A spectral approach to compute performance measures in a correlated single server queue

Authors:
J. Kumaran;K. Mitchell;A. van de Liefvoort
Affiliations:
University of Missouri-Kansas City, Knasas City, Mo;University of Missouri-Kansas City, Knasas City, Mo;University of Missouri-Kansas City, Knasas City, Mo
Venue:
ACM SIGMETRICS Performance Evaluation Review - Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
Year:
2005

Citing 1
Cited 2

Exact and approximate numerical solutions of steady-state distributions arising in the queue GI/G/1

Queueing Systems: Theory and Applications - Numerical computations in queues

Solving the single server semi-Markov queue with matrix exponential kernel matrices for interarrivals and services

valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
System-theoretical algorithmic solution to waiting times in semi-Markov queues

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Abstract

The coupling matrix was introduced in [8] to compute the performance measures of a PH/PH/1 single server queue. This matrix was extended in [1, 2] to include arrival and service processes that are possibly serially correlated processes, although the service process remains independent of the arrival process and all marginal distributions are matrix exponential, and this current paper is an extended abstract of [2]. The coupling matrix is constructed from the arrival and the service distributions without any computational effort, and the performance measures (such as waiting times and queue length distributions) are derived directly from its spectrum.