Xuan Di

Hybrid Extended Kalman Filtering Approach for Traffic Density Estimation Along Signalized Arterials

Estimation of densities on freeways and arterials is critical to traffic control and management. Most previous work, however, focused on freeway density estimation based merely on detector data. This study attempts to estimate traffic density along a signalized arterial by using data from both detectors and a global positioning system (GPS). The approximation to the previously developed MARCOM (Markov compartment) model is adapted to describe arterial traffic states. A hybrid extended Kalman filter is then implemented to integrate the approximated MARCOM with detector and GPS measurements. The proposed model is tested on a single signal link simulated by using VisSim. Test results show that the hybrid extended Kalman filter with GPS data can significantly improve density estimation.

Boundedly Rational User Equilibria (BRUE): Mathematical Formulation and Solution Sets

Abstract Boundedly rational user equilibria (BRUE) represent traffic flow distribution patterns where travellers can take any route whose travel cost is within an ‘indifference band’ of the shortest path cost. Those traffic flow patterns satisfying the above condition constitute a set, named the BRUE solution set. It is important to obtain all the BRUE flow patterns, because it can help predict the variation of the link flow pattern in a traffic network under the boundedly rational behavior assumption. However, the methodology of constructing the BRUE set has been lacking in the established literature. This paper fills the gap by constructing the BRUE solution set on traffic networks with fixed demands connecting multiple OD pairs. According to the definition of the ɛ-BRUE, where ɛ is the indifference band for the perceived travel cost, we formulate the ɛ-BRUE problem as a nonlinear complementarity problem (NCP), so that a BRUE solution can be obtained by solving a BRUE-NCP formulation. To obtain the whole BRUE solution set encompassing all BRUE flow patterns, we firstly propose a methodology of generating various path combinations which may be utilized under the boundedly rational behavior assumption. We find out that with the increase of the indifference band, the path set that contains boundedly rational equilibrium flows will be augmented, and the critical values of indifference bands to augment these path sets can be identified by solving a family of mathematical programs with equilibrium constraints (MPEC) sequentially. After these utilized path sets are attained, the BRUE solution set can be obtained when we assign all traffic demands to these utilized paths. Various numerical examples are given to illustrate our findings.

Ridesharing User Equilibrium and Its Implications for High-Occupancy Toll Lane Pricing

Shared mobility—ridesharing in particular—has become an important research topic in recent years because of the ability to relieve traffic congestion, reduce travel costs, and reduce energy consumption. However, researchers in transportation science still lack an understanding of how to incorporate ridesharing into the transportation planning process, specifically in the traffic assignment problem. This paper presents ridesharing user equilibrium (RUE) as a path-flow–based nonlinear complementarity problem with side constraints. This formulation is extended by considering the presence of high-occupancy toll lanes. A numerical example is given to illustrate the relationships of the path cost coefficients on RUE and on the occurrence of the Braess paradox. The performance of two tolling strategies is compared: one charges single-occupancy vehicles, and the other charges both single-occupancy vehicles and vehicles carrying only one passenger.