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

Authors:
Eleni Vatamidou;Ivo Adan;Maria Vlasiou;Bert Zwart
Affiliations:
EURANDOM and Eindhoven University of Technology;EURANDOM and Eindhoven University of Technology;EURANDOM, CWI, and Eindhoven University of Technology;EURANDOM, CWI, VU University Amsterdam, Georgia Institute of Technology, and Eindhoven University of Technology
Venue:
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)
Year:
2013

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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.