A Two-Stage Algorithm for Origin-Destination Matrices Estimation Considering Dynamic Dispersion Parameter for Route Choice.

Yong Wang,Ke Gong,Xiaolei Ma,Maozeng Xu,Yong Liu,Yinhai Wang,Kristian C Henricakson,Zhong-Ke Gao

doi:10.1371/journal.pone.0146850

Yong Wang, Ke Gong + Show 6 more

Open Access

https://doi.org/10.1371/journal.pone.0146850

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Abstract

This paper proposes a two-stage algorithm to simultaneously estimate origin-destination (OD) matrix, link choice proportion, and dispersion parameter using partial traffic counts in a congested network. A non-linear optimization model is developed which incorporates a dynamic dispersion parameter, followed by a two-stage algorithm in which Generalized Least Squares (GLS) estimation and a Stochastic User Equilibrium (SUE) assignment model are iteratively applied until the convergence is reached. To evaluate the performance of the algorithm, the proposed approach is implemented in a hypothetical network using input data with high error, and tested under a range of variation coefficients. The root mean squared error (RMSE) of the estimated OD demand and link flows are used to evaluate the model estimation results. The results indicate that the estimated dispersion parameter theta is insensitive to the choice of variation coefficients. The proposed approach is shown to outperform two established OD estimation methods and produce parameter estimates that are close to the ground truth. In addition, the proposed approach is applied to an empirical network in Seattle, WA to validate the robustness and practicality of this methodology. In summary, this study proposes and evaluates an innovative computational approach to accurately estimate OD matrices using link-level traffic flow data, and provides useful insight for optimal parameter selection in modeling travelers’ route choice behavior.

Highlights

Urban sprawl and population growth have resulted in increasingly severe traffic congestion in major cities around the world
To solve the Stochastic User Equilibrium (SUE) problem described above, a two-stage algorithm for Generalized Least Square (GLS) estimation and SUE traffic assignment is proposed: First, the OD matrix d and the dispersion parameter θ are simultaneously estimated under the condition of the fixed link flows, link costs, and weight matrix
This is equivalent to a convex optimization problem, where the optimal results tend to converge near the true dispersion parameter value

Summary

Introduction

Urban sprawl and population growth have resulted in increasingly severe traffic congestion in major cities around the world. The estimated OD matrix, link flows, and dispersion parameter are obtained via the fixed-point model and two-stage iterative algorithm using the partial observed link flows from step (2); 4. When a new set of values of d and θ is received, the matrix P of link choice proportions is updated following the procedure described above, and is integrated into the Eq 4 to update the values of d and θ This optimization procedure continues until convergence of the OD matrix and dispersion parameter estimation is reached. To solve the Stochastic User Equilibrium (SUE) problem described above, a two-stage algorithm for GLS estimation and SUE traffic assignment is proposed: First, the OD matrix d and the dispersion parameter θ are simultaneously estimated under the condition of the fixed link flows, link costs, and weight matrix. The RMSE of target OD matrix d relative to the true OD matrix d is defined as RMSE (OD ), where d(t) is replaced by dj in Eq 15

A Hypothetical Network Test

Findings

Conclusions