One-Level Joint Formulation of the Travel Demand Estimation Problem Under User Equilibrium as a Non-Linear Equation System

For decades, Origin Destination (OD) travel demand has played a vital role in traffic planning and operation. Transport planners use OD demand to evaluate the impact of various strategic transportation plans. Reliable OD estimation becomes increasingly useful for many real-time traffic applications, such as the online evaluation of various Intelligent Transportation System (ITS) deployment alternatives or the generation of real-time route guidance via a Dynamic Traffic Assignment. Obtaining an accurate OD matrix is extremely difficult and costly via traditional survey-based methods. Estimating OD demand from traffic data has become one of the most fundamental problems in the transportation Engineering domain and has been extensively studied over the years. The most famous approach for OD demand estimation using traffic data is through the bi-level optimization framework. The bi-level approach considering User Equilibrium constraints is computationally challenging for large-scale networks, which prevents the OD estimation from being scalable. Given this, this paper develops a new single-level OD estimation method that incorporates Stochastic User Equilibrium constraints. The single-level approach would be more efficient and scalable than a bi-level and gives us the possibility to integrate multiple traffic data sources in the estimation process. The single-level formulation proposed in this paper is based on the multinomial logit model. A Jacobian free Trust Region algorithm is proposed to solve this formulation. Numerical experiments are conducted on a small and large laboratory network, along with sensitivity analysis on how many parameters of demand models are relevant to calibrate against how much independent information we have in terms of traffic data. Experiments carried out are based on the following rationale: given a true OD matrix, the corresponding link flows are estimated through a Multinomial Logit Equilibrium assignment. Then, given a random perturbation of the true OD demand, checking the capability of different subsets of link flows and travel time (speed) to reproduce the starting true demand. In general, results indicates that the new single-level formulation, in conjunction with the proposed solution algorithm, can achieve high accuracy, while being computationally efficient, if the number of link counts (number of equations) that we are using for the estimation is roughly equal to the number of unknowns.