François
Baccelli
research_article
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.
1997-11-01
2019-04-10T19:13
301-342
https://scigraph.springernature.com/explorer/license/
false
1997-11
en
http://link.springer.com/10.1023%2FA%3A1019141510202
Transient and stationary waiting times in (max,+)-linear systems with Poisson input
articles
26
3-4
0257-0130
Queueing Systems
1572-9443
readcube_id
43fdd5620451b9180557f1afc1e84126333b981fd1a035bfb6c4c6536fa6117d
Hasenfuss
Sven
University of Ulm
Abteilung Stochastik, Universität Ulm, Helmholtzstr. 18, D-89069, Ulm, Germany
Pure Mathematics
pub.1014272318
dimensions_id
Springer Nature - SN SciGraph project
Mathematical Sciences
Schmidt
Volker
doi
10.1023/a:1019141510202
INRIA Sophia Antipolis, 2004, Route des Lucioles, B.P.93, F-06902, Sophia Antipolis Cedex, France