Embedded Processes in Stochastic Petri Nets
IEEE Transactions on Software Engineering
Arrival theorems for product-form stochastic Petri nets
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
Mean value analysis of stochastic Petri nets
Performance Evaluation
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
The Distribution of Queuing Network States at Input and Output Instants
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Aggregation Methods in Exact Performance Analyssi of Stochastic Petri Nets
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Complexity Results for 1-safe Nets
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
Decidability and Complexity of Petri Net Problems - An Introduction
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net
Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets
Exponential space complete problems for Petri nets and commutative semigroups (Preliminary Report)
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
The model ofSto chastic Petri nets (SPN) with a product form solution (Π-net) is a class ofnets for which there is an analytic expression of the steady state probabilities w.r.t. markings, as for product form queueing networks w.r.t. queue lengths. In this paper, we prove new important properties of this kind of nets. First we provide a polynomial time (w.r.t. the size ofthe net structure) algorithm to check whether a SPN is a Π-net. Then, we give a purely structural characterization of SPN for which a product form solution exists regardless the particular values ofprobabilistic parameters ofthe SPN. We call such nets /Π-nets. We also present untimed properties of Π-nets and /Π-nets such like liveness, reachability, deadlock freeness and characterization of reachable markings. The complexity of the reachability and the liveness problems is also addressed for Π-nets and /Π-nets. These results complement previous studies on these classes ofnets and improve the applicability of Product Form solutions.