A product-form approximation method for general closed queueing networks with several classes of customers

This paper presents a new method for obtaining approximate solutions of general closed queueing networks with several classes of customers. The idea is to associate with each class of customers, a single-class closed queueing network with load-dependent exponential service stations. For each single-class network associated with a particular class of customers, the interactions with the customers belonging to other classes are taken into account in the estimation of the load-dependent service rates. These parameters are obtained by analyzing each station in isolation under the assumption that the arrival process of each class is a state-dependent Markovian process. An iterative algorithm is used to determine the unknown parameters. The main computational charge of the method is due to the analysis of the stations in isolation. A class aggregation technique is proposed that significantly reduces the complexity of these analyses. Although the principle of the method is fairly general, in this paper we only consider queueing networks with general service time distributions and either FIFO or priority disciplines. Numerical results are provided that show that this method is fairly accurate, even when the class aggregation technique is used.