A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.     

A robust optimization approach for dynamic traffic signal control with emission considerations

We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.     

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-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.     

Multi-agent model predictive control of signaling split in urban traffic networks

The operation of large dynamic systems such as urban traffic networks remains a challenge in control engineering to a great extent due to their sheer size, intrinsic complexity, and nonlinear behavior. Recently, control engineers have looked for unconventional means for modeling and control of complex dynamic systems, in particular the technology of multi-agent systems whose appeal stems from their composite nature, flexibility, and scalability. This paper contributes to this evolving technology by proposing a framework for multi-agent control of linear dynamic systems, which decomposes a centralized model predictive control problem into a network of coupled, but small sub-problems that are solved by the distributed agents. Theoretical results ensure convergence of the distributed iterations to a globally optimal solution. The framework is applied to the signaling split control of traffic networks. Experiments conducted with simulation software indicate that the multi-agent framework attains performance comparable to conventional control. The main advantages of the multi-agent framework are its graceful extension and localized reconfiguration, which require adjustments only in the control strategies of the agents in the vicinity.     

Distributed model predictive control for railway traffic management

Every day small delays occur in almost all railway networks. Such small delays are often called “disturbances” in literature. In order to deal with disturbances dispatchers reschedule and reroute trains, or break connections. We call this the railway management problem. In this paper we describe how the railway management problem can be solved using centralized model predictive control (MPC) and we propose several distributed model predictive control (DMPC) methods to solve the railway management problem for entire (national) railway networks. Furthermore, we propose an optimization method to determine a good partitioning of the network in an arbitrary number of sub-networks that is used for the DMPC methods. The DMPC methods are extensively tested in a case study using a model of the Dutch railway network and the trains of the Nederlandse Spoorwegen. From the case study it is clear that the DMPC methods can solve the railway traffic management problem, with the same reduction in delays, much faster than the centralized MPC method.     

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.     

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.     

Arterial traffic signal optimization: A person-based approach

This paper presents a real-time signal control system that optimizes signal settings based on minimization of person delay on arterials. The system’s underlying mixed integer linear program minimizes person delay by explicitly accounting for the passenger occupancy of autos and transit vehicles. This way it can provide signal priority to transit vehicles in an efficient way even when they travel in conflicting directions. Furthermore, it recognizes the importance of schedule adherence for reliable transit operations and accounts for it by assigning an additional weighting factor on transit delays. This introduces another criterion for resolving the issue of assigning priority to conflicting transit routes. At the same time, the system maintains auto vehicle progression by introducing the appropriate delays associated with interruptions of platoons. In addition to the fact that it utilizes readily available technologies to obtain the inputs for the optimization, the system’s feasibility in real-world settings is enhanced by its low computation time. The proposed signal control system is tested on a four-intersection segment of San Pablo Avenue arterial located in Berkeley, California. The findings show the system’s capability to outperform pretimed (i.e., fixed-time) optimal signal settings by reducing total person delay. They have also demonstrated its success in reducing bus person delay by efficiently providing priority to transit vehicles even when they travel in conflicting directions.     

Using high-resolution event-based data for traffic modeling and control: An overview

Research on using high-resolution event-based data for traffic modeling and control is still at early stage. In this paper, we provide a comprehensive overview on what has been achieved and also think ahead on what can be achieved in the future. It is our opinion that using high-resolution event data, instead of conventional aggregate data, could bring significant improvements to current research and practices in traffic engineering. Event data records the times when a vehicle arrives at and departs from a vehicle detector. From that, individual vehicle’s on-detector-time and time gap between two consecutive vehicles can be derived. Such detailed information is of great importance for traffic modeling and control. As reviewed in this paper, current research has demonstrated that event data are extremely helpful in the fields of detector error diagnosis, vehicle classification, freeway travel time estimation, arterial performance measure, signal control optimization, traffic safety, traffic flow theory, and environmental studies. In addition, the cost of event data collection is low compared to other data collection techniques since event data can be directly collected from existing controller cabinet without any changes on the infrastructure, and can be continuously collected in 24/7 mode. This brings many research opportunities as suggested in the paper.     

Dynamic traffic routing in a network with adaptive signal control

In real traffic networks, travellers’ route choice is affected by traffic control strategies. In this research, we capture the interaction between travellers’ route choice and traffic signal control in a coherent framework. For travellers’ route choice, a VANET (Vehicular Ad hoc NETwork) is considered, where travellers have access to the real-time traffic information through V2V/V2I (Vehicle to Vehicle/Vehicle to Infrastructure) infrastructures and make route choice decisions at each intersection using hyper-path trees. We test our algorithm and control strategy by simulation in OmNet++ (A network communication simulator) and SUMO (Simulation of Urban MObility) under several scenarios. The simulation results show that with the proposed dynamic routing, the overall travel cost significantly decreases. It is also shown that the proposed adaptive signal control reduces the average delay effectively, as well as reduces the fluctuation of the average speed within the whole network.     

