Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities

Michiel De Muynck, Herwig Bruneel and Sabine Wittevrongel ()
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Michiel De Muynck: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium
Herwig Bruneel: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium
Sabine Wittevrongel: SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium

Mathematics, 2023, vol. 11, issue 4, 1-21

Abstract: We present the study of a non-classical discrete-time queuing system in which the customers each request a variable amount of service, called their “service demand”, from a system with multiple servers, each of which can provide a variable amount of service, called their “service capacity”, in each time slot. The service demands are independent from customer to customer and follow a general distribution, whereas the service capacities follow a phase-type distribution and are independent from server to server and from slot to slot. Since an exact analytical analysis for this general queuing system is infeasible, we propose several approximations for the key performance characteristics in this system such as the mean system content and the mean customer delay in steady state. The accuracy of each of these approximations is compared to simulations using several numerical examples.

Keywords: discrete-time queuing theory; service demands; service capacities; multi-server (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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