On planning dissaturation control signals for urban areas

The problem of the optimal control of an oversaturated intersection, originally proposed by Gazis and Potts (1965), is reviewed and a feedback solution is obtained for a multi-stream pattern under general assumptions on the variability of input flows and control constraints. The dissaturation control problem is solved in two steps: first, the least dissaturation time is evaluated by taking into account the green split constraints; then a minimum waiting time problem over the least dissaturation horizon is solved to select the optimal output rate pattern.     

Spatiotemporal intersection control in a connected and automated vehicle environment

Current research on traffic control has focused on the optimization of either traffic signals or vehicle trajectories. With the rapid development of connected and automated vehicle (CAV) technologies, vehicles equipped with dedicated short-range communications (DSRC) can communicate not only with other CAVs but also with infrastructure. Joint control of vehicle trajectories and traffic signals becomes feasible and may achieve greater benefits regarding system efficiency and environmental sustainability. Traffic control framework is expected to be extended from one dimension (either spatial or temporal) to two dimensions (spatiotemporal). This paper investigates a joint control framework for isolated intersections. The control framework is modeled as a two-stage optimization problem with signal optimization at the first stage and vehicle trajectory control at the second stage. The signal optimization is modeled as a dynamic programming (DP) problem with the objective to minimize vehicle delay. Optimal control theory is applied to the vehicle trajectory control problem with the objective to minimize fuel consumption and emissions. A simplified objective function is adopted to get analytical solutions to the optimal control problem so that the two-stage model is solved efficiently. Simulation results show that the proposed joint control framework is able to reduce both vehicle delay and emissions under a variety of demand levels compared to fixed-time and adaptive signal control when vehicle trajectories are not optimized. The reduced vehicle delay and CO₂ emissions can be as much as 24.0% and 13.8%, respectively for a simple two-phase intersection. Sensitivity analysis suggests that maximum acceleration and deceleration rates have a significant impact on the performance regarding both vehicle delay and emission reduction. Further extension to a full eight-phase intersection shows a similar pattern of delay and emission reduction by the joint control framework.     

Quasi-optimal feedback control for a system of oversaturated intersections

Oversaturated intersection control is a long-standing problem in traffic science and engineering. The problem becomes even harder when we consider a system of oversaturated intersections. Most of the research works in this area are off-line studies that require fully knowledge of origin–destination demand, which would be difficult to obtain in reality. Although several on-line feedback control methods are proposed, they only aim at preventing queue spillover, not able to minimize vehicular delay time. Moreover, these on-line control strategies are not theoretically evaluated how optimal (or sub-optimal) they are. We propose in this paper a quasi-optimal decentralized QUEUE-based feedback (abbreviated as QUEUE) control strategy for a system of oversaturated intersections. The QUEUE strategy is applied cycle-by-cycle based on measurement of current queue sizes, but its overall result is able to approximate the optimal one derived from off-line studies. Details of the feedback control laws for upstream and downstream intersections, in the queueing period and the queue dissipation period, are discussed. Superior to the existing feedback control strategies, the upper bounds of sub-optimality of the QUEUE strategy generating from demand fluctuation and coupling of intersections are specified quantitatively. It is also theoretically proved that the queue measurement error or demand estimation error would not be amplified by the QUEUE strategy. Numerical examples show that the QUEUE strategy performs very well and is robust to errors.     

A linear programming formulation for autonomous intersection control within a dynamic traffic assignment and connected vehicle environment

This paper develops a novel linear programming formulation for autonomous intersection control (LPAIC) accounting for traffic dynamics within a connected vehicle environment. Firstly, a lane based bi-level optimization model is introduced to propagate traffic flows in the network, accounting for dynamic departure time, dynamic route choice, and autonomous intersection control in the context of system optimum network model. Then the bi-level optimization model is transformed to the linear programming formulation by relaxing the nonlinear constraints with a set of linear inequalities. One special feature of the LPAIC formulation is that the entries of the constraint matrix has only {−1, 0, 1} values. Moreover, it is proved that the constraint matrix is totally unimodular, the optimal solution exists and contains only integer values. It is also shown that the traffic flows from different lanes pass through the conflict points of the intersection safely and there are no holding flows in the solution. Three numerical case studies are conducted to demonstrate the properties and effectiveness of the LPAIC formulation to solve autonomous intersection control.     

