Poisson Queues with Markov Modulated Service Rates

In this paper we investigate an M/MM/1 queueing system that makes transitions between two service rates 'S(slow) and F(fast)' only at service completion epochs. Switching between these 'S and F' states occurs according to an embedded Markov chain rule. Both inter arrival times and service times follow exponential distributions. We also discuss an extension for an M/MM/1/(0, N] ∪ (N, ∞) system. Under steady state conditions, the stationary probability distribution for the system size is obtained by spectral expansion method. To exemplify the tractability of the dynamics of the switching probabilities on the offered work load and the mean waiting time, we provide numerical illustrations.