Towards a synchrony theory for P/T nets
Concurrency and nets: advances in Petri nets
Closed queueing networks with batch services
Queueing Systems: Theory and Applications
Markovian network processes: congestion-dependent routing and processing
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Embedded Processes in Stochastic Petri Nets
IEEE Transactions on Software Engineering
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
The mathematics of product form queuing networks
ACM Computing Surveys (CSUR)
GreatSPN 1.7: graphical editor and analyzer for timed and stochastic Petri nets
Performance Evaluation - Special issue: performance modeling tools
A compositional approach to performance modelling
A compositional approach to performance modelling
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Computational algorithms for closed queueing networks with exponential servers
Communications of the ACM
Approximate Throughput Computation of Stochastic Marked Graphs
IEEE Transactions on Software Engineering
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 Analysis of Multi-Class Synchronized Closed Queueing Networks
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Complexity Results for 1-safe Nets
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
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
Structural techniques and performance bounds of stochastic Petri net models
Advances in Petri Nets 1992, The DEMON Project
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
The research queueing package: past, present, and future
AFIPS '82 Proceedings of the June 7-10, 1982, national computer conference
Deficiency Zero Petri Nets and Product Form
PETRI NETS '09 Proceedings of the 30th International Conference on Applications and Theory of Petri Nets
Synthesis and analysis of product-form petri nets
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
Analysis of stochastic Petri nets with signals
Performance Evaluation
Synthesis and Analysis of Product-form Petri Nets
Fundamenta Informaticae - Applications and Theory of Petri Nets and Other Models of Concurrency, 2011
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Stochastic Petri nets (SPNs) with product-form solution are nets for which there is an analytic expression of the steady-state probabilities with respect to place markings, as it is the case for product-form queueing networks with respect to queue lengths. The most general kind of SPNs with product-form solution introduced by Coleman et al. (and denoted here by S@P-nets) suffers a serious drawback: the existence of such a solution depends on the values of the transition rates. Thus since their introduction, it is an open question to characterize S@P-nets with product-form solution for any values of the rates. A partial characterization has been obtained by Henderson et al. However, this characterization does not hold for every initial marking and it is expressed in terms of the reachability graph. In this paper, we obtain a purely structural characterization of S@P-nets for which a product-form solution exists for any value of probabilistic parameters of the SPN and for any initial marking. This structural characterization leads to the definition of S@P^2-nets (Stochastic Parametric Product-form Petri nets). We also design a polynomial time (with respect to the size of the net structure) algorithm to check whether a SPN is a S@P^2-net. Then, we study qualitative properties of @P-nets and @P^2-nets, the non-stochastic versions of S@P-nets and S@P^2-nets: we establish two results on the complexity bounds for the liveness and the reachability problems, which are central problems in Petri nets theory. This set of results complements previous studies on these classes of nets and improves the applicability of product-form solutions for SPNs.