A Theory of Communicating Sequential Processes
Journal of the ACM (JACM)
Transient analysis of acyclic markov chains
Performance Evaluation
Performance and reliability analysis of computer systems: an example-based approach using the SHARPE software package
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Automated compositional Markov chain generation for a plain-old telephone system
Science of Computer Programming
Semi-numerical transient analysis of Markov models
ACM-SE 33 Proceedings of the 33rd annual on Southeast regional conference
Exploiting structure in solution: decomposing compositional models
Lectures on formal methods and performance analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Structural analysis for stochastic process algebra models
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
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A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the complete global state space of the CTMC. The method works for a fixed number of sequential processes running in parallel and which all synchronize on the same global set of actions. The behaviour of the processes is expressed by the embedded Markov chain of a semi-Markov process and by distribution functions (exponomials) which describe the times between synchronizations. The solution method is exact, hence, the state space explosion problem for this class of processes has been solved. A distributed implementation of the solution technique is straightforward.