Theoretical Computer Science
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Turning back time in Markovian process algebra
Theoretical Computer Science
Compositional reversed Markov processes, with applications to G-networks
Performance Evaluation
A general performance model interchange format
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Automated product-forms with Meercat
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Short communication: Product-forms and functional rates
Performance Evaluation
A unifying approach to product-forms in networks with finite capacity constraints
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Product form approximations for communicating Markov processes
Performance Evaluation
Queueing Systems: Theory and Applications
A numerical algorithm for the solution of product-form models with infinite state spaces
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
State-dependent rates and semi-product-form via the reversed process
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
A PMIF with petri net building blocks
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Performance engineering with product-form models: efficient solutions and applications
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
An initiative for a classified bibliography on G-networks
Performance Evaluation
Hierarchically constructed Petri-nets and product-forms
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Performance engineering and stochastic modelling
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
Bibliography on G-networks, negative customers and applications
Mathematical and Computer Modelling: An International Journal
Analysis of stochastic Petri nets with signals
Performance Evaluation
Product-form results for two-station networks with shared resources
Performance Evaluation
Exploiting product forms solution techniques in multiformalism modeling
Electronic Notes in Theoretical Computer Science (ENTCS)
Sojourn time distributions in tandem batch-networks
ACM SIGMETRICS Performance Evaluation Review
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The reversed compound agent theorem (RCAT) is a compositional result that uses Markovian process algebra (MPA) to derive the reversed process of certain interactions between two continuous time Markov chains at equilibrium. From this reversed process, together with the given, forward process, the joint state probabilities can be expressed as a product-form, although no general algorithm has previously been given. This paper first generalises RCAT to multiple (more than two) cooperating agents, which removes the need for multiple applications and inductive proofs in cooperations of an arbitrary number of processes. A new result shows a simple stochastic equivalence between cooperating, synchronised processes and corresponding parallel, asynchronous processes. This greatly simplifies the proof of the new, multi-agent theorem, which includes a statement of the desired product-form solution itself as a product of given state probabilities in the parallel components. The reversed process and product-form thus derived rely on a solution to certain rate equations and it is shown, for the first time, that a unique solution exists under mild conditions--certainly for queueing networks and G-networks.