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.     

Multi-scale perimeter control approach in a connected-vehicle environment

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors).     

Model-based predictive control for bicycling in urban intersections

In this paper, a model predictive control approach for improving the efficiency of bicycling as part of intermodal transportation systems is proposed. Considering a dedicated bicycle lanes infrastructure, the focus in this paper is to optimize the dynamic interaction between bicycles and vehicles at the multimodal urban traffic intersections. In the proposed approach, a dynamic model for the flows, queues, and number of both vehicles and bicycles is explicitly incorporated in the controller. For obtaining a good trade-off between the total time spent by the cyclists and by the drivers, a Pareto analysis is proposed to adjust the objective function of the MPC controller. Simulation results for a two-intersections urban traffic network are presented and the controller is analyzed considering different methods of including in the MPC controller the inflow demands of both vehicles and bicycles.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.     

Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.     

A hybrid model predictive control for traffic flow stabilization and pollution reduction of freeways

In this work a control system is developed and analyzed for the suppression of moving jamwaves and the reduction of pollutant concentrations near motorways. The system is based on the second-order macroscopic freeway traffic model METANET, joined by an emission dispersion model, introduced in a previous work of the authors. For the control tasks dedicated controllers are designed, both using the nonlinear model predictive control method. The control objectives require a distinction in the utilized control measures, thus different controllers are designed and used in predefined control modes. The first mode of the controller is responsible for keeping pollutant concentrations below prescribed limits under stable conditions. The second mode of the controller is working in case of a shockwave threat, aiming for traffic stabilization. Between the control modes switching is based on an appropriate rule set that satisfies the stability of the controlled system. The hybrid controller structure is realized by a finite automata. A complex case study is presented for the evaluation of the suggested controller.     

Validation of an extended discrete first-order model with variable speed limits

This paper validates the prediction model embedded in a model predictive controller (MPC) of variable speed limits (VSLs). The MPC controller was designed based on an extended discrete first-order model with a triangular fundamental diagram. In our previous work, the extended discrete first-order model was designed to reproduce the capacity drop and the propagation of jam waves, and it was validated with reasonable accuracy without the presence of VSLs. As VSLs influence traffic dynamics, the dynamics including VSLs needs to be validated, before it can be applied as a prediction model in MPC. For conceptual illustrations, we use two synthetic examples to show how the model reproduces the key mechanisms of VSLs that are applied by existing VSL control approaches. Furthermore, the model is calibrated by use of real traffic data from Dutch freeway A12, where the field test of a speed limit control algorithm (SPECIALIST) was conducted. In the calibration, the original model is extended by using a quadrangular fundamental diagram which keeps the linear feature of the model and represents traffic states at the under-critical branch more accurately. The resulting model is validated using various traffic data sets. The accuracy of the model is compared with a second-order traffic flow model. The performance of two models is comparable: both models reproduce accurate results matching with real data. Flow errors of the calibration and validation are around 10%. The extended discrete first-order model-based MPC controller has been demonstrated to resolve freeway jam waves efficiently by synthetic cases. It has a higher computation speed comparing to the second-order model-based MPC.     

Hierarchical perimeter control with guaranteed stability for dynamically coupled heterogeneous urban traffic

Perimeter control based on the Macroscopic Fundamental Diagram (MFD) is widely developed for alleviating or postponing congestion in a protected region. Recent studies reveal that traffic conditions might not be improved if the perimeter control strategies are applied to unstable systems where high demand generates heavy and heterogeneously distributed traffic congestion. Therefore, considering stability of the targeted traffic system is essential, for the sake of developing a feasible and then optimal control strategy. This paper sheds light on this direction. It integrates a stability characterization algorithm of MFD system equations into the Model Predictive Control (MPC) scheme, and features respectively an upper and a lower bound of the feasible control inputs, to guarantee system stability. Firstly, the dynamics of traffic heterogeneity and its effect on the MFD are analyzed, using real data from Guangzhou in China. Piecewise affine functions of average flow are proposed to capture traffic heterogeneity in both regional and subregional MFDs. Secondly, stability of a three-state two-region system is investigated via stable equilibrium and surface boundaries analysis. Finally, a three-layer hierarchical control strategy is introduced for the studied two-region heterogeneous urban networks. The first layer of the controller calculates the stable surface boundaries for the given traffic demands and then determines the bounds of control input (split rate). An MPC approach in the second layer is used to solve an optimization problem with two objectives of minimizing total network delay and maximizing network throughput. Heterogeneity among the subregions is minimized in the last layer by implementing simultaneously a subregional perimeter flow control and an internal flow control. The effectiveness and stability of the proposed control approach are verified by comparison with four existing perimeter control strategies.     

