Petri nets: an introduction
Performance models of multiprocessor systems
Performance models of multiprocessor systems
IEEE Transactions on Computers
Acyclic fork-join queuing networks
Journal of the ACM (JACM)
Generalization of Queueing Network Product Form Solutions to Stochastic Petri Nets
IEEE Transactions on Software Engineering
A Decomposition Procedure for the Analysis of a Closed Fork/Join Queueing System
IEEE Transactions on Computers
Aggregation and disaggregation through insensitivity in stochastic Petri nets
Performance Evaluation
Mean value technique for closed fork-join networks
SIGMETRICS '99 Proceedings of the 1999 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
Place or Transition Petri Nets
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
On the Product Form Solution for Stochastic Petri Nets
Proceedings of the 13th International Conference on Application and Theory of Petri Nets
PNPM '95 Proceedings of the Sixth International Workshop on Petri Nets and Performance Models
Novel Formulae for GSPN Aggregation
MASCOTS '02 Proceedings of the 10th IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems
A study of the convergence of steady state probabilities in a closed fork-join network
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Closed form approximations for steady state probabilities of a controlled fork-join network
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
On parametric steady state analysis of a generalized stochastic petri net with a fork-join subnet
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
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In this paper an aggregation technique for generalised stochastic Petri nets (GSPNs) possessing synchronised parallel structures is presented. Parallel processes featuring synchronisation constraints commonly occur in fields such as product assembly and computer process communications, however their existence in closed networks severely complicates analysis. This paper details the derivation of computationally-simple closed-form expressions which permit the aggregation of a GSPN subnet featuring a fork-join structure. The aggregation expressions presented in this paper do not require the generation of the underlying continuous time Markov chain of the original net, and do not follow an iterative procedure. The resulting aggregated GSPN accurately approximates the stationary token distribution behaviour of the original net, and this is shown by the analysis of a number of example GSPNs.