Computational Aspects of the Workload Distribution in the MMPP/GI/1 Queue

We show how the analysis of Markov modulated rate processes can be used to address the problem of computing the distribution of W, the stationary workload in the MMPP/GI/1 queue. Using the results of papers by Anick et al. (1982); Mitra (1988); and Elwalid et al. (1991), we present the decomposition properties of the Laplace transform of W and efficient computational algorithms for computing its distribution. The techniques are also applied to compute the bounds on the distribution of W developed by Liu et al. (see JACM, vol.44, no.2, p.366-94, 1997). Numerical results illustrating the usefulness of the methods are given for the case of the superposition of independent, nonidentical sources.