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

AN INTEGRATED CONTROL MODEL FOR FREEWAY INTERCHANGES

This dissertation proposes an integrated control framework to deal with traffic congestion at freeway interchanges. In the neighborhood of freeway interchanges, there are six potential problems that could cause severe congestion, namely lane-blockage, link-blockage, green time starvation, on-ramp queue spillback to the upstream arterial, off-ramp queue spillback to the upstream freeway segments, and freeway mainline queue spillback to the upstream interchange. The congestion problem around freeway interchanges cannot be solved separately either on the freeways or on the arterials side. To eliminate this congestion, we should balance the delays of freeways and arterials and improve the overall system performance instead of individual subsystem performance. This dissertation proposes an integrated framework which handles interchange congestion according to its severity level with different models. These models can generate effective control strategies to achieve near optimal system performance by balancing the freeway and arterial delays. The following key contributions were made in this dissertation: 1. Formulated the lane-blockage problem between the movements of an arterial intersection approach as an linear program with the proposed sub-cell concept, and proposed an arterial signal optimization model under oversaturated traffic conditions; 2. Formulated the traffic dynamics of a freeway segment with cell-transmission concept, while considering the exit queue effects on its neighboring through lane traffic with the proposed capacity model, which is able to take the lateral friction into account; 3. Developed an integrated control model for multiple freeway interchanges, which can capture the off-ramp spillback, freeway mainline spillback, and arterial lane and link blockage simultaneously; 4. Explored the effectiveness of different solution algorithms (GA, SA, and SA-GA) for the proposed integrated control models, and conducted a statistical goodness check for the proposed algorithms, which has demonstrated the advantages of the proposed model; 5. Conducted intensive numerical experiments for the proposed control models, and compared the performance of the optimized signal timings from the proposed models with those from Transyt-7F by CORSIM simulations. These comparisons have demonstrated the advantages of the proposed models, especially under oversaturated traffic conditions

Isolated Ramp Metering Feedback Control Utilizing Mixed Sensitivity for Desired Mainline Density and the Ramp Queues

This paper presents a feedback control design for isolated ramp metering control. This feedback control design, unlike the existing isolated feedback ramp controllers, also takes into account the ramp queue length. Using a nonlinear H∞ control design methodology, we formulate the problem in the desired setting to be able to utilize the results of the methodology

AN INTEGRATED TRAFFIC CONTROL SYSTEM FOR FREEWAY CORRIDORS UNDER NON-RECURRENT CONGESTION

This research has focused on developing an advanced dynamic corridor traffic control system that can assist responsible traffic professionals in generating effective control strategies for contending with non-recurrent congestion that often concurrently plagues both the freeway and arterial systems. The developed system features its hierarchical operating structure that consists of an integrated-level control and a local-level module for bottleneck management. The primary function of the integrated-level control is to maximize the capacity utilization of the entire corridor under incident conditions with concurrently implemented strategies over dynamically computed windows, including diversion control at critical off-ramps, on-ramp metering, and optimal arterial signal timings. The system development process starts with design of a set of innovative network formulations that can accurately and efficiently capture the operational characteristics of traffic flows in the entire corridor optimization process. Grounded on the proposed formulations for network flows, the second part of the system development process is to construct two integrated control models, where the base model is designed for a single-segment detour operation and the extended model is designated for general network applications. To efficiently explore the control effectiveness under different policy priorities between the target freeway and available detour routes, this study has further proposed a multi-objective control process for best managing the complex traffic conditions during incident operations. Due to the nonlinear nature of the proposed formulations and the concerns of computing efficiency, this study has also developed a GA-based heuristic along with a successive optimization process that can yield sufficiently reliable solutions for operating the proposed system in a real-time traffic environment. To evaluate the effectiveness and efficiency of the developed system, this study has conducted extensive numerical experiments with real-world cases. The experimental results have demonstrated that with the information generated from the proposed models, the responsible agency can effectively implement control strategies in a timely manner at all control points to substantially improve the efficiency of the corridor control operations. In view of potential spillback blockage due to detour operations, this study has further developed a local-level bottleneck management module with enhanced arterial flow formulations that can fully capture the complex interrelations between the overflow in each lane group and its impact on the neighboring lanes. As a supplemental component for corridor control, this module has been integrated with the optimization model to fine-tune the arterial signal timings and to prevent the queue spillback or blockages at off-ramps and intersections. The results of extensive numerical experiments have shown that the supplemental module is quite effective in producing local control strategies that can prevent the formation of intersection bottlenecks in the local arterial

Hybrid Optimal Control for Time-Efficient Highway Traffic Management

This article examines the hybrid traffic control problem to minimize total travel time (TTT) of a highway network through traffic management infrastructures, including dynamic speed limit signs, ramp metering, and information board.We first build the traffic flow model based on the Moskowitz function for each highway link to predict traffic status within a control horizon. The traffic density is predicted based on the flow dynamic model and corrected periodically by measured traffic flow data. The minimum TTT traffic control problem is then formulated as a mixed-integer quadratic programming problem with quadratic constraints. Numerical simulation of a real world highway network is provided to demonstrate significant reduction of TTT and alleviation of traffic congestion compared to results obtained from ALINEA and PI-ALINEA methods

New Framework and Decision Support Tool to Warrant Detour Operations During Freeway Corridor Incident Management

As reported in the literature, the mobility and reliability of the highway systems in the United States have been significantly undermined by traffic delays on freeway corridors due to non-recurrent traffic congestion. Many of those delays are caused by the reduced capacity and overwhelming demand on critical metropolitan corridors coupled with long incident durations. In most scenarios, if proper detour strategies could be implemented in time, motorists could circumvent the congested segments by detouring through parallel arterials, which will significantly improve the mobility of all vehicles in the corridor system. Nevertheless, prior to implementation of any detour strategy, traffic managers need a set of well-justified warrants, as implementing detour operations usually demand substantial amount of resources and manpower. To contend with the aforementioned issues, this study is focused on developing a new multi-criteria framework along with an advanced and computation-friendly tool for traffic managers to decide whether or not and when to implement corridor detour operations. The expected contributions of this study are: * Proposing a well-calibrated corridor simulation network and a comprehensive set of experimental scenarios to take into account many potential affecting factors on traffic manager\u27s decision making process and ensure the effectiveness of the proposed detour warrant tool; * Developing detour decision models, including a two-choice model and a multi-choice model, based on generated optima detour traffic flow rates for each scenario from a diversion control model to allow responsible traffic managers to make best detour decisions during real-time incident management; and * Estimating the resulting benefits for comparison with the operational costs using the output from the diversion control model to further validate the developed detour decision model from the overall societal perspective

Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

In modern transportation systems, traffic congestion is inevitable. To minimize the loss caused by congestion, various control strategies have been developed most of which rely on observing real-time traffic conditions. As vintage traffic sensors are limited, traffic density estimation is very helpful for gaining network-wide observability. This paper deals with this problem by first, presenting a traffic model for stretched highway having multiple ramps built based on asymmetric cell transmission model (ACTM). Second, based on the assumption that the encompassed nonlinearity of the ACTM is Lipschitz, a robust dynamic observer framework for performing traffic density estimation is proposed. Numerical test results show that the observer yields a sufficient performance in estimating traffic densities having noisy measurements, while being computationally faster the Unscented Kalman Filter in performing real-time estimation.Comment: To appear in the 2020 American Control Conference (ACC'2020), July 2020, Denver, Colorad