Average density detectability in traffic networks using virtual road divisions

Abstract

In this paper, we demonstrate the existence of a reduced-order open-loop observer to estimate the average density in a region of a large scale traffic network. We show that traffic networks are not generally average detectable, but that it is possible to find a virtual representation of the network using inhomogeneous road divisions such that the observer converges to the true values. We express the conditions for the required number of cells per road and their lengths such that the system is average detectable in terms of the network’s topology and physical parameters. Moreover, we propose a method to calculate these divisions and give asymptotic bounds on the quality of the approximations.