Pre-timed control for an under-saturated and over-saturated isolated intersection: a Bee Colony Optimization approach

In this paper we study the problem of determining the optimum cycle and phase lengths for isolated signalized intersections. Calculation of the optimal cycle and green phase lengths is based on the minimization of the average control delay experienced by all vehicles that arrive at the intersection within a given time period. We consider under-saturated as well as over-saturated conditions at isolated intersections. The defined traffic signal timing problem, that belongs to the class of combinatorial optimization problems, is solved using the Bee Colony Optimization (BCO) metaheuristic approach. The BCO is a biologically inspired method that explores collective intelligence applied by honey bees during the nectar collecting process. The numerical experiments performed on some examples show that the proposed approach is competitive with other methods. The obtained results show that the proposed approach is capable of generating high-quality solutions within negligible processing times.     

Methods to reduce dimensionality and identify candidate solutions in multi-objective signal timing problems

Adjusting traffic signal timings is a practical way for agencies to manage urban traffic without the need for significant infrastructure investments. Signal timings are generally selected to minimize the total control delay vehicles experience at an intersection, particularly when the intersection is isolated or undersaturated. However, in practice, there are many other potential objectives that might be considered in signal timing design, including: total passenger delay, pedestrian delays, delay inequity among competing movements, total number of stopping maneuvers, among others. These objectives do not tend to share the same relationships with signal timing plans and some of these objectives may be in direct conflict. The research proposes the use of a new multi-objective optimization (MOO) visualization technique—the mosaic plot—to easily quantify and identify significant tradeoffs between competing objectives using the set of Pareto optimal solutions that are normally provided by MOO algorithms. Using this tool, methods are also proposed to identify and remove potentially redundant or unnecessary objectives that do not have any significant tradeoffs with others in an effort to reduce problem dimensionality. Since MOO procedures will still be needed if more than one objective remains and MOO algorithms generally provide a set of candidate solutions instead of a single final solution, two methods are proposed to rank the set of Pareto optimal solutions based on how well they balance between the competing objectives to provide a final recommendation. These methods rely on converting the objectives to dimensionless values based on the optimal value for each specific objectives, which allows for direct comparison between and weighting of each. The proposed methods are demonstrated using a simple numerical example of an undersaturated intersection where all objectives can be analytically obtained. However, they can be readily applied to other signal timing problems where objectives can be obtained using simulation outputs to help identify the signal timing plan that provides the most reasonable tradeoff between competing objectives.     

Distributed coordinated signal timing optimization in connected transportation networks

This paper presents a Distributed-Coordinated methodology for signal timing optimization in connected urban street networks. The underlying assumption is that all vehicles and intersections are connected and intersections can share information with each other. The novelty of the work arises from reformulating the signal timing optimization problem from a central architecture, where all signal timing parameters are optimized in one mathematical program, to a decentralized approach, where a mathematical program controls the timing of only a single intersection. As a result of this distribution, the complexity of the problem is significantly reduced thus, the proposed approach is real-time and scalable. Furthermore, distributed mathematical programs continuously coordinate with each other to avoid finding locally optimal solutions and to move towards global optimality. We proposed a real-time and scalable solution technique to solve the problem and applied it to several case study networks under various demand patterns. The algorithm controlled queue length and maximized intersection throughput (between 1% and 5% increase compared to the actuated coordinated signals optimized in VISTRO) and reduced travel time (between 17% and 48% decrease compared to actuated coordinated signals) in all cases.     

