System occupancy in a multiclass batch-service queueing system with limited variable service capacity

Jens Baetens (), Bart Steyaert, Dieter Claeys and Herwig Bruneel
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Jens Baetens: Ghent University
Bart Steyaert: Ghent University
Dieter Claeys: Ghent University
Herwig Bruneel: Ghent University

Annals of Operations Research, 2020, vol. 293, issue 1, No 2, 3-26

Abstract: Abstract In multi-class telecommunications or manufacturing systems, customers belonging to the same class can often be processed together. This results in a service capacity that depends on the classes of the customers in the queue. In this paper, we analyse a discrete-time batch-service queue with two customer classes. The single batch server can group all same-class customers at the head of the queue up to a constant class-dependent maximum service capacity. We focus on the analysis of the system occupancy at service initiation opportunities, and also compute both a light- and heavy traffic approximation in order to reduce the numerical complexity introduced by the maximum service capacities. Additionally, we propose a method for interpolating between these approximations in order to study the behaviour in the intermediate region. We also deduce the system occupancy and its approximations at random slot boundaries. In the numerical experiments, we examine the conditions under which these proposed approximations are accurate.

Keywords: Batch service; Two-class; Variable service capacity; Generally distributed service times; Correlated customer types (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03470-1

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