Abstract
Algorithms for matching moments to phase-type distributions are evaluated on the basis of their performance in their intended application, queueing models. The moment-matching algorithms under consideration match two moments to a hyperexponential distribution with balanced means and three moments to a mixture of two Erlang distributions of common order. These algorithms are used to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure approximations is then used to evaluate the moment-matching algorithms. Three performance measures are considered, and attention is focussed on the steady-state mean queue length (number in system) of theGI/M/1 queue. Performance-measure approximations are compared to three-moment bounds and performance-measure values arising from hypothetical approximated distributions.
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Johnson, M.A., Taaffe, M.R. An investigation of phase-distribution moment-matching algorithms for use in queueing models. Queueing Syst 8, 129–147 (1991). https://doi.org/10.1007/BF02412246
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DOI: https://doi.org/10.1007/BF02412246