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Markovian bulk-arriving queues with state-dependent control at idle time

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

Anyue Chen  and
Eric Renshaw
Anyue Chen*
Affiliation:
University of Greenwich
Eric Renshaw*
Affiliation:
University of Strathclyde
*
∗ Postal address: School of Computing and Mathematical Sciences, University of Greenwich, Maritime Greenwich Campus, Old Royal Naval College, Park Row, Greenwich, London SE10 9LS, UK
∗∗ Postal address: Department of Statistics and Modelling Science, Livingstone Tower, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK. Email address: [email protected]
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Abstract

This paper considers a Markovian bulk-arriving queue modified to allow both mass arrivals when the queue is idle and mass departures which allow for the possibility of removing the entire workload. Properties of queues which terminate when the server becomes idle are developed first, since these play a key role in later developments. Results for the case of mass arrivals, but no mass annihilation, are then constructed with specific attention being paid to recurrence properties, equilibrium queue-size structure, and waiting-time distribution. A closed-form expression for the expected queue size and its Laplace transform are also established. All of these results are then generalised to allow for the removal of the entire workload, with closed-form expressions being developed for the equilibrium size and waiting-time distributions.

Keywords

Bulk arrivalbusy period distributionequilibrium distributionidle timequeue sizerecurrencestate-dependent inputwaiting-time distribution

MSC classification

Primary: 60J35: Transition functions, generators and resolvents
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 2 , June 2004 , pp. 499 - 524
Copyright
Copyright © Applied Probability Trust 2004 

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