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Extended generator and associated martingales for M/G/1 retrial queue with classical retrial policy and general retrial times

Published online by Cambridge University Press:  11 January 2022

S. Meziani  and
T. Kernane Open the ORCID record for T. Kernane [Opens in a new window]
S. Meziani
Affiliation:
Department of Probability and Statistics, Faculty of Mathematics, University of Sciences and Technology USTHB, Algiers, Algeria. E-mail: smeziani@usthb.dz
T. Kernane
Affiliation:
Department of Probability and Statistics, Faculty of Mathematics, University of Sciences and Technology USTHB, Algiers, Algeria. E-mail: smeziani@usthb.dz Laboratory of Research in Intelligent Informatics and Applied Mathematics (RIIMA), University of Sciences and Technology USTHB, Algiers, Algeria. E-mail: tkernane@gmail.com
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Abstract

A retrial queue with classical retrial policy, where each blocked customer in the orbit retries for service, and general retrial times is modeled by a piecewise deterministic Markov process (PDMP). From the extended generator of the PDMP of the retrial queue, we derive the associated martingales. These results are used to derive the conditional expected number of customers in the orbit in the transient regime.

Keywords

Extended generatorMartingalePiecewise deterministic Markov processRetrial queue
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 206 - 213
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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