We develop accurate approximations for 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 a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.
Bibliographical noteSpecial Issue on the Eighth International Conference on Matrix-Analytic Methods in Stochastic Models
Vatamidou, E., Adan, I., Vlasiou, M., & Zwart, A. P. (2014). Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment. Stochastic Models, 30(4), 598-638. https://doi.org/10.1080/15326349.2014.956227