Model based urban traffic control,part I: Local model and local model predictive controllers

This paper is the first in a series of reports presenting a framework for the hierarchical design of feedback controllers for traffic lights in urban networks. The goal of the research is to develop an easy to understand methodology for designing model based feedback controllers that use the current state estimate in order to select the next switching times of traffic lights. In this paper we introduce an extension of the cell transmission model that describes with sufficient accuracy the major causes of delay for urban traffic. We show that this model is computationally fast enough such that it can be used in a model predictive controller that decides for each intersection, taking into account the vehicle density as estimated along all links connected to the intersection, what switching time minimizes the local delay for all vehicles over a prediction horizon of a few minutes. The implementation of this local MPC only requires local online measurements and local model information (unlike the coordinated MPC, to be introduced in the next paper in this series, that takes into account interactions between neighbouring intersections). We study the performance of the proposed local MPC via simulation on a simple 4 by 4 Manhattan grid, comparing its delay with an efficiently tuned pretimed control for the traffic lights, and with traffic lights controlled according to the max pressure rule. These simulations show that the proposed local MPC controller achieves a significant reduction in delay for various traffic conditions.     

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).     

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.     

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.     

An optimization method for sustainable traffic control in urban areas

The optimization of traffic signalization in urban areas is formulated as a problem of finding the cycle length, the green times and the offset of traffic signals that minimize an objective function of performance indices. Typical approaches to this optimization problem include the maximization of traffic throughput or the minimization of vehicles’ delays, number of stops, fuel consumption, etc. Dynamic Traffic Assignment (DTA) models are widely used for online and offline applications for efficient deployment of traffic control strategies and the evaluation of traffic management schemes and policies. We propose an optimization method for combining dynamic traffic assignment and network control by minimizing the risk of potential loss induced to travelers by exceeding their budgeted travel time as a result of deployed traffic signal settings, using the Conditional Value-at-Risk model. The proposed methodology can be easily implemented by researchers or practitioners to evaluate their alternative strategies and aid them to choose the alternative with less potential risk. The traffic signal optimization procedure is implemented in TRANSYT-7F and the dynamic propagation and route choice of vehicles is simulated with a mesoscopic dynamic traffic assignment tool (DTALite) with fixed temporal demand and network characteristics. The proposed approach is applied to a reference test network used by many researchers for verification purposes. Numerical experiments provide evidence of the advantages of this optimization method with respect to conventional optimization techniques. The overall benefit to the performance of the network is evaluated with a Conditional Value-at-Risk Analysis where the optimal solution is the one presenting the least risk for ‘guaranteed’ total travel times.     

System dynamics of urban traffic based on its parking-related-states

The urban parking and the urban traffic systems are essential components of the overall urban transportation structure. The short-term interactions between these two systems can be highly significant and influential to their individual performance. The urban parking system, for example, can affect the searching-for-parking traffic, influencing not only overall travel speeds in the network (traffic performance), but also total driven distance (environmental conditions). In turn, the traffic performance can also affect the time drivers spend searching for parking, and ultimately, parking usage. In this study, we propose a methodology to model macroscopically such interactions and evaluate their effects on urban congestion.The model is built on a matrix describing how, over time, vehicles in an urban area transition from one parking-related state to another. With this model it is possible to estimate, based on the traffic and parking demand as well as the parking supply, the amount of vehicles searching for parking, the amount of vehicles driving on the network but not searching for parking, and the amount of vehicles parked at any given time. More importantly, it is also possible to estimate the total (or average) time spent and distance driven within each of these states. Based on that, the model can be used to design and evaluate different parking policies, to improve (or optimize) the performance of both systems.A simple numerical example is provided to show possible applications of this type. Parking policies such as increasing parking supply or shortening the maximum parking duration allowed (i.e., time controls) are tested, and their effects on traffic are estimated. The preliminary results show that time control policies can alleviate the parking-caused traffic issues without the need for providing additional parking facilities. Results also show that parking policies that intend to reduce traffic delay may, at the same time, increase the driven distance and cause negative externalities. Hence, caution must be exercised and multiple traffic metrics should be evaluated before selecting these policies.Overall, this paper shows how the system dynamics of urban traffic, based on its parking-related-states, can be used to efficiently evaluate the urban traffic and parking systems macroscopically. The proposed model can be used to estimate both, how parking availability can affect traffic performance (e.g., average time searching for parking, number of cars searching for parking); and how different traffic conditions (e.g., travel speed, density in the system) can affect drivers ability to find parking. Moreover, the proposed model can be used to study multiple strategies or scenarios for traffic operations and control, transportation planning, land use planning, or parking management and operations.     

