Point of queue size change analysis of the PH/PH/k system with heterogeneous servers

By observing the points only when the queue size changes, we study the PH/PH/k system with heterogeneous servers. We develop Markov chain set ups that are more efficient than studying the systems at arbitrary times, by reducing the sizes of matrices that need to be computed. Specifically we present procedures for constructing the associated Markov chains so one may use matrix-analytic methods for their analysis. This work is carried out for both the continuous and discrete time cases.