Performance evaluation of closed tandem queueing networks with finite buffers

In this paper we propose a new approximation method for the analysis of closed tandem queueing networks with general service times and blocking-after-service. The principle of the method is to decompose the original network consisting of M servers into a set of M subsystems, each subsystem consisting of two servers separated by a finite buffer. In order to determine the distributions of the service times of the two servers of each subsystem, we express relationships among distributions pertaining to the different subsystems. We then propose to use a two-moment approximation. The population constraint of the closed network is taken into account by prescribing that the sum of the average buffer sizes of the subsystems is equal to the number of the customers of the network. We end up with a set of equations that characterize the unknown parameters of the service time distributions of the servers of the subsystems. An iterative procedure is then used to determine these unknown parameters. Numerical results show that the new method is quite accurate.