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.     

A cellular automata (CA) model for motorized vehicle flows influenced by bicycles along the roadside

On many urban low‐grade or branch roads, especially in medium or small cities in China, bicyclists and motorists commonly share the non‐barrier road surface. Because bicycles are unpredictable and unstable when moving, motorized vehicles must reduce their speed to safely approach and overtake them. In this study, the gradual deceleration process a motorized vehicle undergoes before it passes a bicycle was analyzed. The motorist was assumed to prefer a comfortable deceleration and to select a higher deceleration rate only when the distance to the bicycle was insufficient to reduce the car's speed to the expected value at a comfortable deceleration rate. Cellular automata (CA) simulations were used to reveal the flow characteristics of motorized vehicles reacting to bicycles traveling along the roadside, and the results show that for the general velocities of motorized vehicles and bicycles traveling on urban branch roads, the road capacity for motorized vehicles is not related to the number of bicycles present. However, the average travel time of motorized vehicles is significantly affected by the presence of bicycles when the number of motorized vehicles on the road is small. In addition, motorized vehicles' average travel time is more influenced by disturbances in the flow of motorized vehicles than by bicycles when the number of motorized vehicles on the road is large. Field observations and surveys were used to validate the traffic behaviors and simulation results. Copyright © 2016 John Wiley & Sons, Ltd.     

Hierarchical control strategies for energy management of connected hybrid electric vehicles in urban roads

This paper presents a fuel efficient control strategy for a group of connected hybrid electric vehicles (HEVs) in urban road conditions. A hierarchical control architecture is proposed in this paper for every HEV, where the higher level and the lower level controller share information with each other and solve two different problems that aim at improving its fuel efficiency. The higher level controller of each HEV is considered to utilize traffic light information, through vehicle to infrastructure (V2I) communication, and state information of the vehicles in its near neighborhood, via vehicle to vehicle (V2V) communication. Apart from that, the higher level controller of each HEV uses the recuperation information from the lower level controller and provides it the optimal velocity profile by solving its problem in a model predictive control framework. Each lower level controller uses adaptive equivalent consumption minimization strategy (ECMS) for following their velocity profiles, obtained from the higher level controller, in a fuel efficient manner. In this paper, the vehicles are modeled in Autonomie software and the simulation results are provided in the paper that shows the effectiveness of the proposed control architecture.     

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.     

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.     

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.     

Empirical analysis of heterogeneous traffic flow and calibration of porous flow model

Heterogeneous traffic flow, characterized by a free inter-lane exchange, has become an important issue in addressing congestion in urban areas. It is of particular interest in many developing countries, that experience a strong increase in motorcycle use. New approaches to the heterogeneous non-lane-based flow have been proposed. However insufficient empirical verification has been made to estimate vehicle interaction, that is necessary for an accurate representation of mixed-flow conditions. In this paper, we focus on the porous flow approach to capture the complex interactions. The parameters from this approach are estimated from empirical observations. Video data was recorded and processed to capture vehicle interactions at a number of road sections in Surabaya City, Indonesia. The specific behavior of each vehicle in the traffic flow was captured by developing the pore size–density distributions, analyzing the class-specific critical pore sizes, and producing the class specific speed–density and flow–density diagrams. The results reveal how critical pore sizes are based on pore size–density distributions, the flow diagram for each vehicle class, and how traffic flow relationships for motorcyclists and the other vehicles exhibit significant differences. It is concluded that the proposed approach can represent the specific behavior of the motorcyclist in heterogeneous traffic flow, in both the situations of with- and without an exclusive lane for motorcycles, can clarify motorcyclist’s behavior in terms of passenger car unit of motorcycle, and can therefore support policy making on the improvement of urban transport.     

