Analysis of a discrete-time two-class randomly alternating service model with Bernoulli arrivals

Arnaud Devos (), Joris Walraevens (), Dieter Fiems () and Herwig Bruneel ()
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Arnaud Devos: Ghent University
Joris Walraevens: Ghent University
Dieter Fiems: Ghent University
Herwig Bruneel: Ghent University

Queueing Systems: Theory and Applications, 2020, vol. 96, issue 1, No 6, 133-152

Abstract: Abstract We analyze a discrete-time two-class queueing system with a single server which is alternately available for only one customer class. The server is each time allocated to a customer class for a geometrically distributed amount of time. Service times of the customers are deterministically equal to 1 time slot each. During each time slot, both classes can have at most one arrival. The bivariate process of the number of customers of both classes can be considered as a two-dimensional nearest-neighbor random walk. The generating function of this random walk has to be obtained from a functional equation. This type of functional equation is known to be difficult to solve. In this paper, we obtain closed-form expressions for the joint probability distribution for the number of customers of both classes, in steady state.

Keywords: Two-class queueing model; Processor sharing; Singularity analysis; Analytic continuation; Nearest-neighbor random walk; 68M20; 90B22 (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/s11134-020-09663-x

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