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.     

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.     

Eco-routing problem considering fuel consumption and probabilistic travel time budget

Road transportation is one of the major sources of greenhouse gas emissions. To reduce energy consumption and alleviate this environmental problem, this study aims to develop an eco-routing algorithm for navigation systems. Considering that both fuel consumption and travel time are important factors when planning a trip, the proposed routing algorithm finds a path that consumes the minimum amount of gasoline while ensuring that the travel time satisfies a specified travel time budget and an on-time arrival probability. We first develop link-based fuel consumption models based on vehicle dynamics, and then the Lagrangian-relaxation-based heuristic approach is proposed to efficiently solve this NP-hard problem. The performance of the proposed eco-routing strategy is verified in a large-scale network with real travel time and fuel consumption data. Specifically, a sensitivity analysis of fuel consumption reduction for travel demand and travel time buffer is discussed in our simulation study.     

The identification and empirical characterization of vehicular (Lagrangian) fundamental diagrams in multilane traffic flow

Traditional macroscopic traffic flow modeling framework adopts the spatial–temporal coordinate system to analyze traffic flow dynamics. With such modeling and analysis paradigm, complications arise for traffic flow data collected from mobile sensors such as probe vehicles equipped with mobile phones, Bluetooth, and Global Positioning System devices. The vehicle‐based measurement technologies call for new modeling thoughts that address the unique features of moving measurements and explore their full potential. In this paper, we look into the concept of vehicular fundamental diagram (VFD) and discuss its engineering implications. VFD corresponds to a conventional fundamental diagram (FD) in the kinematic wave (KW) theory that adopts space–time coordinates. Similar to the regular FD in the KW theory, VFD encapsulates all traffic flow dynamics. In this paper, to demonstrate the full potential of VFD in interpreting multilane traffic flow dynamics, we generalize the classical Edie's formula and propose a direct approach of reconstructing VFD from traffic measurements in the vehicular coordinates. A smoothing algorithm is proposed to effectively reduce the nonphysical fluctuation of traffic states calculated from multilane vehicle trajectories. As an example, we apply the proposed methodology to explore the next‐generation simulation datasets and identify the existence and forms of shock waves in different coordinate systems. Our findings provide empirical justifications and further insight for the Lagrangian traffic flow theory and models when applied in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

Using automatic passenger counter data in bus arrival time prediction

Artificial neural networks have been used in a variety of prediction models because of their flexibility in modeling complicated systems. Using the automatic passenger counter data collected by New Jersey Transit, a model based on a neural network was developed to predict bus arrival times. Test runs showed that the predicted travel times generated by the models are reasonably close to the actual arrival times.     

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.     

Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data

Vehicle longitudinal control systems such as (commercially available) autonomous Adaptive Cruise Control (ACC) and its more sophisticated variant Cooperative ACC (CACC) could potentially have significant impacts on traffic flow. Accurate models of the dynamic responses of both of these systems are needed to produce realistic predictions of their effects on highway capacity and traffic flow dynamics. This paper describes the development of models of both ACC and CACC control systems that are based on real experimental data. To this end, four production vehicles were equipped with a commercial ACC system and a newly developed CACC controller. The Intelligent Driver Model (IDM) that has been widely used for ACC car-following modeling was also implemented on the production vehicles. These controllers were tested in different traffic situations in order to measure the actual responses of the vehicles. Test results indicate that: (1) the IDM controller when implemented in our experimental test vehicles does not perceptibly follow the speed changes of the preceding vehicle; (2) strings of consecutive ACC vehicles are unstable, amplifying the speed variations of preceding vehicles; and (3) strings of consecutive CACC vehicles overcome these limitations, providing smooth and stable car following responses. Simple but accurate models of the ACC and CACC vehicle following dynamics were derived from the actual measured responses of the vehicles and applied to simulations of some simple multi-vehicle car following scenarios.     

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.     

An agent-based framework for cooperative planning of intermodal freight transport chains

The recent development of Intelligent Transportation Systems offers the possibility of cooperative planning of multi-actor systems in a distributed framework, by enabling prompt exchange of information among actors. This paper proposes a modeling framework for cooperation in intermodal freight transport chains as multi-actor systems. In this framework, the problem of optimizing freight transportation is decomposed into a suitable set of sub-problems, each representing the operations of an actor which are connected using a negotiation scheme. A Discrete Event model is developed which optimizes the system on a rolling horizon basis to account for the dynamics of intermodal freight transport operations. This framework allows for an event driven short/medium term planning of intermodal freight transport chains. The proposed methodology is evaluated using a realistic case study, and the results are compared against the First-Come-First-Served strategy, highlighting the significance of cooperation in systems operating close to capacity.     

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.     

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.     

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.     

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).     

Vehicle platoon formation using interpolating control: A laboratory experimental analysis

This work addresses the formation phase of automatic platooning. The objective is to optimally control the throttle of vehicles, with a given arbitrary initial condition, such that desired ground speed and inter-vehicular spacings are reached. The steering of the vehicles is also controlled, because the vehicles should track a desired path while forming the platoon. In order to address the platoon formation problem, a cooperative strategy is formed by constructing a discrete state space model which represents the dynamics of a set of n vehicles. Once this model is set, a control method known as Interpolating Control, which aims at regulating to the origin an uncertain and/or time-varying linear discrete-time system with state and control constraints, is utilized. The performance of this control method is evaluated and compared with other approaches such as Model Predictive Control (MPC).Simulations are conducted which suggest that the Interpolating Control approach can be seen as an alternative to optimization-based control schemes such as Model Predictive Control, especially for problems for which finding the optimal solution requires calculations, where the Interpolating Control approach can provide a straightforward sub-optimal solution.In the experimental part of this work, the control algorithms for the platoon formation and path tracking problems are combined, and tested in a laboratory environment, using three mobile robots equipped with wireless routers. Validation of the proposed models and control algorithms is achieved by successful experiments.     

