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Markovian Queues With Correlated Arrival Processes

Author

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  • JEFFREY J. HUNTER

    (Institute of Information & Mathematical Sciences, Massey University, Private Bag 102 904, NSMC, Auckland, New Zealand)

Abstract

In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential inter-arrivals to the queueing system, are considered. Two of these models are based upon the upper and lower bounding joint distribution functions given by the Fréchet bounds for bivariate distributions with specified marginals, the third is based on Downton's bivariate exponential distribution and fourthly the usual M/M/1 model. The aim of the paper is to compare conditions for stability and explore the queueing behavior of the different models.

Suggested Citation

  • Jeffrey J. Hunter, 2007. "Markovian Queues With Correlated Arrival Processes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 593-611.
    • Handle: RePEc:wsi:apjorx:v:24:y:2007:i:04:n:s021759590700136x
    DOI: 10.1142/S021759590700136X
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