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.
|Titel||31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation (IFIP WG 7.3 Performance 2013), Vienna, Austria, September 24-26, 2013|
|Plaats van productie||New York|
|Uitgeverij||Association for Computing Machinery, Inc|
|Status||Gepubliceerd - 2013|
|Naam||ACM SIGMETRICS Performance Evaluation Review|
|ISSN van geprinte versie||0163-5999|
Vatamidou, E., Adan, I. J. B. F., Vlasiou, M., & Zwart, B. (2013). Corrected phase-type approximations for the workload of the MAP/G/1 queue with heavy-tailed service times. In 31st International Symposium on Computer Performance, Modeling, Measurements and Evaluation (IFIP WG 7.3 Performance 2013), Vienna, Austria, September 24-26, 2013 (blz. 53-55). (ACM SIGMETRICS Performance Evaluation Review; Vol. 41, Nr. 2). Association for Computing Machinery, Inc. https://doi.org/10.1145/2518025.2518036