Explicit Wiener-Hopf factorizations for the analysis of multidimensional queues

This article discusses Wiener-Hopf factorizations for multidimensional queues. For the analysis of these models, the classical (scalar) Wiener-Hopf factorization for single-server queues is generalized to the matrix case. First, the paper presents the present method for the single-server queue GI/G/1 and derive solutions for the distributions of actual waiting times and virtual waiting times for GI/Km/1 and Km/G/1. Next, it considers two classes of multidimensional queues: (i) Single-server semi-Markov queues and (ii) Multiserver queues with phase-type service times. For both classes the paper discusses general results as well as explicit solutions for important special cases.