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University of Ulm, Faculty of Mathematics and Economics
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Transient and Stationary Waiting Times
in (max,+)-Linear Systems
with Poisson Input
Department of Stochastics
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General Information
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Abstract
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We consider a certain class of vectorial evolution equations, which are
linear in the (max,+) semi-field. They can be
used to model several types of discrete event systems, in particular
queueing networks where we assume that the arrival process of
customers (tokens, jobs, etc.) is Poisson.
Under natural Cramér type conditions on certain variables, we show
that the expected waiting time which the n-th customer has to
spend in a given subarea of such a system can be expanded analytically
in an infinite power series with respect to the arrival intensity.
Furthermore, we state an algorithm for computing all coefficients of this
series expansion and derive an explicit finite representation formula for the
remainder term.
We also give an explicit finite expansion for expected stationary
waiting times in (max,+)-linear systems with deterministic queueing
services.
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