Approximate Analysis of Queueing Networks with Markovian Arrival Processes and Phase Type Service Times

Open queueing networks with Markovian arrival processes and phase type service times are considered. A technique is proposed for the specification of the models. Using such a specification, a Markov chain can be generated automatically. Furthermore, this description can be used immediately for simulation. An approximate disaggregation--aggregation technique for finite state Markov chains is applied. Thus large models with many states can be solved, so large that the state probabilities could neither be stored nor calculated in any computer. Accurate approximations are obtained with different degrees of accuracy, depending on the investigated computational effort. 1 Introduction Queueing networks are widely used in the stochastic modeling of computer, communication, and manufacturing systems. For the restricted class of separable queueing networks, efficient evaluation algorithms are known but if the models are more general exact analysis is expensive or even impossible due to computat..