Abstract
The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling is usually based on dynamic traffic models, whose main input is a dynamic origin–destination (OD) matrix that describes the time dependencies of travel patterns; this is one of the reasons that have fostered large amounts of research on the topic of estimating OD matrices from the available traffic information. The complexity of the problem, its underdetermination, and the many alternatives that it offers are other reasons that make it an appealing research topic. The availability of new traffic data measurements that were prompted by the pervasive penetration of information and communications technology (ICT) applications offers new research opportunities. This study focused on GPS tracking data and explored two alternative modeling approaches regarding how to account for this new information to solve the dynamic origin–destination matrix estimation (DODME) problem, either including it as an additional term in the formulation model or using it in a data-driven modeling method to propose new model formulations. Complementarily, independently of the approach used, a key aspect is the quality of the estimated OD, which, as recent research has made evident, is not well measured by the conventional indicators. This study also explored this problem for the proposed approaches by conducting synthetic computational experiments to control and understand the process.
Highlights
The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling, namely, in traffic management and information systems, especially in urban areas and in real-time applications, stimulate the research interest in dynamic traffic models
Since the relationships between the travel times and the estimated origin-to-destination (OD) matrices cannot be set up in an analytical form, Section 3 proposes resorting to a derivative-free approach to solve the problem, the stochastic perturbation stochastic approximation (SPSA), and Section 4 proposes a variant that involves splitting the gradient into two components: one that is analytical for those terms of the objective function whose gradient can be computed analytically, while the other was approximated using SPSA
The dynamic assignment matrix A(X) = ailtjr is the result of the mapping and ailtjr represents the proportion of the OD flow that departs from origin i in period r and goes to destination j that crosses link l ∈ L ⊆ L in period t ≥ r. These analytical approaches to the dynamic origin–destination matrix estimation (DODME) problem show that all of them rely on the availability of the assignment matrix A = ailtjr for the various time intervals, which are calculated at the lower level of the bi-level problem using the dynamic traffic assignment at each time interval
Summary
The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling, namely, in traffic management and information systems, especially in urban areas and in real-time applications, stimulate the research interest in dynamic traffic models. The main components of the core engine of these systems use a dynamic origin-to-destination (OD) matrix that describes the time dependencies of travel patterns in urban scenarios as the main input This is a relevant reason for drawing the continuous attention of researchers to the dynamic origin–destination matrix estimation (DODME) problem, as a quick look at recent publications shows [1,2,3,4,5,6,7,8,9,10,11]. Since the relationships between the travel times and the estimated origin-to-destination (OD) matrices cannot be set up in an analytical form, Section 3 proposes resorting to a derivative-free approach to solve the problem, the stochastic perturbation stochastic approximation (SPSA), and Section 4 proposes a variant that involves splitting the gradient into two components: one that is analytical for those terms of the objective function whose gradient can be computed analytically, while the other was approximated using SPSA.
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