Signalized intersections with variable flow rates: II A model for delay estimation

This second part of our work develops a model for delay estimation at intersections whose traffic signal controls are continuously being updated. Generally, these traffic signals are centrally controlled. The foundation for the delay estimation model is based on a queuing theory model called “Preemptive resume discipline for M/G/1 with two priority levels.” This queuing model assumes that two customers arrive at acertain point by a Poisson arrival process, and that one customer has service priority over the second customer. The analogy for the case of intersection control is that the preferred customers are the red lights and the secondary customers are the vehicles. In order to adapt the model to the realistic behavior of vehicle traffic at continuously adjusted signals, components are derived to modify the model. The simulation results of the first part of this work are used to calculate adjustment factors that fairly accurately reproduce the simulated delays. This gives rise to the advantage of using in practice a closed mathematical model, in particular when trying to optimize the operation of signalized intersections at the network level.     

A two-stage fuzzy logic controller for traffic signals

This paper presents the design and evaluation of a fuzzy logic traffic signal controller for an isolated intersection. The controller is designed to be responsive to real-time traffic demands. The fuzzy controller uses vehicle loop detectors, placed upstream of the intersection on each approach, to measure approach flows and estimate queues. These data are used to decide, at regular time intervals, whether to extend or terminate the current signal phase. These decisions are made using a two-stage fuzzy logic procedure. In the first stage, observed approach traffic flows are used to estimate relative traffic intensities in the competing approaches. These traffic intensities are then used in the second stage to determine whether the current signal phase should be extended or terminated. The performance of this controller is compared to that of a traffic-actuated controller for different traffic conditions on a simulated four-approach intersection.     

Nonlinear gating control for urban road traffic network using the network fundamental diagram

This work proposes a nonlinear model predictive controller for the urban gating problem. The system model is formalized based on a research on existing models of the network fundamental diagram and the perimeter control systems. For the existing models, modifications are suggested: additional state variables are allocated to describe the queue dynamics at the network gates. Using the extended model, a nonlinear model predictive controller is designed offering a ‘non‐greedy’ policy compared with previous, ‘greedy’ gating control designs. The greedy and non‐greedy nonlinear model predictive control (NMPC) controllers are compared with a greedy linear feedback proportional‐integral‐derivative (PID) controller in different traffic situations. The proposed non‐greedy NMPC controller outperforms the other two approaches in terms of travel distance performance and queue lengths. The performance results justify the consideration of queue lengths in dynamic modeling, and the use of NMPC approach for controller design. Copyright © 2014 John Wiley & Sons, Ltd.     

Development of a delay model for unsignalized intersections applicable to traffic assignment

Abstract

This paper develops a model for estimating unsignalized intersection delays which can be applied to traffic assignment (TA) models. Current unsignalized intersection delay models have been developed mostly for operational purposes, and demand detailed geometric data and complicated procedures to estimate delay. These difficulties result in unsignalized intersection delays being ignored or assumed as a constant in TA models.

Video and vehicle license plate number recognition methods are used to collect traffic volume data and to measure delays during peak and off-peak traffic periods at four unsignalized intersections in the city of Tehran, Iran. Data on geometric design elements are measured through field surveys. An empirical approach is used to develop a delay model as a function of influencing factors based on 5- and 15-min time intervals. The proposed model estimates delays on each approach based on total traffic volumes, rights-of-way of the subject approach and the intersection friction factor. The effect of conflicting traffic flows is considered implicitly by using the intersection friction factor. As a result, the developed delay model guarantees the convergence of TA solution methods.

A comparison between delay models performed using different time intervals shows that the coefficients of determination, R ², increases from 43.2% to 63.1% as the time interval increases from 5- to 15-min. The US Highway Capacity Manual (HCM) delay model (which is widely used in Iran) is validated using the field data and it is found that it overestimates delay, especially in the high delay ranges.     

Integration of signal timing estimation model and dynamic traffic assignment in feedback loops: system design and case study

This paper presents an integrated framework for effective coupling of a signal timing estimation model and dynamic traffic assignment (DTA) in feedback loops. There are many challenges in effectively integrating signal timing tools with DTA software systems, such as data availability, exchange format, and system coupling. In this research, a tight coupling between a DTA model with various queue‐based simulation models and a quick estimation method Excel‐based signal control tool is achieved and tested. The presented framework design offers an automated solution for providing realistic signal timing parameters and intersection movement capacity allocation, especially for future year scenarios. The framework was used to design an open‐source data hub for multi‐resolution modeling in analysis, modeling and simulation applications, in which a typical regional planning model can be quickly converted to microscopic traffic simulation and signal optimization models. The coupling design and feedback loops are first demonstrated on a simple network, and we examine the theoretically important questions on the number of iterations required for reaching stable solutions in feedback loops. As shown in our experiment, the current coupled application becomes stable after about 30 iterations, when the capacity and signal timing parameters can quickly converge, while DTA's route switching model predominately determines and typically requires more iterations to reach a stable condition. A real‐world work zone case study illustrates how this application can be used to assess impacts of road construction or traffic incident events that disrupt normal traffic operations and cause route switching on multiple analysis levels. Copyright © 2014 John Wiley & Sons, Ltd.     