Network traffic control based on a mesoscopic dynamic flow model

The paper focuses on Network Traffic Control based on aggregate traffic flow variables, aiming at signal settings which are consistent with within-day traffic flow dynamics. The proposed optimisation strategy is based on two successive steps: the first step refers to each single junction optimisation (green timings), the second to network coordination (offsets). Both of the optimisation problems are solved through meta-heuristic algorithms: the optimisation of green timings is carried out through a multi-criteria Genetic Algorithm whereas offset optimisation is achieved with the mono-criterion Hill Climbing algorithm. To guarantee proper queuing and spillback simulation, an advanced mesoscopic traffic flow model is embedded within the network optimisation method. The adopted mesoscopic traffic flow model also includes link horizontal queue modelling. The results attained through the proposed optimisation framework are compared with those obtained through benchmark tools.     

Traffic noise and traffic light control

An optimal control problem of traffic light duration is considered. The traffic noise level is introduced as a state variable in a dynamical optimization problem. A closed loop control system is designed which influences the green duration of the lights according to the equivalent noise level. Real time considerations lead to sub-optimal control implementation. This control policy decreases the noise levels at intensive traffic intersections. The traffic lights adapt their duration according to the noise pollution. Simulation and experimental results are discussed.     

A sensitivity-based approach for adaptive decomposition of anticipatory network traffic control

Anticipatory optimal network control is defined as the problem of determining the set of control actions that minimizes a network-wide objective function. This not only takes into account local consequences on the propagation of flows, but also the global network-wide routing behavior of the users. Such an objective function is, in general, defined in a centralized setting, as knowledge regarding the whole network is needed to correctly compute it. Reaching a level of centralization sufficient to attain network-wide control objectives is however rarely realistic in practice. Multiple authorities are influencing different portions the network, separated either hierarchically or geographically. The distributed nature of networks and traffic directly influences the complexity of the anticipatory control problem.This is our motivation for this work, in which we introduce a decomposition mechanism for the global anticipatory network traffic control problem, based on dynamic clustering of traffic controllers. Rather than solving the full centralized problem, or blindly performing a full controller-wise decomposition, this technique allows recognizing when and which controllers should be grouped in clusters, and when, instead, these can be optimized separately.The practical relevance with respect to our motivation is that our approach allows identification of those network traffic conditions in which multiple actors need to actively coordinate their actions, or when unilateral action suffices for still approximating global optimality.This clustering procedure is based on well-known algebraic and statistical tools that exploit the network’s sensitivity to control and its structure to deduce coupling behavior. We devise several case studies in order to assess our newly introduced procedure’s performances, in comparison with fully decomposed and fully centralized anticipatory optimal network control, and show that our approach is able to outperform both centralized and decomposed procedures.     

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 dual control approach for repeated anticipatory traffic control with estimation of network flow sensitivity

This paper investigates a strategic signal control, which anticipates travelers' route choice response and determines signal timings to optimize network‐wide objectives. In general traffic assignment models are used for anticipating this route choice response. However, model‐reality mismatch usually brings suboptimal solutions to the real system. A repeated anticipatory control resolves the suboptimality and addresses the modeling error by learning from information on model bias. This paper extends the repeated control approach and focuses on the estimation of flow sensitivity as well as its influence on control, which is a crucial issue in implementation of model bias correction. The main objective of this paper is first to analyze the estimation error in the real flow derivative that is estimated from noisy measurements. A dual control method is then presented, improving both optimization objective function and derivative estimation during the control process. The proposed dual algorithm is tested on a simple network as well as on a midsize network. Numerical examples confirm the reliable performance of the new reality‐tracking control strategy and its ability to identify (local) optimal solutions on real traffic networks. Copyright © 2016 John Wiley & Sons, Ltd.     

A model for the visualization and analysis of elevator traffic

ABSTRACT

Analysis of elevator traffic in high rise buildings is critical to the performance evaluation of elevator group control systems (EGCS). Elevator dispatching methods or parking algorithms in an EGCS can be designed or modified according to analyses of traffic flow. However, interpretation of traffic flow based solely on numerical data may not be explicit and transparent for EGCS experts as well as for other non-expert building administration. In this study, we present a model for visualization and analysis of elevator traffic. First, we present an alternative approach for traffic analysis which we call route visualization. In the proposed approach, we initially decompose elevator traffic into its component parts and investigate each component independently. Then, using superposition of components we obtain a reconstructed model of overall traffic. This modeling approach provides component-based traffic analysis and representation of routes with intensities through data visualization. In the second part we introduce a multi-dimensional analysis of time parameters in ECGS. This approach provides a comparative analysis of several control algorithms such as dispatch or park algorithms for different combinations of traffic components.