Simulation and Estimation of Traffic Dynamics on a Graph

This paper considers simulation and estimation with cellular automata based stochastic models of traffic of agents on a graph. For the purposes of Bayesian estimation, an inhomogeneous hidden Markov model is abstracted from the cellular automata model. The uncertainty-based metric of relative entropy is proposed to assess performance with the estimation. This metric is used to compare the actual distribution of agents on a graph to the estimated distribution. Simulations show that the location of sensor arrays on the graph influences not only the effectiveness of the estimator, but also the time-window in which it best estimates the actual distribution. By distributing these sensors intelligently within the graph, one can obtain a good estimate over the entire simulation time-span.