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## Matrix Product Form Solution For Closed Synchonized Queuing Networks.

Florin, G.;
Natkin, S.
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.

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