Matrix-Geometric Solution for Finite Capacity Queues with Phase- Type Distributions.
Makowski, Armand M.
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This paper presents a class of Quasi-Birth-and-Death processes with finite state space for which the invariant probability vector is found to admit a matrix-geometric representation. The corresponding rate matrix is given explicitly in terms of the model parameters, and the resulting closed-form expression is proposed as a basis for efficient calculation of the invariant probability vector. The framework presented in this paper provides a unified approach to the study of several well-known queueing system.