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• Studies network Macroscopic Fundamental Diagram of urban network with hierarchical streets. • Presence of hierarchy leads to non-unimodal patterns in MFD when hierarchical streets present and users route according to UE principles. • Findings obtained with simple analytical model and confirmed with simulations and empirical data. Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks—so called network Macroscopic Fundamental Diagrams (MFDs)—have recently been shown to exist on homogeneous street networks. When present, MFD relationships facilitate the modeling of traffic congestion at a regional level and have led to the development of various regional traffic control strategies. However, real street networks are not homogeneous—they generally have a hierarchical structure where some streets (e.g., arterials) promote higher mobility than others (e.g., local roads). This paper examines how the presence of hierarchical roadway structures may potentially cause non-unimodal patterns in a network's MFD. These are observed using three types of tools: analytical models of simple network structures, simulations of various idealized roadway networks, and empirical data. The impacts of street hierarchy depend on how vehicles use different roadway types to move within the network; i.e., their routing strategy. The findings suggest that the presence of roadway hierarchies may lead to MFDs that have non-unimodal or non-concave patterns on the free-flow branch when vehicles route themselves according to user equilibrium principles, which is closest to what would be observed in realistic situations. Such patterns are contrary to what is traditionally assumed in most MFD-based modeling frameworks. However, the unimodal and concave MFD should be expected under system optimal routing conditions that maximize network productivity for a given traffic state. [ABSTRACT FROM AUTHOR]

Focusing on a freeway lane running with mixed semi-autonomous vehicles (semi-AVs) and fully-autonomous vehicles (fully-AVs), this study aims to investigate the heterogeneous platooning effect of the two types of autonomous vehicles (AVs) on the travel efficiency of the mixed traffic. Such impact in the mixed semi-/fully-AV traffic, to the best of our knowledge, has not been well addressed in the literature as the existing mixed traffic studies on platooning effect typically focused on the traffic scenes with only human-driven vehicles (HVs) and fully-AVs. The existence of semi-AVs, which are optionally controlled by human drivers and semi-autonomous driving systems, and their significant difference in platooning behavior from the fully-AVs have received very limited attention. To fill the gap, we first characterize the semi- and fully-AVs' difference in connection ability and willingness to platoon in the vehicle platooning process, and derive the heterogeneous platooning probabilities of semi- and fully-AVs. To formulate the platooned traffic after vehicle platooning process, we proceed to develop a novel Markov chain model to determine the probability distributions of vehicular platoon size and headway type among the mixed semi-/fully-AV traffic analytically. Furthermore, with the probability distributions, we derive the fundamental diagram (FD) and the capacity of the freeway lane for the mixed semi-/fully-AV traffic, and are thus able to investigate impact of platooning on the travel efficiency numerically. The developed models and unveiled insights in this study will help researchers and practitioners better understand the role, potential and prospect of automated transport system in the transitional stage with semi-AVs, which will be useful for guiding the mixed AV traffic management and control in near future. • Heterogeneous platooning behavior of semi- and fully-AVs is modeled. • Closed-form solutions for platoon size and headway type are derived. • A general approach to the FD and capacity is proposed. • Managerial insights into platooning impact of semi-AVs are provided. [ABSTRACT FROM AUTHOR]

Jam density, or its reciprocal jam spacing, is a parameter difficult to estimate. In fact, most traffic signal control and traffic state estimation studies published until date generally assume a given value, with no estimation from data whatsoever. Nevertheless, estimating jam density is crucial, since any deviation from its true value will propagate to queue lengths and volume estimates. In the possession of only trajectory data, its estimation is even harder since not all vehicles are observed. In this paper, we first define the data generating process of the jam spacing parameter using sparse trajectory data. Then, we propose several estimators to estimate jam spacing and its variance. We use as measurements the distances between successive vehicle stops. The first estimator is a Maximum-Likelihood estimator (MLE) of a Geometrically Skewed Normal (GSN) distribution, to be used whenever there is lane information. The second estimator is a MLE of a shifted GSN with Normal Stopbar (SGSN-NSB) to be used when observed distances are measured from the stopbar estimate. In addition, we propose two least-squares counterparts, LSE and LSE-SB, based on least absolute remainders. Finally, we assess and compare the bias and efficiency of the estimators in both synthetic and real-world data, obtaining satisfactory results. MLE estimators are shown to outperform their LSE counterparts in both situations. • We estimate jam spacing from distances between successive observed vehicle stops. • Data generation process is defined as a geometric mixture of normals. • Two Maximum Likelihood estimators and two Least Squares estimators are proposed. • With no lane information, jam spacing and stopbar location are estimated together. • Estimators are robust against the presence of long vehicles. [ABSTRACT FROM AUTHOR]

