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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approximation
perturbation
statistical analysis
arrivals
evaluation

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Vatamidou, E., Adan, I. J. B. F., Vlasiou, M., & Zwart, A. P. (2013). Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times. Poster session presented at International Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland, Wrocław, Poland.
Vatamidou, E. ; Adan, I.J.B.F. ; Vlasiou, M. ; Zwart, A.P. / Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times. Poster session presented at International Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland, Wrocław, Poland.1 p.
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author = "E. Vatamidou and I.J.B.F. Adan and M. Vlasiou and A.P. Zwart",
year = "2013",
language = "English",
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Vatamidou, E, Adan, IJBF, Vlasiou, M & Zwart, AP 2013, 'Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times', International Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland, Wrocław, Poland, 15/07/13 - 19/07/13.

Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times. / Vatamidou, E.; Adan, I.J.B.F.; Vlasiou, M.; Zwart, A.P.

2013. Poster session presented at International Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland, Wrocław, Poland.

Research output: Contribution to conferencePosterAcademic

TY - CONF

T1 - Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times

AU - Vatamidou, E.

AU - Adan, I.J.B.F.

AU - Vlasiou, M.

AU - Zwart, A.P.

PY - 2013

Y1 - 2013

N2 - 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, andwe exhibit their performance with a numerical study.

AB - 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, andwe exhibit their performance with a numerical study.

M3 - Poster

ER -

Vatamidou E, Adan IJBF, Vlasiou M, Zwart AP. Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times. 2013. Poster session presented at International Conference on Levy Processes, 15-19 July 2013, Wrocław, Poland, Wrocław, Poland.