The M/M/C queueing system in a random environment

An M/M/C queueing system operating in a Markovian environment is studied. This paper focuses on the stationary behavior and presents the theoretical framework. For a special case, analytical results are derived that are analogous to the classical solutions for the simple M/M/C queue. The elaborate analysis of a specific case is given to illustrate the basic idea of the framework. A technical proof with respect to the existence of d−1 roots is displayed to sustain the corresponding theory.