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%.     

Identification of oversaturated intersections using high-resolution traffic signal data

Conceptually, an oversaturated traffic intersection is defined as one where traffic demand exceeds the capacity. Such a definition, however, cannot be applied directly to identify oversaturated intersections because measuring traffic demand under congested conditions is not an easy task, particularly with fixed-location sensors. In this paper, we circumvent this issue by quantifying the detrimental effects of oversaturation on signal operations, both temporally and spatially. The detrimental effect is characterized temporally by a residual queue at the end of a cycle, which will require a portion of green time in the next cycle; or spatially by a spill-over from downstream traffic whereby usable green time is reduced because of the downstream blockage. The oversaturation severity index (OSI), in either the temporal dimension (T-OSI) or the spatial dimension (S-OSI) can then be measured using high-resolution traffic signal data by calculating the ratio between the unusable green time due to detrimental effects and the total available green time in a cycle. To quantify the T-OSI, in this paper, we adopt a shockwave-based queue estimation algorithm to estimate the residual queue length. S-OSI can be identified by a phenomenon denoted as “Queue-Over-Detector (QOD)”, which is the condition when high occupancy on a detector is caused by downstream congestion. We believe that the persistence duration and the spatial extent with OSI greater than zero provide an important indicator for measuring traffic network performance so that corresponding congestion mitigation strategies can be prepared. The proposed algorithms for identifying oversaturated intersections and quantifying the oversaturation severity index have been field-tested using traffic signal data from a major arterial in the Twin Cities of Minnesota.     

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.     

Robustness of the off-line a priori stochastic dynamic traffic assignment solution for on-line operations

This paper focuses on the off-line stochastic dynamic traffic assignment (DTA) problem as part of a hybrid framework that combines off-line and on-line strategies to solve the on-line DTA problem. The primary concept involves the explicit recognition of stochasticity in O–D demand and/or network supply conditions to determine a robust off-line a priori solution that serves as the initial solution on-line. This strategy ensures that the computationally intensive components, which exploit historical data, are executed off-line while circumventing the need for very accurate on-line O–D demand forecast models. Thereby, efficient on-line reactive strategies could be used to address unfolding traffic conditions. The paper investigates the robustness of the off-line a priori DTA solution under plausible on-line situations. The results illustrate the superiority of the a priori solution over the currently used mean O–D demand-based solution for on-line route guidance applications.     

Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic.     

Improving noise assessment at intersections by modeling traffic dynamics

Three families of road noise prediction models can be distinguished. Static noise models only consider free-flow constant-speed traffic with uniformly distributed vehicles. Analytic noise models assume that all vehicles are isolated from one another but account for their mean kinematic profile over the network. Micro-simulation noise models relax the hypothesis of no interaction between vehicles and fully capture traffic flow dynamic effects such as queue evolution. This study compares the noise levels obtained by these three methodologies at signalized intersections and roundabouts. It reveals that micro-simulation noise models outperform the other approaches. Particularly, they are able to capture the effects of stochastic transient queues in under-saturated conditions as well as stop-and-go behaviors in oversaturated regime. Accounting for traffic dynamics is also shown to improve predictions of noise variations due to different junction layouts. In this paper, a roundabout is found to induce a 2.5 dB(A) noise reduction compared to a signalized intersection in under-saturated conditions while the acoustic contributions of both kinds of junctions balance in oversaturated regime.     

Hybrid simulated annealing and genetic algorithm for optimizing arterial signal timings under oversaturated traffic conditions

The implementation of system‐wide signal optimization models requires efficient solution algorithms that can quickly generate optimal or near‐optimal signal timings. This paper presents a hybrid algorithm based on simulated annealing (SA) and a genetic algorithm (GA) for arterial signal timing optimization. A decoding scheme is proposed that exploits our prior expectations about efficient solutions, namely, that the optimal green time distribution should reflect the proportion of the critical lane volumes of each phase. An SA algorithm, a GA algorithm and a hybrid SA‐GA algorithm are developed here using the proposed decoding scheme. These algorithms can be adapted to a wide range of signal optimization models and are especially suitable for those optimizing phase sequences with oversaturated intersections. To comparatively evaluate the performance of the proposed algorithms, we apply them to a signal optimization model for oversaturated arterial intersections based on an enhanced cell transmission model. The numerical results indicate that the SA‐GA algorithm outperforms both SA and GA in terms of solution quality and convergence rate. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi-stage stochastic program to optimize signal timings under coordinated adaptive control

