A token-based central queue with order-independent service rates
| Autor: | Urtzi Ayesta, J.L. Dorsman, Tejas Bodas, Ina Maria Verloop |
|---|---|
| Přispěvatelé: | Stochastics (KDV, FNWI) |
| Rok vydání: | 2019 |
| Předmět: |
Service (business)
FOS: Computer and information sciences Matching (statistics) Computer Science - Performance Theoretical computer science Computer science Probability (math.PR) 020206 networking & telecommunications 02 engineering and technology Management Science and Operations Research Type (model theory) Security token 01 natural sciences Computer Science Applications Set (abstract data type) Performance (cs.PF) 010104 statistics & probability Product (mathematics) 0202 electrical engineering electronic engineering information engineering Redundancy (engineering) FOS: Mathematics 0101 mathematics Queue Mathematics - Probability |
| Zdroj: | Operations Research, 70(1), 545-561. INFORMS Inst.for Operations Res.and the Management Sciences |
| ISSN: | 0030-364X |
| DOI: | 10.48550/arxiv.1902.02137 |
| Popis: | 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, an assignment rule determines which token will be claimed. The service rate obtained by a customer is state-dependent, i.e., 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 (2011) and the model of Visschers et al. (2012). 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, multi-server models with redundancy and matching models. For some of these models, we present expressions for performance measures that have not been derived before. Comment: 28 pages, 1 figure |
| Databáze: | OpenAIRE |
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