An interpolation approximation for queueing systems with Poisson input
Operations Research
Open queueing systems in light traffic
Mathematics of Operations Research
Queueing Systems: Theory and Applications
A characterisation of (max,+)-linear queueing systems
Queueing Systems: Theory and Applications
Laplace Transform and Moments of Waiting Times in Poisson Driven (max,+) Linear Systems
Queueing Systems: Theory and Applications
Weak Differentiability of Product Measures
Mathematics of Operations Research
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part II
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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 \lambda. 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.