A platoon based cooperative eco-driving model for mixed automated and human-driven vehicles at a signalised intersection

The advancements in communication and sensing technologies can be exploited to assist the drivers in making better decisions. In this paper, we consider the design of a real-time cooperative eco-driving strategy for a group of vehicles with mixed automated vehicles (AVs) and human-driven vehicles (HVs). The lead vehicles in the platoon can receive the signal phase and timing information via vehicle-to-infrastructure (V2I) communication and the traffic states of both the preceding vehicle and current platoon via vehicle-to-vehicle (V2V) communication. We propose a receding horizon model predictive control (MPC) method to minimise the fuel consumption for platoons and drive the platoons to pass the intersection on a green phase. The method is then extended to dynamic platoon splitting and merging rules for cooperation among AVs and HVs in response to the high variation in urban traffic flow. Extensive simulation tests are also conducted to demonstrate the performance of the model in various conditions in the mixed traffic flow and different penetration rates of AVs. Our model shows that the cooperation between AVs and HVs can further smooth out the trajectory of the latter and reduce the fuel consumption of the entire traffic system, especially for the low penetration of AVs. It is noteworthy that the proposed model does not compromise the traffic efficiency and the driving comfort while achieving the eco-driving strategy.     

Enhancing the performance of existing urban traffic light control through extremum-seeking

Urban traffic light controllers are responsible for maintaining good performance within the transport network. Most existing and proposed controllers have design parameters that require some degree of tuning, with the sensitivity of the performance measure to the parameter often high. To date, tuning has been largely treated as a manual calibration exercise but ignores the effects of changes in traffic condition, such as demand profile evolution due to urban population growth. To address this potential shortcoming, we seek to use a newly developed extremum-seeker to calibrate the parameters of existing urban traffic light controllers in real-time such that a certain performance measure is optimised. The results are demonstrated for three categories of traffic controllers on a microscopic urban traffic simulation. It is demonstrated that the extremum-seeking scheme is able to seek the optimal parameters, with respect to a certain performance measure, for each of these traffic light controllers in an urban, uni-modal traffic environment.     

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.     

Evaluation of a model predictive control framework for motorway traffic involving conventional and automated vehicles

A Model Predictive Control (MPC) strategy for motorway traffic management, which takes into account both conventional control measures and control actions executed by vehicles equipped with Vehicle Automation and Communication Systems (VACS), is presented and evaluated using microscopic traffic simulation. A stretch of the motorway A20, which connects Rotterdam to Gouda in the Netherlands, is taken as a realistic test bed. In order to ensure the reliability of the application results, extensive speed and flow measurements, collected from the field, are used to calibrate the site’s microscopic traffic simulation model. The efficiency of the MPC framework, applied to this real sizable and complex network under realistic traffic conditions, is examined for different traffic conditions and different penetration rates of equipped vehicles. The adequacy of the control application when only VACS equipped vehicles are used as actuators, is also considered, and the related findings underline the significance of conventional control measures during a transition period or in case of increased future demand.     

Feedback control strategy of a new car-following model based on reducing traffic accident rates

ABSTRACT

To reduce the traffic accident death rate effectively and alleviate the traffic congestion phenomenon, this study proposes a new type of car-following model under the influence of drivers’ time-varying delay response time. Based on Lyapunov function theory, this paper reduces the traffic accident rate problem to the stability issues of the new model. By constructing suitable Lyapunov functions and using the linear matrix inequality method, the stability problem of the new car-following model is studied. The model, under the action of the controller, can effectively restrain traffic congestion. Using the traffic accident rate model proposed by Solomon, compared with the car-following model without the controller, the model under the controller shows a stronger convergence. This also means that the traffic congestion phenomenon has been effectively suppressed while greatly reducing the mortality rate of traffic accidents.     

Optimally combined headway and timetable reliable public transport system

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated.     

Paradoxes of reservation-based intersection controls in traffic networks

Reservation-based intersection control is a revolutionary idea for using connected autonomous vehicle technologies to improve intersection controls. Vehicles individually request permission to follow precise paths through the intersection at specific times from an intersection manager agent. Previous studies have shown that reservations can reduce delays beyond optimized signals in many demand scenarios. The purpose of this paper is to demonstrate that signals can outperform reservations through theoretical and realistic examples. We present two examples that exploit the reservation protocol to prioritize vehicles on local roads over vehicles on arterials, increasing the total vehicle delay. A third theoretical example demonstrates that reservations can encourage selfish route choice leading to arbitrarily large queues. Next, we present two realistic networks taken from metropolitan planning organization data in which reservations perform worse than signals. We conclude with significantly positive results from comparing reservations and signals on the downtown Austin grid network using dynamic traffic assignment. Overall, these results indicate that network-based analyses are needed to detect adverse route choices before traffic signals can be replaced with reservation controls. In asymmetric intersections (e.g. local road-arterial intersections), reservation controls can cause several potential issues. However, in networks with more symmetric intersections such as a downtown grid, reservations have great potential to improve traffic.