Product form in networks of queues with batch arrivals and batch services
Queueing Systems: Theory and Applications
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
Product form solution for a class of PEPA models
IPDS '98 Proceedings of the third IEEE international performance and dependability symposium on International performance and dependability symposium
IEEE Transactions on Software Engineering
Product form solution for an insensitive stochastic process algebra structure
Performance Evaluation - Unified specification and performance evaluation using stochastic process algebras
Performance Evaluation of Buffer Policies with Stochastic Automata Networks
Proceedings of the IFIP TC6 Task Group/WG6.4 International Workshop on Performance of Communication Systems: Modelling and Performance Evaluation of ATM Technology
Compositional reversed Markov processes, with applications to G-networks
Performance Evaluation
PEPS2007 - Stochastic Automata Networks Software Tool
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Product form for stochastic automata networks
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Discrete Time Markov Chains Competing over Resources: Product Form Steady-State Distribution
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Short communication: Product-forms and functional rates
Performance Evaluation
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We consider first discrete-time Markov chains (DTMCs) in competition over a set of resources. We build a multidimensional Markov chain based on the Cartesian product of the state space and on competition rules between the chains. We then generalize this approach to DTMCs with collaboration between components. The competition and the collaboration between chains simply assume that when a resource is owned by a component (or when a component is in a specific subset of states) it affects the transition probabilities of the other components of the chain. We prove that under some competition rules the steady-state distribution of the multidimensional chain has a product form. This work extends Boucherie's theory based on continuous-time chains. The proof relies on algebraic properties of the generalized tensor product defined by Plateau and Stewart.