Modelling an oversaturated intersection

The traffic intersection with deterministic arrivals over a planning period is modelled by analogy with a reservoir. Under fixed cycle lengths, light setting are determined which minimize average line lengths of waiting vehicle. Under certain conditions, the fixed-cycle requirement may be relaxed, resulting in approximately optimal cycle lengths. Constraints on maximum waiting time, maximum queue length, and minimum clearance during a cycle are appended to the fundamental model and tradeoff analyses are suggested. Maximum line length may, in addition, be explicitly minimized. The single intersection is investigated for the case of two one-way intersecting streets. The case of two two-way intersecting streets is an obvious and easy extension of the two one-way intersecting streets model. Extensions to serial intersections with limited waiting room are suggested. All problems are neatly cast as linear programs and hence are readily optimizable.     

A reverse causal-effect modeling approach for signal control of an oversaturated intersection

A novel approach is presented in which signalized intersections are treated as normal highway bottlenecks for improved computational efficiency. It is unique in two ways. First, it treats the signalized intersections as common freeway bottlenecks by a reversed cause and effect modeling approach. Both traffic arrivals and departures are modeled by smooth continuous functions of time as if there were no interruptions to traffic flows from signals. The use of smooth continuous functions for departure curves instead of commonly used step functions makes it easy to apply differential calculus in optimization and future extension to a system of intersections. Second, a dynamic linear programming (LP) model is then developed to maximize the total vehicular output from the intersection during the entire period of congestion subject to prevailing capacity and other operational constraints. The continuous optimal departure flow rate (the effect) is then converted to signal timing parameters (the cause) that can be readily implemented. Two numerical examples are presented to demonstrate the properties of the proposed algorithm and examine its performance.     

A continuous-flow-intersection-lite design and traffic control for oversaturated bottleneck intersections

Oversaturation has become a severe problem for urban intersections, especially the bottleneck intersections that cause queue spillover and network gridlock. Further improvement of oversaturated arterial traffic using traditional mitigation strategies, which aim to improve intersection capacity by merely adjusting signal control parameters, becomes challenging since exiting strategies may (or already) have reached their “theoretical” limits of optimum. Under such circumstance, several novel unconventional intersection designs, including the well-recognized continuous flow intersection (CFI) design, are originated to improve the capacity at bottleneck intersections. However, the requirement of installing extra sub-intersections in a CFI design would increase vehicular stops and, more critically, is unacceptable in tight urban areas with closed spaced intersections. To address these issues, this research proposes a simplified continuous flow intersection (called CFI-Lite) design that is ideal for arterials with short links. It benefits from the CFI concept to enable simultaneous move of left-turn and through traffic at bottleneck intersections, but does not need installation of sub-intersections. Instead, the upstream intersection is utilized to allocate left-turn traffic to the displaced left-turn lane. It is found that the CFI-Lite design performs superiorly to the conventional design and regular CFI design in terms of bottleneck capacity. Pareto capacity improvement for every traffic stream in an arterial system can be achieved under effortless conditions. Case study using data collected at Foothill Blvd in Los Angeles, CA, shows that the new design is beneficial in more than 90% of the 408 studied cycles. The testing also shows that the average improvements of green bandwidths for the synchronized phases are significant.     

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.     

Quasi-optimal feedback control for an isolated intersection under oversaturation

How to manage signalized intersections under oversaturated conditions is a long-standing problem in traffic science and engineering. However, although research works in this area date back to 1960s, an on-line control strategy with theoretically bounded performance is missing, even for the control of an isolated intersection under oversaturation. This paper makes one step further in this area by proposing a QUEUE-based quasi-optimal feedback control (abbreviated as QUEUE) strategy for an isolated oversaturated intersection. The QUEUE strategy is intuitive, simple, and proved to match the off-line optimum in the case of constant demand. More importantly, the bounds of sub-optimality of the QUEUE strategy can be specified quantitatively in general piece-wise constant demand cases. To better deal with the maximum queue constraints, the oversaturation period is divided into the queuing period and the dissipation period with two different objectives. In the queuing period, the primary objective is to keep the queue length within the maximum value; but for the dissipation period, the primary objective is to eliminate all queues at the earliest time. Interestingly, we found that both control objectives can be realized with the same QUEUE strategy. Numerical examples show that the QUEUE strategy approximates the off-line optimum very well. The average sub-optimality in comparison with the off-line optimum in the challenging conditions with Poisson distributed random demand is below 5%.     

