Matrix product form solution for closed synchronized queuing networks

A new solution is presented for the steady-state probability computing of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). The authors show that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form solution using a matrix and vectors instead of scalars. A prototype solver developed from the preceding result is presented.<>