The key principles of optimal train control—Part 2: Existence of an optimal strategy,the local energy minimization principle,uniqueness, computational techniques

We discuss the problem of finding an energy-efficient driving strategy for a train journey on an undulating track with steep grades subject to a maximum prescribed journey time. In Part 1 of this paper we reviewed the state-of-the-art and established the key principles of optimal train control for a general model with continuous control. We assumed only that the tractive and braking control forces were bounded by non-increasing speed-dependent magnitude constraints and that the rate of energy dissipation from frictional resistance was given by a non-negative strictly convex function of speed. Partial cost recovery from regenerative braking was allowed. Our aim was to minimize the mechanical energy required to drive the train. We examined the characteristic optimal control modes, studied allowable control transitions and established the existence of optimal switching points. We found algebraic formulae for the adjoint variables in terms of speed on track with piecewise-constant gradient and drew phase plots of the associated optimal evolutionary lines for the state and adjoint variables. In Part 2 we will establish integral forms of the necessary conditions for optimal switching, find general bounds on the positions of the optimal switching points, justify an extended local energy minimization principle and show how these ideas can be used to calculate the optimal strategy. We prove that an optimal strategy always exists and use a perturbation analysis to show that the optimal strategy is unique. Finally we discuss computation of optimal switching points in two realistic examples with steep grades and describe the optimal control strategies and corresponding speed profiles for a complete journey with several different allowed journey times. In practice the strategies described here have been shown to reduce the costs of energy used by as much as 20%.     

Modeling and controlling an isolated urban intersection based on cooperative vehicles

In this paper, we propose a new approach for controlling the traffic at isolated intersections. We assume that all vehicles are equipped with on-board units (ITS station) that make them able to wirelessly negotiate the “right of way” according to the measurements done by the positioning system during their travel. A vehicle is allowed to cross the intersection if the green color is displayed to the driver in an on-board screen. The control aims to smooth the traffic through the sequence of vehicles authorized to traverse the intersection. The main challenge raised with the assumption is that the sequence must be dynamically formed by a real time application. The dynamic behavior of the traffic is considered discrete, in order to determine the switching rule according to the instantly observed events. We propose a model based on Timed Petri Nets with Multipliers (TPNM) which allows us to propose the control policy through the structural analysis. The resulting switching rules are very simplistic and efficient for isolated intersections. Indeed, microscopic simulations show that they perform as well as the optimal sequence based on the detection of vehicles at the entrance of the intersection. Moreover, the proposed approach has been tested through a real intersection.     

The key principles of optimal train control—Part 1: Formulation of the model,strategies of optimal type,evolutionary lines,location of optimal switching points

We discuss the problem of finding an energy-efficient driving strategy for a train journey on an undulating track with steep grades subject to a maximum prescribed journey time. We review the state-of-the-art and establish the key principles of optimal train control for a general model with continuous control. The model with discrete control is not considered. We assume only that the tractive and braking control forces are bounded by non-increasing speed-dependent magnitude constraints and that the rate of energy dissipation from frictional resistance is given by a non-negative strictly convex function of speed. Partial cost recovery from regenerative braking is allowed. The cost of the strategy is the mechanical energy required to drive the train. Minimising the mechanical energy is an effective way of reducing the fuel or electrical energy used by the traction system. The paper is presented in two parts. In Part 1 we discuss formulation of the model, determine the characteristic optimal control modes, study allowable control transitions, establish the existence of optimal switching points and consider optimal strategies with speed limits. We find algebraic formulae for the adjoint variables in terms of speed on track with piecewise-constant gradient and draw phase plots of the associated optimal evolutionary lines for the state and adjoint variables. In Part 2 we will establish important integral forms of the necessary conditions for optimal switching, find general bounds on the positions of the optimal switching points, justify the local energy minimization principle and show how these ideas are used to calculate optimal switching points. We will prove that an optimal strategy always exists and use a perturbation analysis to show the strategy is unique. Finally we will discuss computational techniques in realistic examples with steep gradients and describe typical optimal strategies for a complete journey.     

