Embedded Processes in Stochastic Petri Nets
IEEE Transactions on Software Engineering
A compositional approach to performance modelling
A compositional approach to performance modelling
Concurrency control: methods, performance, and analysis
ACM Computing Surveys (CSUR)
Theoretical Computer Science
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
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
The theory of interactive generalized semi-Markov processes
Theoretical Computer Science
IEEE Transactions on Software Engineering
Towards Performance Evaluation with General Distributions in Process Algebras
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
On Petri nets with deterministic and exponentially distributed firing times
Advances in Petri Nets 1987, covers the 7th European Workshop on Applications and Theory of Petri Nets
Extended Stochastic Petri Nets: Applications and Analysis
Extended Stochastic Petri Nets: Applications and Analysis
Exploiting structure in solution: decomposing compositional models
Lectures on formal methods and performance analysis
Turning back time in Markovian process algebra
Theoretical Computer Science
Collaboration of discrete-time Markov chains: Tensor and product form
Performance Evaluation
Product form approximations for communicating Markov processes
Performance Evaluation
Structural analysis for stochastic process algebra models
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
Operational semantics for product-form solution
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Operational semantics for product-form solution
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
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Recent research has investigated ways in which generally distributed random variables may be incorporated into stochastic process algebra (SPA). These proposals allow the arbitrary use of such variables, improving expressibility, but in general this makes performance evaluation difficult. Typically, simulation techniques must be employed. We attack the goal of generally distributed random variables from the opposite direction, using the stochastic property of insensitivity. In this paper we describe a construction which guarantees the insensitivity of certain concurrently enabled non-conflicting SPA activities. We give a derived combinator for constructing process algebra models. Use of this combinator guarantees that the stochastic process underlying the model is insensitive to a particular set of activities. Therefore, the user need not assume these activities are exponentially distributed, yet may still use familiar Markovian techniques to solve the model. We find that the model structure we identify has a product form solution and the criteria we list do not match any of those currently proposed for SPA. We highlight our technique with an example drawn from the field of transaction processing systems. Our analysis uses the SPA PEPA, and its associated conventions.