Chen, A. and Renshaw, E.
(2004)
*Markovian bulk-arriving queues with state-dependent control at idle time.*
Advances in Applied Probability, 36.
pp. 499-524.
ISSN 0001-8678

## 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.

Item type: | Article |
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ID code: | 4593 |

Keywords: | equilibrium distribution, waiting-time distribution, recurrence, statistics, probability, Probabilities. Mathematical statistics, Applied Mathematics, Statistics and Probability |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 06 Nov 2007 |

Last modified: | 10 Dec 2015 17:03 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4593 |

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