Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

Arnaud Devos, Joris Walraevens, Dieter Fiems and Herwig Bruneel
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Arnaud Devos: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium
Joris Walraevens: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium
Dieter Fiems: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium
Herwig Bruneel: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGENT), Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium

Mathematics, 2021, vol. 9, issue 21, 1-25

Abstract: This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.

Keywords: queueing theory; discrete-time; server-sharing; scheduling; heavy-traffic; boundary value problems; correlation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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