Tuning Temporal Features within the Stochastic π-Calculus

The stochastic π-calculus is a formalism that have been shown of interest for modelling systems where the stochasticity and the delay of transitions are important features, such as the biochemical reactions. Commonly, duration of transitions within stochastic π-calculus models follow an exponential random variable. Underlying dynamics of such distributed models are expressed in terms of continuous-time Markov chains and can then be efficiently simulated and model-checked. However, the exponential law comes with a huge variance making difficult the modelling of systems with accurate temporal constraints. In this report, a technique for tuning temporal features within the stochastic π-calculus is presented. This method relies on the introduction of a stochasticity absorption factor by replacing the exponential distribution by the Erlang distribution, that is the sum of exponential random variables. A construction of this stochasticity absorption factor in the classical exponentially distributed stochastic π-calculus is provided. This report also offers tools for manipulating the stochasticity absorption factor and its link with timed intervals for firing transitions. Finally, the model-checking of such designed models is tackled through the support for the stochasticity absorption factor in the stochastic π-calculus translation to the probabilistic model checker PRISM.