A Single-Server Queue with Markov Modulated Service Times
We study an M/MMPP/1 queuing system, where the arrival process is Poisson and service requirements are Markov modulated. When the Markov Chain modulating service times has two states, we show that the distribution of the number-in-system is a superposition of two matrix-geometric series and provide a simple algorithm for computing the rate and coefficient matrices. These results hold for both finite and infinite waiting space systems and extend results obtained in Neuts  and Naoumov . Numerical comparisons between the performance of the M/MMPP/1 system and its M/G/1 analogue lead us to make the conjecture that the M/MMPP/1 system performs better if and only if the total switching probabilities between the two states satisfy a simple condition. We give an intuitive argument to support this conjecture.
In order to set up a list of libraries that you have access to,
you must first login
or sign up.
Then set up a personal list of libraries from your profile page by
clicking on your user name at the top right of any screen.