Research of M/M/C +M queues with Markov modulated service processes

In this paper, we consider queues with Markov modulated service processes (MMSP) whose service rates change according to an external environment that governed by Markov process. We established the M/M/C +M queueing models where servers operate in a Markov environment and customers are allowed to abandon service (+M). Randomly occurring server breakdown induces service rates change with time. We obtain a matrix differential equation about the generation function in different server states in steady state and present how to get the expected number of customers in the system. Through some special cases we verified the correctness of this model. So this can be as a supplement of previous work.