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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 nth 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 λ. 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.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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