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A non-exponential queueing system with independent arrivals and batch servicing

Published online by Cambridge University Press:  14 July 2016

Nico M. Van Dijk  and
Eric Smeitink
Nico M. Van Dijk
Affiliation:
Free University, Amsterdam
Eric Smeitink*
Affiliation:
Free University, Amsterdam
*
∗Postal address for both authors: Faculty of Economics and Econometrics, Free University, P.O. Box 7161, 1007 MC Amsterdam, The Netherlands.
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Abstract

We study a queueing system with a finite number of input sources. Jobs are individually generated by a source but wait to be served in batches, during which the input of that source is stopped. The service speed of a server depends on the mode of other sources and thus includes interdependencies. The input and service times are allowed to be generally distributed. A classical example is a machine repair system where the machines are subject to shocks causing cumulative damage. A product-form expression is obtained for the steady state joint queue length distribution and shown to be insensitive (i.e. to depend on only mean input and service times). The result is of both practical and theoretical interest as an extension of more standard batch service systems.

Keywords

PRODUCT FORMINSENSITIVITYSOURCE BALANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 401 - 408
Copyright
Copyright © Applied Probability Trust 1990 

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