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

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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
Title of host publication31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation (IFIP WG 7.3 Performance 2013), Vienna, Austria, September 24-26, 2013
Place of PublicationNew York
PublisherAssociation for Computing Machinery, Inc
Pages53-55
DOIs
Publication statusPublished - 2013

Publication series

NameACM SIGMETRICS Performance Evaluation Review
Number2
Volume41
ISSN (Print)0163-5999

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