Alexandros Sopasakis
Centre for Mathematics
Lund University
Lund
A novel microscopic stochastic lattice-free process is developed
and presented. The stochastic process is considered in order to resolve
shortcomings due to finite size effects when considering lattice based
models. The effect of the dynamics on the model parameters can be
considerable especially when equilibrium is not certain. We examine how
information theory can be applied in resolving the dynamics and obtaining
the needed parameter values from available data.
Specifically we develop two different tools, the Relative Entropy Rate and
the Fisher Information Matrix whose task is to reconstruct the Markov
Chain and emulate the dynamics from available but incomplete data through
Monte Carlo simulations.
We demonstrate this process by simulating a problem in vehicular traffic.
In that respect a look-ahead potential is employed and an anisotropic
simple exclusion process (ASEP) is created which moves particles in only
one direction. The process is implemented using a kinetic Monte Carlo
method and contrasted against other similar "state of the art"
lattice-based approaches in that area. We present concrete results under
rush-hour, traffic data from highway US-101 in Los Angeles, California.