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Approximation of periodic queues

Published online by Cambridge University Press:  01 July 2016

Tomasz Rolski
Tomasz Rolski*
Affiliation:
University of Wrocław
*
∗Postal address: Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50–384 Wroclaw, Poland.
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Abstract

In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.

Keywords

MARKOV MODULATED QUEUEWORKLOADWORKLOAD AT THE TIME OF DAYUNIFORM INTEGRABILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987 , pp. 691 - 707
Copyright
Copyright © Applied Probability Trust 1987 

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