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

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

Anyue Chen and Eric Renshaw

Source: Adv. in Appl. Probab. Volume 36, Number 2 (2004), 499-524.

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.

Primary Subjects: 60J35

Secondary Subjects: 60J27, 60K25

Keywords: Bulk arrival; busy period distribution; equilibrium distribution; idle time; queue size; recurrence; state-dependent input; waiting-time distribution

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1086957583
Mathematical Reviews number (MathSciNet): MR2058147
Digital Object Identifier: doi:10.1239/aap/1086957583
Zentralblatt MATH identifier: 1046.60080

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