Analysis of a two-class queueing system with service times dependent on the presence of a certain class

Sara Sasaninejad (), Joris Walraevens, Arnaud Devos and Sabine Wittevrongel
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Sara Sasaninejad: Ghent University
Joris Walraevens: Ghent University
Arnaud Devos: Ghent University
Sabine Wittevrongel: Ghent University

Mathematical Methods of Operations Research, 2023, vol. 98, issue 3, No 2, 376 pages

Abstract: Abstract Most queueing models and their analysis have a rich history and follow a process of increased generality and complexity. In this paper, we introduce a new model, namely a multiclass queueing model where service times depend on the presence of one of the classes. Our model is motivated by road traffic, where the presence of heavy vehicles in a queue slows down the entire system, or, in contrast, where the presence of emergency vehicles may speed up the service. The specific assumption we impose is that the service time of each customer depends on whether at least one customer of that particular class is present in the system at the time of service. Although we study a fairly simple discrete-time model, we show that analysis is not straightforward. Furthermore, numerical examples expose that the impact of particular customers in the system can lead to a substantial slow down (or, in contrast, speed up) of the entire system.

Keywords: Queueing theory; Discrete-time; Dependent service times; Probability generating function; Multiclass (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00842-z

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