In the wake of traffic congestion at intersections, it is imperative to shorten delays in corridors with stochastic arrivals. Coordinated adaptive control can adjust green time flexibly to deal with a stochastic demand, while maintaining a minimum through-band for coordinated intersections. In this paper, a multi-stage stochastic program based on phase clearance reliability (PCR) is proposed to optimize base timing plans and green split adjustments of coordinated intersections under adaptive control. The objective is to minimize the expected intersection delay and overflow of the coordinated approach. The overflow or oversaturated effect is explicitly addressed in the delay calculation, which greatly increases the modeling complexity due to the interaction of overflow delays across cycles. The notion of PCR separates the otherwise related green time settings of consecutive cycles into a number of stages, in which the base timing plan and actual timing plan in different cycles are handled sequentially. We then develop a PCR based solution algorithm to solve the problem, and apply the model and the solution algorithm to actual intersections in Shanghai to investigate its performance as compared with Allsop’s method and Webster’s method. Preliminary results show the PCR-based method can significantly shorten delays and almost eliminates overflow for the coordinated approaches, with acceptable delay increases of the non-coordinated approaches. A comparison between the proposed coordinated adaptive logic and a coordinated actuated logic is also conducted in the case study to show the advantages and disadvantages.     

Continuum signalized junction model for dynamic traffic networks: Offset,spillback, and multiple signal phases

This paper extends the continuum signalized intersection model exhaustively studied in Han et al. (2014) to more accurately account for three realistic complications: signal offsets, queue spillbacks, and complex signal phasing schemes. The model extensions are derived theoretically based on signal cycle, green split, and offset, and are shown to approximate well traffic operations at signalized intersections treated using the traditional (and more realistic) on-and-off model. We propose a generalized continuum signal model, which explicitly handles complex vehicle spillback patterns on signalized networks with provable error estimates. Under mild conditions, the errors are small and bounded by fixed values that do not grow with time. Overall, this represents a significant improvement over the original continuum model, which had errors that grew quickly with time in the presence of any queue spillbacks and for which errors were not explicitly derived for different offset cases. Thus, the new model is able to more accurately approximate traffic dynamics in large networks with multiple signals under more realistic conditions. We also qualitatively describe how this new model can be applied to several realistic intersection configurations that might be encountered in typical urban networks. These include intersections with multiple entry and exit links, complex signal phasing, all-red times, and the presence of dedicated turning lanes. Numerical tests of the models show remarkable consistency with the on-and-off model, as expected from the theory, with the added benefit of significant computational savings and higher signal control resolution when using the continuum model.     

Model based urban traffic control,part II: Coordinated model predictive controllers

The present paper describes how to use coordination between neighbouring intersections in order to improve the performance of urban traffic controllers. Both the local MPC (LMPC) introduced in the companion paper (Hao et al., 2018) and the coordinated MPC (CMPC) introduced in this paper use the urban cell transmission model (UCTM) (Hao et al., 2018) in order to predict the average delay of vehicles in the upstream links of each intersection, for different scenarios of switching times of the traffic lights at that intersection. The feedback controller selects the next switching times of the traffic light corresponding to the shortest predicted average delay. While the local MPC (Hao et al., 2018) only uses local measurements of traffic in the links connected to the intersection in comparing the performance of different scenarios, the CMPC approach improves the accuracy of the performance predictions by allowing a control agent to exchange information about planned switching times with control agents at all neighbouring intersections. Compared to local MPC the offline information on average flow rates from neighbouring intersections is replaced in coordinated MPC by additional online information on when the neighbouring intersections plan to send vehicles to the intersection under control. To achieve good coordination planned switching times should not change too often, hence a cost for changing planned schedules from one decision time to the next decision time is added to the cost function. In order to improve the stability properties of CMPC a prediction of the sum of squared queue sizes is used whenever some downstream queues of an intersection become too long. Only scenarios that decrease this sum of squares of local queues are considered for possible implementation. This stabilization criterion is shown experimentally to further improve the performance of our controller. In particular it leads to a significant reduction of the queues that build up at the edges of the traffic region under control. We compare via simulation the average delay of vehicles travelling on a simple 4 by 4 Manhattan grid, for traffic lights with pre-timed control, traffic lights using the local MPC controller (Hao et al., 2018), and coordinated MPC (with and without the stabilizing condition). These simulations show that the proposed CMPC achieves a significant reduction in delay for different traffic conditions in comparison to these other strategies.     

