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Explicit Wiener-Hopf factorizations for the analysis of multidimensional queues. (English) Zbl 0845.60099
Dshalalow, Jewgeni H. (ed.), Advances in queueing. Theory, methods, and open problems. Boca Raton, FL: CRC Press. Probability and Stochastics Series. 293-309 (1995).
Summary: This chapter 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, we present our method for the single-server queue $$GI/G/1$$ and derive solutions for the distributions of actual waiting times and virtual waiting times for $$GI/K_m/1$$ and $$K_m/G/1$$. Next, we consider two classes of multidimensional queues: (i) single-server semi-Markov queues and (ii) multiserver queues with phase-type service times. For both classes we discuss general results as well as explicit solutions for important special cases.
For the entire collection see [Zbl 0836.00013].

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research