Model reduction for reduced order estimation in traffic models

This paper is concerned with model reduction for a complex Markov chain using state aggregation. The work is motivated in part by the need for reduced order estimation of occupancy in a building during evacuation. We propose and compare two distinct model reduction techniques, each of which is based on the potential matrix for the Markov semigroup. The first method is based on spectral graph partitioning where the weights are defined by the entries of the potential matrix. The second approach is based on aggregating states with similar long term uncertainty, where uncertainty is captured using conditional entropy. It is shown that entropy can be conveniently expressed in terms of the potential matrix. In application to the building model, the entries of the potential matrix correspond to the mean time an individual occupies a given cell. Numerical results are described, including a simulation study of the reduced order estimator.