A queueing system with discrete autoregressive arrivals

Bara Kim, Yong Chang, Yeong Cheol Kim, Bong Dae Choi

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)

    Abstract

    We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.

    Original languageEnglish
    Pages (from-to)148-161
    Number of pages14
    JournalPerformance Evaluation
    Volume64
    Issue number2
    DOIs
    Publication statusPublished - 2007 Feb

    Bibliographical note

    Funding Information:
    This work was supported by grant No. R01-2001-00007 from the Korea Science & Engineering Foundation.

    Keywords

    • DAR(1)
    • Discrete time queue
    • Queue size
    • Recursive formula
    • Stochastic decomposition
    • Waiting time

    ASJC Scopus subject areas

    • Software
    • Modelling and Simulation
    • Hardware and Architecture
    • Computer Networks and Communications

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