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

• 成果类型: Article
• 署名作者: Ayesta, Urtzi; Bodas, Tejas; Dorsman, Jan-Pieter L.; Verloop, Ina Maria
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National Polytechnique de Toulouse; Basque Foundation for Science; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); University of Basque Country; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Dharwad; University of Amsterdam
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2020.2088
• 发表日期: 2022
• 页码: 545-561
• 关键词: form; networks

摘要

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.