Explicit solution for the stationary distribution of a discrete-time finite buffer queue

Bara Kim, Jeongsim Kim

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    We consider a discrete-time single server queue with finite buffer. The customers arrive according to a discrete-time batch Markovian arrival process with geometrically distributed batch sizes and the service time is one time slot. For this queueing system, we obtain an exact closed-form expression for the stationary queue length distribution. The expression is in a form of mixed matrix-geometric solution.

    Original languageEnglish
    Pages (from-to)1121-1133
    Number of pages13
    JournalJournal of Industrial and Management Optimization
    Volume12
    Issue number3
    DOIs
    Publication statusPublished - 2016

    Bibliographical note

    Funding Information:
    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 Re-search Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A4A01003813).

    Keywords

    • Discrete-time batch markovian arrival process
    • Discrete-time queue
    • Mixed matrix-geometric solution
    • Quadratic matrix equation
    • Stationary distribution

    ASJC Scopus subject areas

    • Business and International Management
    • Strategy and Management
    • Control and Optimization
    • Applied Mathematics

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