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.     

Analysis of intersection delay under real-time adaptive signal control

The United States Department of Transportation has recently begun implementation of the national demonstration project for suburban Advanced Traffic Management Systems (ATMS) utilizing the Sydney Coordinated Adaptive Traffic System (SCATS). SCATS is an automated, real time, traffic responsive signal control strategy. The expected benefit from the system comes from its ability to constantly modify signal timing patterns to most effectively accommodate changing traffic conditions. The objectives of this research study were to analyze the differences in certain delay parameters which would occur as a result of implementing SCATS signal control. The study employed a macroscopic simulation procedure to compute intersection delay under both a strategy that changed signal timings once per hour and SCATS signal control. A comparison of delay under both forms of control is presented. The study findings demonstrated mixed results regarding the benefit of SCATS control. A general conclusion of the study was that SCATS distributed the delay across competing approaches more evenly. However, in some cases this resulted in an increase in the total intersection delay. The observed delay change was attributed primarily to the saturation equalization objective of the SCATS control program. SCATS attempts to allocate green time to the intersection approaches based on the degree of saturation. Under this philosophy the system is able to balance the percentage of green time between all approaches, resulting in more uniform delay.     

Efficient intersection control for minimally guided vehicles: A self-organised and decentralised approach

An important question for the practical applicability of the highly efficient traffic intersection control is about the minimal level of intelligence the vehicles need to have so as to move beyond the traffic light control. We propose an efficient intersection traffic control scheme without the traffic lights, that only requires a majority of vehicles on the road to be equipped with a simple driver assistance system. The algorithm of our scheme is completely decentralised, and takes into full account the non-linear interaction between the vehicles at high density. For vehicles approaching the intersection in different directions, our algorithm imposes simple interactions between vehicles around the intersection, by defining specific conditions on the real-time basis, for which the involved vehicles are required to briefly adjust their dynamics. This leads to a self-organised traffic flow that is safe, robust, and efficient. We also take into account of the driver comfort level and study its effect on the control efficiency. The scheme has low technological barrier, minimal impact on the conventional driving behaviour, and can coexist with the traffic light control. It also has the advantages of being easily scalable, and fully compatible with both the conventional road systems as well as the futuristic scenario in which driverless vehicles dominate the road. The mathematical formulation of our scheme permits large scale realistic numerical simulations of busy intersections, allowing a more complete evaluation of the control performance, instead of just the collision avoidance at the intersection.     

Stochastic simulation of the traffic of an uncontrolled road intersection

The paper describes the logic and results of a stochastic simulation model for uncontrolled intersections with poor visibility where the right of way belongs to the driver on the right. The model deals with crossings with and without turning movements. Several runs have been made with realistic input values. Finally, conclusions are drawn and traffic volume warrants are proposed for establishing two way stop/yield controls on uncontrolled crossings.     

A new algorithm for optimal signal control in congested networks

Optimization of traffic lights in a congested network is formulated as a linear programming problem. The formulation adapted here takes into account particular capacity constraints for road links and for intersections. A necessary prerequisite for the determination of optimal green times is that representative a-priori information about the origin-destination and route choice pattern inside the network is available. Because any particular control strategy temporarily alters the effective turning rates at intersections, an iterative procedure is proposed here which accomplishes convergence of optimal signal control and resulting O-D flows. The efficiency of this optimization procedure is demonstrated in a case study for a network with fifteen intersections.     

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.     

Modelling supported driving as an optimal control cycle: Framework and model characteristics

Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper puts forward a receding horizon control framework to model driver assistance and cooperative systems. The accelerations of automated vehicles are controlled to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller design of Adaptive Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and C-ACC model characteristics are investigated analytically, with focus on equilibrium solutions and stability properties. The proposed ACC model produces plausible human car-following behaviour and is unconditionally locally stable. By careful tuning of parameters, the ACC model generates similar stability characteristics as human driver models. The proposed C-ACC model results in convective downstream and absolute string instability, but not convective upstream string instability observed in human-driven traffic and in the ACC model. The control framework and analytical results provide insights into the influences of ACC and C-ACC systems on traffic flow operations.     

