2014/05/01 by Eleni Vatamidou, Ivo J. B. F. Adan, Vatamidou, Eleni +5 · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1405.0138
Received the Marcel Neuts Student Paper Award at the 8th International Conference on Matrix Analytic Methods in Stochastic Models 2014
arxiv created 2014/05/01 · arxiv updated 2014/05/02
Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly 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 bounded relative error. 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 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.