Stochastic Process

Recent research has investigated ways in which general probability distributions may be incorporated into stochastic process algebra. These proposals allow the arbitrary use of such distributions, improving expressibility, but in general this makes performance evaluation diicult. Typically, simulation techniques must be employed. We attack the goal of general probability distributions from the opposite direction, using the stochastic phenomenon of insensitivity. In this paper we describe a construction which guarantees the insensitivity of certain concurrently enabled non-connicting stochastic process algebra 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 nd that the model structure we identify has a product form solution which does not match any of those currently known to exist for stochastic process algebra. We highlight our technique with an example drawn from the eld of transaction processing systems. Our analysis uses the stochastic process algebra PEPA, and its associated conventions.