Analisi di modelli ad Agenti Markoviani attraverso l' approssimazione Fluida

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODE) when their indexing parameter grows very large. In this thesis we apply this approximation to study a Markovian Agent models (MAMs). An MAM is formed by different agents, each of which is characterised by an own discrete-state continuous-time Markov chain (CTMC). Therefore we approximate these CTMCs when the number of objects inside the system increases, that is one of the most important difficulties of these models. In particular we study the foraging behaviour of ants, and we show that with this approach we are able to simulate a system with a large number of ants, exceeding the difficulties described in the literature.