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COMPARISONS BETWEEN CERTAIN QUEUING SYSTEMS

Published online by Cambridge University Press:  11 January 2002

Torgny Lindvall
Torgny Lindvall
Affiliation:
Department of Mathematics, University of Göteborg, 41296 Göteborg, Sweden, E-mail: [email protected]
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Abstract

We use a Poisson imbedding technique to investigate the possibilities of generalizing some pathwise and stochastic monotonicity results from the M/M/k queues to systems with monotone failure rate service time distribution. A dichotomy between the decreasing failure rate (DFR) and the increasing failure rate (IFR) cases is revealed: In the DFR case, we achieve that the number of customers in the systems is stochastically increasing if it is idle at time 0, whereas in the IFR case, there is an alternating character that renders a bound between two identical systems that have different initial conditions. We also explore how our methods work in a comparison between systems with different numbers of stations but the same maximal capacity.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 1 , January 2002 , pp. 1 - 17
Copyright
© 2002 Cambridge University Press

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