Waiting time distributions in an M/G/1 retrial queue with two classes of customers

Bara Kim, Jeongsim Kim

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    We consider an M/ G/ 1 retrial queueing system with two classes of customers, in which the service time distributions are different for both classes of customers. When the server is unavailable, an arriving class-1 customer is queued in the queue with infinite capacity, whereas class-2 customer enters the retrial group. In this paper, we are concerned with the analysis of the waiting time distribution. We obtain the joint transform of the waiting time of a class-2 customer and the number of class-2 customers as well as the Laplace–Stieltjes transform of the waiting time of a class-1 customer. We also obtain all the moments of the waiting time distributions of class-1 and class-2 customers.

    Original languageEnglish
    Pages (from-to)121-134
    Number of pages14
    JournalAnnals of Operations Research
    Volume252
    Issue number1
    DOIs
    Publication statusPublished - 2017 May 1

    Bibliographical note

    Funding Information:
    We are grateful to the reviewers for their valuable comments and suggestions, which improved this paper. B. Kim’s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831). J. Kim’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A4A01003813).

    Publisher Copyright:
    © 2015, Springer Science+Business Media New York.

    Keywords

    • Queue length
    • Retrial queue with two classes of customers
    • Transform
    • Waiting time

    ASJC Scopus subject areas

    • General Decision Sciences
    • Management Science and Operations Research

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