Stochastic Modelling and Simulation of Mobile Systems

Distributed systems with mobile components are naturally modelled by graph transformations. To formalise and predict properties such as performance or reliability of such systems, stochastic methods are required. Stochastic graph transformations allow the integrated modelling of these two concerns by associating with each rule and match a probability distribution governing the delay of its application. Depending on the nature of these distributions, different techniques for analysis are available, ranging from stochastic model checking for exponential distributions to simulation for systems with general distributions.

In this paper we explore further the second notion, adding a model of global time to avoid the overhead of frequent local clock updates. We also transfer the notion of stochastic graph transformation system from an algebraic to a general background, allowing an arbitrary graph transformation approach to be used for the underlying system. We present a correspondingly extended semantic model, simulation algorithm and tool. The concepts are justified and illustrated by an accident management scenario which requires a model of physical mobility and sophisticated transformation concepts.