the literature. Firstly, the functional may correspond to the end-to-end response time of the event graph. Secondly, for two queues in tandem, the functional may correspond to the sojourn time in the second queue. Our results allow for more general networks; we illustrate this by studying the asymptotics of the resequencing delay due to multi-path routing.

By: A. B. Dieker; Marc Lelarge

Published in: RC23591 in 2005


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