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, signicant 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 heavy-tailed 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.
Original languageEnglish
Number of pages1
Publication statusPublished - 2013
EventInternational Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland: Theory and Applications - Wrocław, Poland
Duration: 15 Jul 201319 Jul 2013
Conference number: 7
http://bcc.impan.pl/13Levy/

Conference

ConferenceInternational Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland
CountryPoland
CityWrocław
Period15/07/1319/07/13
Internet address

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