KI-Net Organizational Meeting

Applications of kinetic theory to flows on networks

Christian Ringhofer

Arizona State University

Kinetic theory is essentially about the random movement of particles (agents) in an environment. Traditionally (going back to the work of Maxwell and Boltzmann) this environment is given by a continuous three dimensional space (R^3). In this talk, we will present novel applications of kinetic theory in a more complex topology, given by flows on arbitrarily complex networks. The main goal of a kinetic theory is to reduce the dimensionality of the problem to a manageable size by removing additional dimensions of the problem, using long time (or ensemble) averages, using entropy estimates to guarantee validity of the reduced model. In the application to flows on networks, this is complicated by the, often nontrivial, topology of the network. In this talk we will discuss some of the issues (and open problems) of applying kinetic theory to multi agent models for flows on networks. Applications will include the spread of rumors in social networks, the dynamics of product flow in production networks, the movement of passengers in transportation networks, and the movement of data in massively parallel computing environments.