Continuous approximation of collective system behaviour: A tutorial

In this paper we present an overview of the field of deterministic approximation of Markov processes, both in discrete and continuous times. We will discuss mean field approximation of discrete time Markov chains and fluid approximation of continuous time Markov chains, considering the cases in which the deterministic limit process lives in continuous time or discrete time. We also consider some more advanced results, especially those relating to the limit stationary behaviour. We assume a knowledge of modelling with Markov chains, but not of more advanced topics in stochastic processes

Scaling performance analysis using fluid-flow approximation

The fluid interpretation of the process calculus PEPA provides a very useful tool for the performance evaluation of large-scale systems because the tractability of the numerical solution does not depend upon the population levels of the system under study. This paper offers a tutorial on how to use this technique by analysing a case study of a service-oriented application to support an e-University infrastructure