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The BMAP/GI/1 queue with server set-up times and server vacations

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Josep M. Ferrandiz
Josep M. Ferrandiz*
Affiliation:
Hewlett-Packard Laboratories
*
∗Postal address: Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol, BS12 6QZ, UK.
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Abstract

Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP/GI/1 queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a customer finding an empty system. In the latter case we will talk of a server set-up time. The distribution of a set-up time or of a vacation period after a departure leaving a non-empty system behind is conditionally independent of the queue length and workload. Furthermore, the distribution of the server set-up times may be different from the distribution of vacations at service completion times. The results are particularized to the M/GI/1 queue and to the BMAP/GI/1 queue (without vacations).

Keywords

PALM-MARTINGALE CALCULUSQUEUES WITH VACATIONSBATCH MARKOVIAN ARRIVAL PROCESSESSERVER SET-UP

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 235 - 254
Copyright
Copyright © Applied Probability Trust 1993 

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