Multi-modal traffic signal control with priority,signal actuation and coordination

Both coordinated-actuated signal control systems and signal priority control systems have been widely deployed for the last few decades. However, these two control systems are often conflicting with each due to different control objectives. This paper aims to address the conflicting issues between actuated-coordination and multi-modal priority control. Enabled by vehicle-to-infrastructure (v2i) communication in Connected Vehicle Systems, priority eligible vehicles, such as emergency vehicles, transit buses, commercial trucks, and pedestrians are able to send request for priority messages to a traffic signal controller when approaching a signalized intersection. It is likely that multiple vehicles and pedestrians will send requests such that there may be multiple active requests at the same time. A request-based mixed-integer linear program (MILP) is formulated that explicitly accommodate multiple priority requests from different modes of vehicles and pedestrians while simultaneously considering coordination and vehicle actuation. Signal coordination is achieved by integrating virtual coordination requests for priority in the formulation. A penalty is added to the objective function when the signal coordination is not fulfilled. This “soft” signal coordination allows the signal plan to adjust itself to serve multiple priority requests that may be from different modes. The priority-optimal signal timing is responsive to real-time actuations of non-priority demand by allowing phases to extend and gap out using traditional vehicle actuation logic. The proposed control method is compared with state-of-practice transit signal priority (TSP) both under the optimized signal timing plans using microscopic traffic simulation. The simulation experiments show that the proposed control model is able to reduce average bus delay, average pedestrian delay, and average passenger car delay, especially for highly congested condition with a high frequency of transit vehicle priority requests.     

Two-class freeway traffic regulation to reduce congestion and emissions via nonlinear optimal control

The objective of this paper is the regulation of freeway traffic by means of optimal control techniques. A first innovative aspect of the proposed approach is the adopted objective function in which, besides the reduction of traffic congestion (which is typically considered in traffic control schemes), the minimization of traffic emissions is also included. Moreover, a multi-class framework is defined in which two classes of vehicles (cars and trucks) are explicitly modelled, and specific control actions for each vehicle class are sought. This results in the formulation of a multi-objective optimal control problem which is described in the paper and for which a specific solution algorithm is developed and used. The algorithm exploits a specific version of the feasible direction algorithm whose effectiveness is demonstrated in the paper by means of simulation results.     

Hierarchical network-based equilibrium model and algorithm for a mixed-traffic urban transport system

Abstract

Many equilibrium models and algorithms based on homogeneous motorized traffic have been devised to model urban transport systems in developed countries, but they are inadequate when it comes to represent mixed-traffic urban transport systems, including automobiles, transit, bicycles, and pedestrians, in developing countries such as China or India. In these cases, traffic flow on a road segment is an aggregated result of travellers' combined mode/route choices and corresponding interactions. Therefore, a special assignment model and algorithm are needed for modeling these distinct behaviors. In this article, the structure of a mixed-traffic urban transport system is analyzed and then expanded and represented using a hierarchical network model based on graph theory. Based on the analysis of travelers' combined mode/route choices, generalized travel cost functions and link impedance functions for different modes are formulated, where the interferences between different modes on the same road segments are taken into account. Due to the ‘asymmetric’ nature of these functions, a variational inequality model is proposed to represent the equilibrium assignment problem in a mixed-traffic urban transport system. The corresponding solution algorithm is also presented. Finally, a numerical example is provided to illustrate the practicality of the proposed model and 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.     

Variability in sound power levels: Implications for static and dynamic traffic models

Classically, one mean vehicle representative of each category is used by both static and dynamic traffic noise prediction models. The spectrum associated with this mean vehicle is determined from a linear statistical regression analysis based on measurement campaigns on a track or in situ. However, the variability of individual vehicle emissions can influence predictions and hinder comparison between static and dynamic models. In order to estimate the induced bias, statistical analysis of the distributions of sound power levels emitted by the individual passage of vehicles during 82 measurement campaigns was carried out. The results show that 92% of the residual regression distributions are Gaussian and that standard deviations can reach 3.6 dBA. The value of the proposed correction term for this case study could reach 1.4 dBA for light vehicles and 1.2 dBA for heavy vehicles. This analysis also shows that the variability in sound power levels and thus the corresponding corrections are higher at the lowest speeds that correspond to urban driving conditions.