We develop accurate approximations of the delay distribution of the MArP/G/1 queue that capture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.
|Titel||Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014|
|Plaats van productie||s.l.|
|Status||Gepubliceerd - 2014|
Vatamidou, E., Adan, I. J. B. F., Vlasiou, M., & Zwart, A. P. (2014). Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. In Proceedings of the 8th International Conference on Matrix-Analytic Methods in Stochastic Models (MAM8), Kerala, India, January 6-10, 2014 (blz. 113-141). s.n.. http://arxiv.org/pdf/1405.0138