The equilibrium-based origin-destination matrix estimation problem

This paper examines a model due to Nguyen for estimating origin-destination (O-D) matrices from observed traffic flows on each network link. It is shown that the previous bilevel optimization models for choosing an O-D matrix can be transformed into single convex programs. Under the condition that the observed link flow pattern is an equilibrium, Nguyen's model is demonstrated to be equivalent to an underspecified system of linear equations with non-negative variables. By exploiting the properties of the system's feasible region, simpler methods, such as a least squares technique, can be used to obtain an O-D matrix that, when user-optimally assigned to the network, reproduces the observed link flows.