In: PNPM89. Proceedings of the Third International Workshop On Petri Nets and Performance Models, 1989, Kyoto, Japan, pages 29-37. Los Alamitos, CA, USA: IEEE Computer Society Press, 1990.
Abstract: This paper presents a new solution for the steady state probability computing of closed synchronized queuing networks which is a particular Markov stochastic Petri net (a bounded and monovaluated Petri net with a stongly connected reachability graph and constant firing rates). The paper shows that the steady state probability distribution can be expressed using matrix products. The solution is similar to the Gordon-Newell product form using matrix and vectors instead of scalars. A prototype solver developed from the preceding result is presented.
Keywords: matrix product form solution; closed synchonized queueing network; steady state probability; Markov stochastic net; reachability graph.