New Look at Finite Single Server Queue with Poisson Input and Semi-Markov Service Times

Krzysztof Rusek; Zdzisław Papir

paper

New Look at Finite Single Server Queue with Poisson Input and Semi-Markov Service Times

arXiv:1806.05462

Abstract

The mathematics of the finite single server queue with Poisson input and semi-Markov service times( $M / S M /1/ b$ ) is similar to that used for $B M A P / G /1/ b$ systems. This observation results in new analytical formulas for a queue size in the $M / S M /1/ b$ system. Both stationary and the transient solutions are considered