Stochastic Bounding of PEPA Models

Stochastic bounds are a valuable tool for analysing large Markov chains. If the chain is too large to solve, we can construct upper and lower bounding chains that are easier to solve, and whose steady state solutions will bound that of the original chain. In [Fourneau et al, 2004], an algorithm is presented to construct lumpable bounding chains, which can be aggregated and solved. In a stochastic process algebra, models are constructed compositionally, and so a natural extension of the above work is to construct bounds compositionally. We show how to do this for a class of models in the Performance Evaluation Process Algebra (PEPA). We present the necessary conditions for component bounds to be preserved under composition, and outline how to algorithmically compute these.