Structural and fluid analysis for large scale PEPA models - with applications to content adaptation systems
The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the 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. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.