Optimal vehicle speed trajectory on a signalized arterial with consideration of queue

Vehicle speed trajectory significantly impacts fuel consumption and greenhouse gas emissions, especially for trips on signalized arterials. Although a large amount of research has been conducted aiming at providing optimal speed advisory to drivers, impacts from queues at intersections are not considered. Ignoring the constraints induced by queues could result in suboptimal or infeasible solutions. In this study, a multi-stage optimal control formulation is proposed to obtain the optimal vehicle trajectory on signalized arterials, where both vehicle queue and traffic light status are considered. To facilitate the real-time update of the optimal speed trajectory, a constrained optimization model is proposed as an approximation approach, which can be solved much quicker. Numerical examples demonstrate the effectiveness of the proposed optimal control model and the solution efficiency of the proposed approach.     

Platoons of connected vehicles can double throughput in urban roads

Intersections are the bottlenecks of the urban road system because an intersection’s capacity is only a fraction of the maximum flows that the roads connecting to the intersection can carry. This capacity can be increased if vehicles cross the intersections in platoons rather than one by one as they do today. Platoon formation is enabled by connected vehicle technology. This paper assesses the potential mobility benefits of platooning. It argues that saturation flow rates, and hence intersection capacity, can be doubled or tripled by platooning. The argument is supported by the analysis of three queuing models and by the simulation of a road network with 16 intersections and 73 links. The queuing analysis and the simulations reveal that a signalized network with fixed time control will support an increase in demand by a factor of (say) two or three if all saturation flows are increased by the same factor, with no change in the control. Furthermore, despite the increased demand vehicles will experience the same delay and travel time. The same scaling improvement is achieved when the fixed time control is replaced by the max pressure adaptive control. Part of the capacity increase can alternatively be used to reduce queue lengths and the associated queuing delay by decreasing the cycle time. Impediments to the control of connected vehicles to achieve platooning at intersections appear to be small.     

A traffic-condition-based route guidance strategy for a single destination road network

Most of existing route guidance strategies achieves user optimal equilibrium by comparing travel time. Measuring travel time, however, might be uneasy on an urban road network. To contend with the issue, the paper mainly considers easily obtained inflow and outflow of a link and road capacity as input, and proposes a route guidance strategy for a single destination road network based on the determination of free-flow or congested conditions on alternative routes. An extended strategy for a complex network and a feedback approximation for avoiding forecast are further explored. Weaknesses of the strategy are also explicitly analyzed. To test the strategy, simulation investigations are conducted on two networks with multiple parallel routes. The results indicate that the strategy is able to provide stable splitting rates and to approximate user optimal equilibrium in different conditions, in particular when traffic demand is high. This strategy has potential to be applied in an urban road network due to its simplicity and easily obtained input data. The strategy is also applicable for single destination if some alternatives and similar routes are available.     

A real-time adaptive signal control in a connected vehicle environment

The state of the practice traffic signal control strategies mainly rely on infrastructure based vehicle detector data as the input for the control logic. The infrastructure based detectors are generally point detectors which cannot directly provide measurement of vehicle location and speed. With the advances in wireless communication technology, vehicles are able to communicate with each other and with the infrastructure in the emerging connected vehicle system. Data collected from connected vehicles provides a much more complete picture of the traffic states near an intersection and can be utilized for signal control. This paper presents a real-time adaptive signal phase allocation algorithm using connected vehicle data. The proposed algorithm optimizes the phase sequence and duration by solving a two-level optimization problem. Two objective functions are considered: minimization of total vehicle delay and minimization of queue length. Due to the low penetration rate of the connected vehicles, an algorithm that estimates the states of unequipped vehicle based on connected vehicle data is developed to construct a complete arrival table for the phase allocation algorithm. A real-world intersection is modeled in VISSIM to validate the algorithms. Results with a variety of connected vehicle market penetration rates and demand levels are compared to well-tuned fully actuated control. In general, the proposed control algorithm outperforms actuated control by reducing total delay by as much as 16.33% in a high penetration rate case and similar delay in a low penetration rate case. Different objective functions result in different behaviors of signal timing. The minimization of total vehicle delay usually generates lower total vehicle delay, while minimization of queue length serves all phases in a more balanced way.     

Isolated intersection control for various levels of vehicle technology: Conventional,connected, and automated vehicles

