Performance models of multiprocessor systems
Performance models of multiprocessor systems
G-networks with multiple classes of negative and positive customers
Theoretical Computer Science
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
A BCMP extension to multiserver stations with concurrent classes of customers
SIGMETRICS '86/PERFORMANCE '86 Proceedings of the 1986 ACM SIGMETRICS joint international conference on Computer performance modelling, measurement and evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Performance Evaluation
Multiple Class G-Networks with Jumps back to Zero
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Turning back time in Markovian process algebra
Theoretical Computer Science
Compositional reversed Markov processes, with applications to G-networks
Performance Evaluation
Product-form and stochastic Petri nets: a structural approach
Performance Evaluation
Separable equilibrium state probabilities via time reversal in Markovian process algebra
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Deficiency Zero Petri Nets and Product Form
PETRI NETS '09 Proceedings of the 30th International Conference on Applications and Theory of Petri Nets
Analysis and Synthesis of Computer Systems: Texts)
Analysis and Synthesis of Computer Systems: Texts)
G-networks with synchronised arrivals
Performance Evaluation
Computing the steady-state distribution of g-networks with synchronized partial flushing
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
A queueing network model with catastrophes and product form solution
Operations Research Letters
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Product-form models facilitate the efficient analysis of large stochastic models and have been sought after for some three decades. Apart from the dominating work on queueing networks, some product-forms were found for stochastic Petri nets (SPNs) that allow fork-join constructs and for queueing networks extended to include special customers called signals, viz. G-networks. We appeal to the Reversed Compound Agent Theorem (RCAT) to prove new product-form solutions for SPNs in which there are special transitions, the firings of which act in a similar way to signals in G-networks, but which may be generated by synchronised firings (or service completions) and may affect several places simultaneously. We show that SPNs with signals are strict generalisations of G-networks with negative customers, triggers and catastrophes, and illustrate with copious examples.