A Token-Based Central Queue with Order-Independent Service Rates

Urtzi Ayesta (), Tejas Bodas (), Jan-Pieter L. Dorsman () and Ina Maria Verloop ()
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Urtzi Ayesta: CNRS, IRIT, 31071 Toulouse, France; IKERBASQUE–Basque Foundation for Science, 48011 Bilbao, Spain; Université de Toulouse, INP, 31071 Toulouse, France; UPV/EHU, University of the Basque Country, 20018 Donostia, Spain
Tejas Bodas: Indian Institute of Technology Dharwad, Karnataka, 580011, India
Jan-Pieter L. Dorsman: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1090 GE Amsterdam, Netherlands
Ina Maria Verloop: CNRS, IRIT, 31071 Toulouse, France; Université de Toulouse, INP, 31071 Toulouse, France

Operations Research, 2022, vol. 70, issue 1, 545-561

Abstract: We study a token-based central queue with multiple customer types. Customers of each type arrive according to a Poisson process and have an associated set of compatible tokens. Customers may only receive service when they have claimed a compatible token. If, upon arrival, more than one compatible token is available, then an assignment rule determines which token will be claimed. The service rate obtained by a customer is state-dependent, that is, it depends on the set of claimed tokens and on the number of customers in the system. Our first main result shows that, provided the assignment rule and the service rates satisfy certain conditions, the steady-state distribution has a product form. We show that our model subsumes known families of models that have product-form steady-state distributions, including the order-independent queue of Krzesinski and the multi-type customer and server model of Visschers et al. Our second main contribution involves the derivation of expressions for relevant performance measures such as the sojourn time and the number of customers present in the system. We apply our framework to relevant models, including an M/M/K queue with heterogeneous service rates, the MSCCC queue, and multiserver models with redundancy. For some of these models, we present expressions for performance measures that have not been derived before.

Keywords: Stochastic Models; product form; token-based; order-independent queue; redundancy system; matching model (search for similar items in EconPapers)
Date: 2022
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