The optimization of lane assignment and signal timing at the tandem intersection with pre‐signal

This paper presents an integrated model for optimizing lane assignment and signal timing at tandem intersection, which is introduced recently. The pre‐signal is utilized in the tandem intersection to reorganize the traffic flow; hence, the vehicles, regardless of whether left‐turns or through vehicles, can be discharged in all the lanes. However, the previous work does not consider the extra traffic disruption and the associated delay caused by the additional pre‐signal. In the paper, the extra delay aroused by the coordination is incorporated in a lane assignment and signal timing optimization model, and the problem is converted into a mixed‐integer non‐linear programming. A feasible directions method is hence introduced to solve the mixed‐integer non‐linear programming. The result of the optimization shows that the performance of the tandem intersection is improved and the average delay is minimized. The comparison between the tandem and the conventional configuration is presented, and the results verify that the former shows better performance than the latter. In addition, the optimal sequence corresponding to the turning proportion and the optimal lane assignment at the upstream approach of the pre‐signal are presented. Furthermore, if the number of lanes is equal in all arms, the paper proves that the average delay will be reduced if lane assignment is proportional to the turning proportion and the vehicles with low proportion are discharged in advance. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating intersection O-D matrices from observed time-series of traffic counts: The zellner estimator

The problem of estimating intersection O-D matrices from input and output time-series of traffic counts is considered in this paper. Because of possible existence of significant correlation between the error terms across structural equations forming the O-D matrices, the seemingly unrelated estimator (Zellner estimator) was suggested. Estimation results showed evidence of strong correlation between error terms across-equations. Generally, the Zellner estimator produced more efficient estimates than did the ordinary least-squares estimator. Furthermore, the Zellner estimator satisfied all constraints and reproduced turning movements comparable to the actual ones.     

Optimal feeder bus routes on irregular street networks

The methodology presented here seeks to optimize bus routes feeding a major intermodal transit transfer station while considering intersection delays and realistic street networks. A model is developed for finding the optimal bus route location and its operating headway in a heterogeneous service area. The criterion for optimality is the minimum total cost, including supplier and user costs. Irregular and discrete demand distributions, which realistically represent geographic variations in demand, are considered in the proposed model. The optimal headway is derived analytically for an irregularly shaped service area without demand elasticity, with non‐uniformly distributed demand density, and with a many‐to‐one travel pattern. Computer programs are designed to analyze numerical examples, which show that the combinatory type routing problem can be globally optimized. The improved computational efficiency of the near‐optimal algorithm is demonstrated through numerical comparisons to an optimal solution obtained by the exhaustive search (ES) algorithm. The CPU time spent by each algorithm is also compared to demonstrate that the near‐optimal algorithm converges to an acceptable solution significantly faster than the ES algorithm.     

Development of a signal-head-free intersection control logic in a fully connected and autonomous vehicle environment

Establishment of effective cooperation between vehicles and transportation infrastructure improves travel reliability in urban transportation networks. Lack of collaboration, however, exacerbates congestion due mainly to frequent stops at signalized intersections. It is beneficial to develop a control logic that collects basic safety message from approaching connected and autonomous vehicles and guarantees efficient intersection operations with safe and incident free vehicle maneuvers. In this paper, a signal-head-free intersection control logic is formulated into a dynamic programming model that aims to maximize the intersection throughput. A stochastic look-ahead technique is proposed based on Monte Carlo tree search algorithm to determine the near-optimal actions (i.e., acceleration rates) over time to prevent movement conflicts. Our numerical results confirm that the proposed technique can solve the problem efficiently and addresses the consequences of existing traffic signals. The proposed approach, while completely avoids incidents at intersections, significantly reduces travel time (ranging between 59.4% and 83.7% when compared to fixed-time and fully-actuated control strategies) at intersections under various demand patterns.     

The symmetric intersection design and traffic control optimization

It is well recognized that the left-turning movement reduces the intersection capacity significantly, because exclusive left turn phases are needed to discharge left turn vehicles only. This paper proposes the concept of Left-Hand Traffic (LHT) arterial, on where vehicles follow left-hand traffic rules as in England and India. The unconventional intersection where a LHT arterial intersects with a Right-Hand Traffic (RHT) arterial is named as symmetric intersection. It is only need three basic signal phases to separate all conflicts at symmetric intersection, while it at least need four signal phases at a conventional intersection. So, compared with the conventional intersection, the symmetric intersection can provide longer green time for the left-turning and the through movement, which can increase the capacity significantly. Through-movement waiting areas (TWAs) can be set at the symmetric intersection effectively, which can increase the capacity and short the cycle length furthermore. And the symmetric intersection is Channelized to improve the safety of TWAs. The Binary-Mixed-Integer-Linear-Programming (BMILP) model is employed to formulate the capacity maximization problem and signal cycle length minimization problem of the symmetric intersection. The BMILP model can be solved by standard branch-and-bound algorithms efficiently and outputs the lane allocation, signal timing decisions, and other decisions. Experiments analysis shows that the symmetric intersection with TWAs can increase the capacity and short the signal cycle length.     

Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods.     

Optimal distance between two branches of uncontrolled split intersection

This work examines the possibility of splitting an uncontrolled “X” intersection into two adjacent uncontrolled “T” intersections. This splitting aims to improve both the movement and safety of traffic. The problem addressed in this work is how to determine the optimal distance between the two adjacent T intersections. The best type of split, based on previous studies, is the one in which vehicles approach first the right turn and then the left turn in both directions of travel. The main conclusions drawn in this work refer to this preferred type. The optimal distance is arrived at on the basis of an objective function of minimal delay subject to blocking queues, passing (another vehicle) probabilities, budget limitations and safety threshold. The input data consist of 12 traffic volumes associated with all the traffic movements of an X intersection. The main findings are: (a) under a medium level of traffic volume, the blocking queue lengths are of the order of hundreds of meters and are very sensitive to the increase of volume toward and beyond saturation flow; (b) the passing probability function along the road segment between the two adjacent T intersections increases with the length of the segment and stabilizes at a length of a few hundred meters; (c) there is a relationship between accident frequency (accident rate and density) and the distance between the split intersections. An example of this relationship is introduced; and (d) the optimal distance between the two adjacent T intersections is found not only theoretically, but also practically for possible implementations.     

城市平面交叉口汽车排放优化策略研究

文章针对城市平面交叉口交通污染严重的问题,分析城市平面交叉口交通及行为特性、影响机动车排放的相关因素,从平面交叉口交通规划、交通控制二个方面阐述汽车排放优化措施。     

On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model

In this paper, we study the pricing strategies in the discrete time single bottleneck model with general heterogeneous commuters. We first prove that in the system optimal assignment, the queue time must be zero for all the departures. Based on this result, the system optimal problem is formulated as a linear program. The solution existence and uniqueness are discussed. Applying linear programming duality, we then prove that the optimal dual variable values provide an optimal toll with which the system optimal solution is also an equilibrium solution. Extensive computational results are reported to demonstrate the insights gained from the formulations in this paper. These results confirm that a system optimal equilibrium can be found using the proposed approach.     

A gradient boosting logit model to investigate driver’s stop-or-run behavior at signalized intersections using high-resolution traffic data

Driver’s stop-or-run behavior at signalized intersection has become a major concern for the intersection safety. While many studies were undertaken to model and predict drivers’ stop-or-run (SoR) behaviors including Yellow-Light-Running (YLR) and Red-Light-Running (RLR) using traditional statistical regression models, a critical problem for these models is that the relative influences of predictor variables on driver’s SoR behavior could not be evaluated. To address this challenge, this research proposes a new approach which applies a recently developed data mining approach called gradient boosting logit model to handle different types of predictor variables, fit complex nonlinear relationships among variables, and automatically disentangle interaction effects between influential factors using high-resolution traffic and signal event data collected from loop detectors. Particularly, this research will first identify a series of related influential factors including signal timing information, surrounding traffic information, and surrounding drivers’ behaviors using thousands drivers’ decision events including YLR, RLR, and first-to-stop (FSTP) extracted from high-resolution loop detector data from three intersections. Then the research applies the proposed data mining approach to search for the optimal prediction model for each intersection. Furthermore, a comparison was conducted to compare the proposed new method with the traditional statistical regression model. The results show that the gradient boosting logit model has superior performance in terms of prediction accuracy. In contrast to other machine learning methods which usually apply ‘black-box’ procedures, the gradient boosting logit model can identify and rank the relative importance of influential factors on driver’s stop-or-run behavior prediction. This study brings great potential for future practical applications since loops have been widely implemented in many intersections and can collect data in real time. This research is expected to contribute to the improvement of intersection safety significantly.