Connected vehicle technology can be beneficial for traffic operations at intersections. The information provided by cars equipped with this technology can be used to design a more efficient signal control strategy. Moreover, it can be possible to control the trajectory of automated vehicles with a centralized controller. This paper builds on a previous signal control algorithm developed for connected vehicles in a simple, single intersection. It improves the previous work by (1) integrating three different stages of technology development; (2) developing a heuristics to switch the signal controls depending on the stage of technology; (3) increasing the computational efficiency with a branch and bound solution method; (4) incorporating trajectory design for automated vehicles; (5) using a Kalman filter to reduce the impact of measurement errors on the final solution. Three categories of vehicles are considered in this paper to represent different stages of this technology: conventional vehicles, connected but non-automated vehicles (connected vehicles), and automated vehicles. The proposed algorithm finds the optimal departure sequence to minimize the total delay based on position information. Within each departure sequence, the algorithm finds the optimal trajectory of automated vehicles that reduces total delay. The optimal departure sequence and trajectories are obtained by a branch and bound method, which shows the potential of generalizing this algorithm to a complex intersection.Simulations are conducted for different total flows, demand ratios and penetration rates of each technology stage (i.e. proportion of each category of vehicles). This algorithm is compared to an actuated signal control algorithm to evaluate its performance. The simulation results show an evident decrease in the total number of stops and delay when using the connected vehicle algorithm for the tested scenarios with information level of as low as 50%. Robustness of this algorithm to different input parameters and measurement noises are also evaluated. Results show that the algorithm is more sensitive to the arrival pattern in high flow scenarios. Results also show that the algorithm works well with the measurement noises. Finally, the results are used to develop a heuristic to switch between the different control algorithms, according to the total demand and penetration rate of each technology.     

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.     

Using connected vehicle technology to improve the efficiency of intersections

Information from connected vehicles, such as the position and speed of individual vehicles, can be used to optimize traffic operations at an intersection. This paper proposes such an algorithm for two one-way-streets assuming that only a certain percentage of cars are equipped with this technology. The algorithm enumerates different sequences of cars discharging from the intersection to minimize the objective function. Benefits of platooning (multiple cars consecutively discharging from a queue) and signal flexibility (adaptability to demand) are also considered. The goal is to gain insights about the value (in terms of delay savings) of using connected vehicle technology for intersection control.Simulations are conducted for different total demand values and demand ratios to understand the effects of changing the minimum green time at the signal and the penetration rate of connected cars. Using autonomous vehicle control systems, the signal could rapidly change the direction of priority without relying on the reaction of drivers. However, without this technology a minimum green time is necessary. The results of the simulations show that a minimum green time increases the delay only for the low and balanced demand scenarios. Therefore, the value of using cars with autonomous vehicle control can only be seen at intersections with this kind of demand patterns, and could result in up to 7% decrease in delay. On the other hand, using information from connected vehicles to better adapt the traffic signal has proven to be indeed very valuable. Increases in the penetration rate from 0% up to 60% can significantly reduce the average delay (in low demand scenarios a decrease in delay of up to 60% can be observed). That being said, after a penetration rate of 60%, while the delays continue to decrease, the rate of reduction decreases and the marginal value of information from communication technologies diminishes. Overall, it is observed that connected vehicle technology could significantly improve the operation of traffic at signalized intersections, at least under the proposed algorithm.     

Coordinated ramp metering for freeway networks – A model-predictive hierarchical control approach

A nonlinear model-predictive hierarchical control approach is presented for coordinated ramp metering of freeway networks. The utilized hierarchical structure consists of three layers: the estimation/prediction layer, the optimization layer and the direct control layer. The previously designed optimal control tool AMOC (Advanced Motorway Optimal Control) is incorporated in the second layer while the local feedback control strategy ALINEA is used in the third layer. Simulation results are presented for the Amsterdam ring-road. The proposed approach outperforms uncoordinated local ramp metering and its efficiency approaches the one obtained by an optimal open-loop solution. It is demonstrated that metering of all on-ramps, including freeway-to-freeway intersections, with sufficient ramp storage space leads to the optimal utilization of the available infrastructure.     

Design and evaluation of dynamic traffic management strategies for congested conditions

This paper presents a procedure for dynamic design and evaluation of traffic management strategies in oversaturated conditions. The method combines a dynamic control algorithm and a disutility function. The dynamic algorithm designs signal control parameters to manage formation and dissipation of queues on system links with explicit consideration of current and projected queue lengths and demands. The disutility function measures the relative performance of the dynamic control algorithm based on preset system performance goals. The user may statically select the management strategy, or alternatively the system may be instructed to set off different management schemes based on predefined performance thresholds. The problem was formulated as one of output maximization subject to state, control, and traffic management strategy choices. Solutions were obtained using genetic algorithms. Four traffic management plans were tested to show the capabilities of the new procedure. The results show that the procedure is able to generate suitable signal control schemes that are favorable to attaining the desired traffic management goals. The results showed that multiple, or hybrids of single measures of effectiveness may need to be examined in order to correctly assess system performance. The procedure has potential for real-time implementation in an intelligent transportation system setting.     

Perimeter and boundary flow control in multi-reservoir heterogeneous networks

In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a single-reservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.