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.     

Control of interacting machines in automated container terminals using a sequential planning approach for collision avoidance

The control of automated container terminals is complex since Quay Cranes (QCs), Automated Guided Vehicles (AGVs) and Automated Stacking Cranes (ASCs) interact intensively for transporting containers, while collision avoidance of equipment must be ensured. This paper proposes a methodology to generate collision-free trajectories of free-ranging AGVs in automated container terminals, while minimizing the makespan of the whole container handling system. A hierarchical control architecture is proposed to integrate the scheduling of interacting machines and trajectory planning of AGVs. Following a so-called overall graph sequence by a scheduler, the collision-free trajectories of AGVs are determined by solving a collection of mixed integer linear programming problems sequentially. Simulation results illustrate the potential of the proposed methodology.     

A probabilistic model for traffic at actuated control signals

Vehicle actuated controls are designed to adapt green and red times automatically, according to the actual dynamics of the arrival, departure and queuing processes. In turn, drivers experience variable delays and waiting times at these signals. However, in practice, delays and waiting times are computed at these systems with models that assume stationariety in the arrival process, and that are capable of computing simply expectation values, while no information is given on the uncertainty around this expectation. The growing interest on measures like travel time reliability, or network robustness motivates the development of models able to quantify the variability of traffic at these systems.This paper presents a new modeling approach for estimating queues and signal phase times, based on probabilistic theory. This model overcomes the limitations of existing models in that it does not assume stationary arrival rates, but it assumes any temporal distribution as input, and allows one to compute the temporal evolution of queue length and signal sequence probabilities. By doing so, one can also quantify the uncertainty in the estimation of delays and waiting times as time-dependent processes. The results of the probabilistic approach have been compared to the results of repeated microscopic simulations, showing good agreement. The smaller number of parameters and shorter computing times required in the probabilistic approach makes the model suitable for, e.g., planning and design problems, as well as model-based travel time estimation.     

Hybrid predictive control for real-time optimization of public transport systems’ operations based on evolutionary multi-objective optimization

A hybrid predictive control formulation based on evolutionary multi-objective optimization to optimize real-time operations of public transport systems is presented. The state space model includes bus position, expected load and arrival time at stops. The system is based on discrete events, and the possible operator control actions are: holding vehicles at stations and skipping some stations. The controller (operator) pursues the minimization of a dynamic objective function to generate better operational decisions under uncertain demand at bus stops. In this work, a multi-objective approach is conducted to include different goals in the optimization process that could be opposite. In this case, the optimization was defined in terms of two objectives: waiting time minimization on one side, and impact of the strategies on the other. A genetic algorithm method is proposed to solve the multi-objective dynamic problem. From the conducted experiments considering a single bus line corridor, we found that the two objectives are opposite but with a certain degree of overlapping, in the sense that in all cases both objectives significantly improve the level of service with respect to the open-loop scenario by regularizing the headways. On average, the observed trade-off validates the proposed multi-objective methodology for the studied system, allowing dynamically finding the pseudo-optimal Pareto front and making real-time decisions based on different optimization criteria reflected in the proposed objective function compounds.     

基于指定到达追踪间隔的高铁车站接车进路长度研究

确定合理的高铁车站接车进路长度对压缩到达追踪间隔时间有重要意义。本文首先通过构建满足到达追踪间隔时间的高铁车站接车进路长度计算模型,提出了接车进路长度的主要影响因素为由线路限制速度、站前坡坡度、制动力使用系数三因素(简称三因素)所确定的车载设备监控制动距离内列车运行时间。然后,通过对常见的线路限制速度、站前坡坡度、制动力使用系数取值下的车载设备监控制动距离内列车运行时间进行牵引计算仿真,并运用三因素方差分析法分析了三因素的影响显著度,得到了线路限制速度、站前坡坡度对高铁车站接车进路长度影响显著的结论。最后,基于高铁车站接车进路长度计算模型,得到了一组指定到达追踪间隔下的高铁车站接车进路长度表,为高铁车站设计提供思路。     

Learning-based framework for transit assignment modeling under information provision

The modeling of service dynamics has been the focus of recent developments in the field of transit assignment modeling. The emerging focus on dynamic service modeling requires a corresponding shift in transit demand modeling to represent appropriately the dynamic behaviour of passengers and their responses to Intelligent Transportation Systems technologies. This paper presents the theoretical development of a departure time and transit path choice model based on the Markovian Decision Process. This model is the core of the MIcrosimulation Learning-based Approach to TRansit Assignment. Passengers, while traveling, move to different locations in the transit network at different points in time (e.g. at stop, on board), representing a stochastic process. This stochastic process is partly dependent on the transit service performance and partly controlled by the transit rider’s trip choices. This can be analyzed as a Markovian Decision Process, in which actions are rewarded and hence passengers’ optimal policies for maximizing the trip utility can be estimated. The proposed model is classified as a bounded rational model, with a constant utility term and a stochastic choice rule. The model is appropriate for modeling information provision since it distinguishes between individual’s experience with the service performance and information provided about system dynamics.