Development and justification of the Power-series algorithm for BMAP -Systems

The applicability of the Power-Series Algorithm is extended to batch Markovian arrival processes and phase-type service time distributions. This is done for systems with a single queue, but the results can readily be extended to models with more queues like fork-join models, networks of queues and polling models. The theoretical justification of the algorithm is improved by showing that in light traffic the steady-state probabilities are analytic functions of the load of the system. For the BMAP/PH/1 queue a recursive algorithm is derived to calculate the coefficients of the power-series expansions of the steady-state probabilities and moments of both the queue-length and the waiting time distribution