  In order to avoid the state space explosion problem encountered in the
quantitative analysis of large scale PEPA models, a fluid approximation
approach has recently been proposed, which results in a set of ordinary
differential equations (ODEs) to approximate the underlying continuous time
Markov chain (CTMC). This paper presents a mapping semantics from PEPA to ODEs
based on a numerical representation scheme, which extends the class of PEPA
models that can be subjected to fluid approximation. Furthermore, we have
established the fundamental characteristics of the derived ODEs, such as the
existence, uniqueness, boundedness and nonnegativeness of the solution. The
convergence of the solution as time tends to infinity for several classes of
PEPA models, has been proved under some mild conditions. For general PEPA
models, the convergence is proved under a particular condition, which has been
revealed to relate to some famous constants of Markov chains such as the
spectral gap and the Log-Sobolev constant. This thesis has established the
consistency between the fluid approximation and the underlying CTMCs for PEPA,
i.e. the limit of the solution is consistent with the equilibrium probability
distribution corresponding to a family of underlying density dependent CTMCs.
