Transient and stationary waiting times in (max,+)-linear systems with Poisson input View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1997-11

AUTHORS

François Baccelli, Sven Hasenfuss, Volker Schmidt

ABSTRACT

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. More... »

PAGES

301-342

References to SciGraph publications

Journal

TITLE

Queueing Systems

ISSUE

3-4

VOLUME

26

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1019141510202

DOI

http://dx.doi.org/10.1023/a:1019141510202

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1014272318


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