A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure

Scalability of car-following and lane-changing models in microscopic traffic simulation systems

Microscopic simulation models are more and more widely used to support real-time control and management functions in the field of transportation engineering. However, even with today¡¯s advancement in computing power, microscopic simulation modeling remains a computationally intensive process that imposes limitations on its potential use for modeling large-scale transportation networks. While microscopic features of a simulated system collectively define the overall system characteristics, it is argued here that the simulation process itself is not necessarily free of redundancy which, if reduced, could substantially improve the computational efficiency of simulation processes without substantially compromising the overall integrity of the simulation process. The idea of this research is to explore the concept of scalability for microscopic traffic simulation systems in order to improve their computational efficiency and cost-effectiveness. In an attempt to strike the balance between simulation performance and computational resources, we present an optimized downsampling procedure to transform the full-scale simulation system into an equivalent reduced-scale system. The primary goal of this research is to maximize the fidelity to microscopic simulation properties while maintaining the same macroscopic properties, such as flow rate, speed, and density. Experimental analysis was conducted on a homogeneous freeway corridor to examine the behavioral scalability of sophisticated nonlinear car-following models. A methodology to address lane-changing scalability is also included in this research study

Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control

We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cell-based formulations of the DTA problem results in a linear program. However, solutions to the relaxed problem can be infeasible with respect to traffic dynamics. Previous work has shown that such solutions can be made feasible by proper choice of ramp metering and variable speed limit control for specific traffic networks. We extend this procedure to arbitrary networks and provide insight into the structure and robustness of the proposed optimal controllers. For a network consisting only of ordinary, merge, and diverge junctions, where the cells have linear demand functions and affine supply functions with identical slopes, and the cost is the total traffic volume, we show, using the maximum principle, that variable speed limits are not needed in order to achieve optimality in the FNC problem, and ramp metering is sufficient. We also prove bounds on perturbation of the controlled system trajectory in terms of perturbations in initial traffic volume and exogenous inflows. These bounds, which leverage monotonicity properties of the controlled trajectory, are shown to be in close agreement with numerical simulation results

A Review Analysis of Optimal Velocity Models

To understand traffic behavior, we require a thorough knowledge of traffic stream parameters and their mutual relationships. This relationship between the traffic parameters results many researches yielded many mathematical models named Traffic flow models. This paper presents an overview of two great approaches of traffic flow: macroscopic and microscopic models. We aim to provide an historical overview of the development of microscopic models, particularly car-following models which are fundamental in the replication of traffic flow and thus they have received considerable attention. In this work, we present a survey of recent researches based on the optimal velocity model proposed by Bando and we discuss the capability of these models, their strong points and also their weakness

Accounting for midblock pedestrian activity in the HCM 2010 urban street segment analysis

The Urban Street segment analysis Chapter of the 2010 Highway Capacity Manual (HCM 2010) provides a methodology for analyzing automobile performance on signalized roadway segments within an urban roadway network. The methodology involves applying a platoon dispersion model to: a) predict the vehicle arrival flow profiles at a downstream signalized intersection; b) use the predicted arrivals to compute the proportion of vehicle arrivals on green; and c) subsequently estimate the delay, travel speed and Level of Service (LOS) under which the segment operates. Vehicles arriving during the red interval at a signalized intersection generally accumulate and form a platoon. When the signal turns green, the platoon of vehicles is discharged from the upstream intersection to the downstream intersection. As vehicle speeds fluctuate, the platoon will disperse before it arrives at the downstream intersection. This is called Platoon dispersion. Notwithstanding its importance and application in evaluating the performance of urban roadway segments, the predictive ability of the HCM 2010 platoon dispersion model under friction and non-friction traffic conditions has not been evaluated. Friction traffic conditions include midblock pedestrian activity, on-street parking activity, and medium to high truck volume. Furthermore, one key limitation of the methodology for evaluating automobile performance on urban street segment is that it does not account for the delay incurred by platoon vehicles due to pedestrian activity at midblock (or mid-segment) crosswalks Therefore, the first objective of this research is to evaluate the predictive performance of the HCM 2010 platoon dispersion model under friction and non-friction traffic conditions using field data collected at four urban street segments. The second and primary objective is to develop an integrated deterministic-probabilistic (stochastic) model that estimates the delay incurred by platoon vehicles due to midblock pedestrian activity on urban street segments. Results of the statistical model evaluation show statistically significant difference between the observed and predicted proportion of arrivals on green under traffic. The results, however, show no statistically significant difference between the observed and predicted proportion of vehicle arrivals on under no traffic friction condition. In addition, the developed delay model was validated using field measured data. Results of the statistical validation show the developed midblock delay model performs well when compared to delays measured in the field. Sensitivity analysis is also performed to study the relationship between midblock delay and certain model parameters and variables. The model parameters are increased and decreased by 50% of their baseline values