MARKOVIAN QUEUES WITH CORRELATED ARRIVAL PROCESSES

Jeffrey J. Hunter ()
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Jeffrey J. Hunter: Institute of Information & Mathematical Sciences, Massey University, Private Bag 102 904, NSMC, Auckland, New Zealand

Asia-Pacific Journal of Operational Research (APJOR), 2007, vol. 24, issue 04, 593-611

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.

Keywords: M/M/1 queue; SM/M/1 queue; bivariate distributions; correlated arrival process; Fréchet bounds; Markov chain (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S021759590700136X

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