Design of the feasible region for demand values in a congested urban road network

The present paper is devoted to the study of the feasible region for demand values in a congested urban road network. Travel demand estimation is considered to be the inverse of the traffic assignment problem, formulated as a congestion game. We show that the corresponding estimation problem has the form of a bilevel optimization program with a weak-defined feasible set of upper-level solution variables (even a trivial solution leads to the global optimum). However, we are lucky to prove that for any congested urban road network there is a polygon in the space of demand values, which significantly narrows the area of optimal solution search for the considering bilevel problem. Moreover, such a polygon appears to be easily designed for an arbitrary road network, using solely observed congestion as input data. Thus, the findings obtained in the paper contribute to the development of tools for travel demand estimation in a congested urban road network.