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Exponential approximation of waiting time and queue size for queues in heavy traffic

Published online by Cambridge University Press:  01 July 2016

Władysław Szczotka
Władysław Szczotka*
Affiliation:
Wrocław University
*
∗Postal address: Mathematical Institute, Wrocław University, Pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland.
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Abstract

An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.

Keywords

STATIONARY WAITING TIME DISTRIBUTIONSTATIONARY QUEUE SIZE DISTRIBUTIONASYMPTOTIC STATIONARITYSTATIONARY REPRESENTATIONWIENER PROCESSCONVERGENCE IN DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 230 - 240
Copyright
Copyright © Applied Probability Trust 1990 

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