Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times

E. Vatamidou, I.J.B.F. Adan, M. Vlasiou, B. Zwart

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Abstract

In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a small relative error. Motivated by statistical analysis, we assume that the service times are a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive our approximations as a sum of the workload distribution of the MAP/PH/1 queue and a heavytailed component that depends on the perturbation parameter. We refer to our approximations as corrected phase-type approximations, and we exhibit their performance with a numerical study. Keywords: Markovian Arrival Process (MAP); Workload distribution; Heavy-tailed service times; Tail asymptotics; Perturbation analysis.
Original languageEnglish
Number of pages3
JournalSIGMETRICS performance evaluation review
Volume41
Issue number2
DOIs
Publication statusPublished - 2013
Externally publishedYes

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