A New Quantitative Analytical Framework for Large-Scale Distributed Interacting Systems

A Markovian Agent Model (MAM) is a stochastic model that provides a flexible, powerful and scalable way for an- alyzing complex systems of distributed interacting objects. The constituting bricks of a MAM are the Markovian Agents (MA) represented by a finite state continuous time Markov chain (CTMC) whose infinitesimal generator is composed by a fixed component (the local behaviour) and an induced component that depends on the interaction with the other MAs. An additional innovative aspect is that the single MA keeps track of its position so that the overall MAM model is spatial dependent. MAMs are expressed with analytical formulas suited for numerical solution. Extensive applications in different domains have shown the effectiveness of the approach. In the present paper, we propose an example that illustrates how the MAM technique can cope with extremely large state spaces.