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

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

Chen, Anyue and Renshaw, Eric (2004) Markovian bulk-arriving queues with state-dependent control at idle time. Advances in Applied Probability, 36 (2). pp. 499-524. ISSN 1475-6064 (Print), 0001-8678 (Online) (doi:10.1239/aap/1086957583)

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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.

Item Type: Article
Uncontrolled Keywords: bulk arrival, busy period distribution, equilibrium distribution, idle time, queue size, recurrence, state-dependent input, waiting-time distribution
Subjects: Q Science > QA Mathematics
Pre-2014 Departments: School of Computing & Mathematical Sciences
Related URLs:
Last Modified: 14 Oct 2016 09:01
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/720

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