A note on highway capacity

This note shows that on a homogeneous, uninterrupted flow highway there can be three kinds of capacity for any location: one for acceleration flow, one for deceleration flow and another for stationary flow. It is the stationary (equilibrium) flow capacity that one should adopt as the ideal capacity of a roadway, as defined by the highway capacity manual.     

Performance analysis of the phase swap sorting strategy for an isolated intersection

A separate left-turn phase wastes the capacity of intersection, because all the lanes on the approach are not fully utilized during either the left-turn or through green phase. Under the phase swap sorting strategy (Xuan, 2011), different types of movements can be reorganized by a pre-signal so that all the lanes in the sorting area can be used to discharge vehicles during their green phases. Thus the capacity is improved significantly. In fact, when a pre-signal is installed upstream of the intersection signal (also named main signal), the two signals will have a great impact on not only the capacity, but other traffic performances, such as delays, queue formations, maximum queue length, residual queue, and spillback, etc., which are very important performance factors for the design and application of the phase swap sorting strategy. In order to more fully quantify and characterize the performance of the phase swap sorting strategy, a three-dimensional Markov queueing model is presented. Two levels of performance evaluation indices are formulated using the matrix analytic techniques. All these indices can be used to establish a more comprehensive analytical framework to evaluate the use of the phase swap sorting strategy. Model validation shows that the proposed model can provide a reliable performance analysis for the phase swap sorting strategy under various different conditions. In addition, in order to intuitively illustrate the effects of various factors on the performance of the phase swap sorting strategy, a series of numerical experiments is conducted.     

Evaluation of the dry port concept from an environmental perspective: A note

This study evaluates the dry port concept from an environmental perspective using modelling and simulation. A model of a transport system, with and without a dry port, is created and the results of the simulations compared. The benefits of the dry port implementation are defined from an environmental perspective; calculated CO₂ emissions are approximately 25% lower with an implemented dry port for the chosen case, while congestion and truck waiting times at the terminal are significantly reduced.     

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.     

A technical note on the derivation of the Bayesian-Ramsey pricing rule

“Bayesian-Ramsey pricing” has been offered to correct for the undue sensitivity of the Baumol and Bradford formulation of Ramsey pricing to relatively small errors in the highly uncertain least-squares estimates of the relevant demand elasticities. This paper provides a derivation of the Ramsey pricing equation under uncertainty and of the required expectations for the case of linear demand curve under uncertainty characterized by a truncated normal posterior distribution. Such a posterior would arise from normal sample data in combination with an improper prior. These equations were used in a previously published paper in this journal to evaluate the Bayesian approach.     

Evaluation of vehicle acceleration models for emission estimation at an intersection

We evaluate the constant acceleration, linearly decreasing acceleration, and aaSIDRA models in terms of generating second-by-second speed profiles for emission estimations at an intersection. The models are first calibrated using field data from individual vehicle trajectories. With the calibrated models, second-by-second speed and acceleration data are produced, and emissions are estimated using MOVES. Emission estimations based on the calibrated acceleration models are then compared with those based on field trajectory data. The constant acceleration model tends to overestimate emissions; both the linearly decreasing acceleration model and the aaSIDRA model provide accurate emission estimations.     

Nonlinear programming methods based on closed-form expressions for optimal train control

This paper proposes a novel approach to solve the complex optimal train control problems that so far cannot be perfectly tackled by the existing methods, including the optimal control of a fleet of interacting trains, and the optimal train control involving scheduling. By dividing the track into subsections with constant speed limit and constant gradient, and assuming the train’s running resistance to be a quadratic function of speed, two different methods are proposed to solve the problems of interest. The first method assumes an operation sequence of maximum traction – speedholding – coasting – maximum braking on each subsection of the track. To maintain the mathematical tractability, the maximum tractive and maximum braking functions are restricted to be decreasing and piecewise-quadratic, based on which the terminal speed, travel distance and energy consumption of each operation can be calculated in a closed-form, given the initial speed and time duration of that operation. With these closed-form expressions, the optimal train control problem is formulated and solved as a nonlinear programming problem. To allow more flexible forms of maximum tractive and maximum braking forces, the second method applies a constant force on each subsection. Performance of these two methods is compared through a case study of the classic single-train control on a single journey. The proposed methods are further utilised to formulate more complex optimal train control problems, including scheduling a subway line while taking train control into account, and simultaneously optimising the control of a leader-follower train pair under fixed- and moving-block signalling systems.