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Time-changing and truncating K-capacity queues from one K to another

Published online by Cambridge University Press:  14 July 2016

Paul Glasserman  and
Wei-Bo Gong
Paul Glasserman
Affiliation:
AT&T Bell Laboratories
Wei-Bo Gong*
Affiliation:
University of Massachusetts, Amherst
*
∗∗ Postal address: Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA.
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Abstract

For , we obtain a K′- capacity queue from a K- capacity queue through a random time change and a truncation, provided arrivals are Poisson or service is exponential. In the case of an M/G/1/K queue, the time change erases service intervals that begin with more than K′ customers in the systems. This construction yields a straightforward sample path proof of Keilson's result on the proportionality of the ergodic queue length probabilities in M/G/1/K queues. The same approach proves a strengthened result for ‘detailed' state probabilities. It also reproduces a proportionality result for a vacation model, due to Keilson and Servi. A ‘dual' construction yields a different kind of proportionality for the G/M/1/K queue.

Keywords

SAMPLE PATH ANALYSISM/G/1/K QUEUEERGODIC QUEUE-LENGTH DISTRIBUTIONRANDOM TIME-CHANGE
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 647 - 655
Copyright
Copyright © Applied Probability Trust 1991 

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Footnotes

∗

Present address: Graduate School of Business, Columbia University, 403 Uris Hall, New York, NY 10027, USA.

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