Exact analysis of queueing networks with multiple job classes and blocking-after-service

Two models of closed queueing networks with blocking-after-service and multiple job classes are analyzed. The first model is a network with N stations and each station has either type II or type III. The second model is a star-like queueing network, also called a central server model, in which the stations may have either type I or type IV, with the condition that the neighbors of these stations must be of type II or type III such that blocking will be caused by only this set of station types. Exact product form solutions are obtained for the equilibrium state probabilities in both models. Formulae for performance measures such as throughput and the mean number of jobs are also derived.