Analysis of a queue with general service demands and correlated service capacities

Michiel Muynck (), Herwig Bruneel () and Sabine Wittevrongel ()
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Michiel Muynck: Ghent University
Herwig Bruneel: Ghent University
Sabine Wittevrongel: Ghent University

Annals of Operations Research, 2020, vol. 293, issue 1, No 5, 73-99

Abstract: Abstract We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots and the service demands of consecutive customers form two independent and identically distributed sequences. However, we allow the service capacities in consecutive time slots to be correlated according to a discrete-batch Markovian process. We study this model analytically and obtain expressions for the probability generating function of the steady-state system content and customer delay, as well as their moments and an approximation for their tail probabilities. The results are illustrated with several numerical examples.

Keywords: Discrete-time queueing theory; Service demands; Correlated service capacities; Discrete-batch Markovian service process (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-019-03396-8

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