Performance models with product form steady-state distributions

• Authors: Patrice Moreaux
• Venue: VECoS'07 Proceedings of the First international conference on Verification and Evaluation of Computer and Communication Systems
• Year: 2007

Stochastic models of discrete events systems have been proven for many years to be powerful tools for modelling and evaluating the performances of systems like parallel and distributed systems, database systems, communication networks, etc. For the steady-state performance analysis, it is usually necessary to compute the steady-state distribution of a Continuous Time Markov Chain (CTMC) derived from the model. This is the case for Queueing Networks (QN), Stochastic Process Algebras (SPA) and Stochastic Petri Nets (SPN) models. Because of the huge state space describing these complex systems, it is often extremely difficult to compute the exact numerical solution of this CTMC. This situation is obviously even worse with infinite state space models which prevent such a computation. A first attempt to overcome this so called state space explosion problem is to leave the domain of exact solutions. Three main approaches have been and are still developed in this area: discrete-event simulation, approximate methods and computation of bounds.