Product form solution for an insensitive stochastic process algebra structure
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.
product form solution insensitivity stochastic process algebra generally distributed random variables