Discrete Time Stochastic Petri Nets
IEEE Transactions on Software Engineering
Embedded Processes in Stochastic Petri Nets
IEEE Transactions on Software Engineering
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
The Distribution of Queuing Network States at Input and Output Instants
Journal of the ACM (JACM)
The Operational Analysis of Queueing Network Models
ACM Computing Surveys (CSUR)
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
Approximate Mean Value Analysis for Stochastic Marked Graphs
IEEE Transactions on Software Engineering - Special issue: best papers of the sixth international workshop on Petri nets and performance models (PNPM'95)
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Structural Characterization and Qualitative Properties of Product Form Stochastic Petri Nets
ICATPN '01 Proceedings of the 22nd International Conference on Application and Theory of Petri Nets
On the success of stochastic Petri nets
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
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We consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition's input bag and just before tokens are entered into the places specified by the same transition's output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state. This is the basis for the development of a Mean Value Analysis algorithm for the computation of performance indices for Product-Form Stochastic Petri Nets.