This paper presents an approximation via an N-environments diffusion model to a queueing system with Markov modulated Poisson process (MMPP) arrivals and general service time distribution. There are, in general, no closed form expressions for the waiting time distribution of queueing systems with MMPP arrivals. The authors propose an approximate closed form solution for the (m)th moment of the waiting time distribution with two-states MMPP arrivals. They also propose an algorithm for the approximate solution of one server queueing systems with N states MMPP arrivals. The accuracy of this approximation is shown to be less than 3% relative error through numerical examples. [In Japanese.]
