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Symmetric queues with batch departures and their networks

Part of:Special processes

Published online by Cambridge University Press:  01 July 2016

Masakiyo Miyazawa and
Ronald W. Wolff
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
Ronald W. Wolff*
Affiliation:
Tokyo Metropolitan University
*
* Postal address: Department of Information Science, Science University of Tokyo, Noda-City, Chiba 278, Japan.
** Postal address: Faculty of Economics, Tokyo Metropolitan University, Minami-Oosawa 1 chome, Hachioji-shi, Tokyo 192–03, Japan.
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Abstract

Batch departures arise in various applications of queues. In particular, such models have been studied recently in connection with production systems. For the most part, however, these models assume Poisson arrivals and exponential service times; little is known about them under more general settings. We consider how their stationary queue length distributions are affected by the distributions of interarrival times, service times and departing batch sizes of customers. Since this is not an easy problem even for single departure models, we first concentrate on single-node queues with a symmetric service discipline, which is known to have nice properties. We start with pre-emptive LIFO, a special case of the symmetric service discipline, and then consider symmetric queues with Poisson arrivals. Stability conditions and stationary queue length distributions are obtained for them, and several stochastic order relations are considered. For the symmetric queues and Poisson arrivals, we also discuss their network. Stability conditions and the stationary joint queue length distribution are obtained for this network.

Keywords

BATCH DEPARTURESYMMETRIC QUEUESTOCHASTIC ORDERINGNETWORK QUEUEPRODUCT FORMSTABILITYSTATIONARY DISTRIBUTION

MSC classification

Primary:60K25: Queueing theory

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996, pp. 308 - 326
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

This paper was initiated when Ronald W. Wolff visited the Science University of Tokyo in June, 1993. Masakiyo Mayazawa is partially supported by NEC C&C Laboratories.

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