Stochastic Simulation of Graph Transformation Systems

Stochastic graph transformation systems (SGTS) [1] support integrated modelling of architectural reconfiguration and non-functional aspects such as performance and reliability. In its simplest form a SGTS is a graph transformation system (GTS) where each rule name is associated with a rate of an exponential distribution governing the delay of its application. However, this approach has its limitations. Model checking with explicit states does not scale well to models with large state space. Since performance and reliability properties often depend on the behaviour of large populations of entities (network nodes, processes, services, etc.), this limitation is significant. Also, exponential distributions do not always provide the best abstraction. For example, the time it takes to make a phone call or transmit a message is more likely to follow a normal distribution. To counter these limitations, generalised SGTS [2] allow for general distributions dependent on rule match pairs (rather than just rule names). Generalised semi-Markov processes provide a semantic model for such systems, supporting stochastic simulation. Rather than model checking, simulations provide a more flexible tradeoff between analysis effort and confidence in the result and so allow to verify soft performance targets in large-scale systems. We present a tool called GraSS, for Graph-based Stochastic Simulation, to enable the analysis of such processes. The tool is developed in Java-Eclipse, extending the VIATRA model transformation plugin with a control based on the SSJ library for Stochastic Simulation in Java. The main performance challenge, in finding, at each state of the simulation, all matches for all rules, is alleviated by VIATRA’s RETE-style incremental pattern-matching approach [3], which stores precomputed matching information and updates it during transformation. We illustrate and evaluate the application of the tool by the simulation of the original P2P reconfiguration model as well as an improved and scaled-up version.