A Nonlinear Diffusion Pepa Model Analysis

The stochastic process algebra PEPA is a powerful modelling formalism, which has enjoyed successful applications in performance modelling of computer and communication systems. However, the state-space explosion problem will result from a large scale systems due to its large numbers of components. Both quantitative and qualitative analysis of large model systems suffer from this problem, which has redtricted wider application of the PEPA language. Thus, this paper introduce a more perfect numerical representation scheme and a fluid approximation approach for PEPA to overcome the state-space explosion problems. Base on this, this paper presents an extension of the fluid approximation to the diffusion approximation for a simple PEPA model. The diffusion approximation leads to a reaction diffusion system, which makes up with the spatial or location information while it is missed in the fluid approximation approach. Furthermore, we research the fundamental characteristics of the derived reaction-diffusion equations.In Chapter1, the background, history about the related work and the origin of our qustion are first introduced and the major work of this paper is pesented.Chapter2is devoted to introducing PEPA, explaining the state-space explosion problem and presenting the numerical representation scheme and the fluid approximation approach which results in a set of ordinal differential equations (ODEs).Chaper3will propose an extension from the ODEs to a reaction-diffusion system for a simple PEPA model. Moreover, some fundamental properties about the reaction-diffusion equations such as the existence and uniquness, positivity and convergence of the solution will be established.In Chapter4, the corresponding numerical simulations are given by Matlab to illustrate the main result.Finally the Chapter5will conclude the paper and propose future work.