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Asymptotic analysis of queueing systems with identical service

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

F. I. Karpelevitch  and
A. Ya. Kreinin
F. I. Karpelevitch*
Affiliation:
Moscow Institute of Railway Transport Engineers
A. Ya. Kreinin*
Affiliation:
University of Toronto
*
∗Postal address: Moscow Institute of Railway Transport Engineers, 129851 Moscow, 3-ya Mytishchinskaya 10, Russia.
∗∗Postal address: Computer Systems Research Institute, University of Toronto, 6 King's College Road, Toronto, Ontario, Canada M5S 1A1. (Present address: Algorithmics Inc., 822 Richmond Street West, Toronto, Ontario, Canada M6J 1C9.)
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Abstract

We consider a heavy traffic regime in queueing systems with identical service. These systems belong to the class of multi-phase systems with dependent service times in different service nodes. We study the limit behaviour of the waiting time vector in heavy traffic. Both transient behaviour and the stationary regime are considered. Our analysis is based on the conception of ‘approximated functionals', which appeared to be fruitful in weak convergence theory of stochastic processes.

Keywords

ARRIVAL PROCESSHEAVY TRAFFIC LIMITSIDENTICAL SERVICEJOINT STATIONARY DISTRIBUTIONSQUEUEING SYSTEMSREFLECTED DIFFUSION PROCESSESSOJOURN TIMESWAITING TIMESWEAK CONVERGENCE

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 267 - 281
Copyright
Copyright © Applied Probability Trust 1996 

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