Encoding G-Networks into the Stochastic Process Algebra PEPA

Abstract

In my thesis I study models of G-Networks, encoding them into the Stochastic Process Algebra PEPA. Up to now there was the general belief that G-Networks could not be caught by a traditional stochastic process algebra and my thesis demonstrates the opposite. G-Networks are a specific case in the queues theory and are used to describe, for example, a computer, a network or communication systems. The encoding I propose allows one to analyze the dynamic behavior and then the performance of those networks using the existing tools for PEPA. These analysis are useful in real-life modern systems, whose complexity and size are indeed very large and the corresponding models are huge and complex. With the aid of the stochastic process algebra PEPA, we can apply a compositional approach to perform not only qualitative analysis but also quantitative ones. This approach consists in decomposing the entire system into small and more simple subsystems. The main idea is that "The smaller they are, the more easily they can be modeled and consequently the more easily the analysis can be". In the thesis I will first analyze the current literature on these topics, then model some G-Networks in PEPA proving that my models are coherent with the original analyzed G-Networks. Finally I apply the product form theorem of Harrison to my model and give some guidelines about how a G-Network can be encoded in PEPA.