Traffic Signal Controllers (TSCs) used to manage intersections can influence the residual queues at intersections. These residual queues can lead to an irreversible state of network gridlock. This paper discovers the advantages of locally adaptive TSCs utilizing traffic information on both upstream and downstream approaches of an intersection (e.g., back-pressure or BP control) over employing only upstream approaches information (e.g., proportional control) in avoiding gridlock. Although BP algorithms are mathematically proven to be throughput optimal as they bound network queues for all feasible demands, the proofs exist only for networks with infinite link capacities, fixed-route choices, or for TSCs with no minimum green-time requirement. We propose a simple asymmetric two-bin model to study the influence of the BP control on network behavior (e.g., gridlock probability, average time to gridlock and maximum throughput) and compare it with the other control policy. Theoretical insights from the asymmetric two-bin model are verified using microsimulation results of the asymmetric two-ring model. Both analytical and simulation results imply that BP-based TSCs have an increased capability of delaying or avoiding gridlock in heavy traffic with a larger time step at the cost of potentially lower throughput in undersaturated networks. The paper provides a framework to evaluate control policies in inhomogeneous networks and shows the superiority of BP-based TSCs against gridlock in grid networks with finite capacities of links. • Develop an asymmetric two-bin model to study gridlock in a rectangular grid network. • Compare Back-Pressure based Traffic Signal Controller with proportional scheme. • Demonstrate advantages of BP-based TSC in avoiding/delaying network-level gridlock. [ABSTRACT FROM AUTHOR]

Traffic at urban intersections constitute a series of complex conflicting vehicular movements and contribute greatly to the problems of traffic congestion and air pollution. The emerging of connected and automated vehicle (CAV) technologies inspires innovative ideas in traffic management at intersections; it not only enables new control paradigms, but also allows for possibilities to revolutionize the geometric layouts of intersections. This study proposes a novel intersection design called knotted intersection (KI), to resolve the complexity of conflicting relations at intersections in a full CAV environment. This new design is associated with a set of neat control rules for vehicles to realize the smooth traffic operation at these intersections. The design problem of intersection geometry and control strategy is optimized jointly and formulated as a mixed-integer linear program (MILP), and some basic theoretical properties of KI design are derived, including nearly throughput-maximizing property and bounded within-intersection delay of vehicles. Furthermore, the KI design is then extended to a road network composed of multiple intersections to improve the overall efficiency. The optimal design of multiple knotted intersections (MKI) is developed to coordinate the traffic organization methods among intersections and a two-level solution method is proposed to solve the optimization efficiently. Numerical and simulation experiments are conducted at both the intersection level and network level under various cases, and the results validate the superior performance of the proposed methods compared to classical traffic signal control (TSC) strategies. • Knotted intersection design for resolving the complexity of intersection conflicts • Joint design of intersection geometric layout and traffic control strategy • Theoretical properties for nearly-maximum throughput and bounded delay • Optimal design of multiple knotted intersections to enhance network efficiency [ABSTRACT FROM AUTHOR]

• A specific "cycle-averaged" interpretation of "continuous signal modeling" for time-aggregated of traffic signal boundary conditions and turn movements is presented, which complies with the logic behind it. • Regarding the above-mentioned specific interpretation requirements of a continuous signalized node model are presented and mathematically formulated, which define the continuous signalized (or COS) node model. • A convergent algorithm that solves COS numerically is presented. • Via a series of simple numerical cases it is showed that COS is the only continuous signalized node model that respects all the relevant boundary conditions. In macroscopic dynamic network loading, the role of the node model is to determine transfer volumes between each in- and outgoing link, while respecting in a consistent way all forward and backward-moving traffic waves (or boundary conditions) and desired turning fractions. In addition, capacity constraints on the node itself need to be respected; they result from priority rules on conflict points, or from traffic signal control. The most common way in literature to implement signalized node models is to track second by second which turns have green or are blocked by red. This imposes a fine – and thus computationally demanding – time discretization step in the numerical solution algorithm of the entire dynamic network loading, often unnecessary or even undesired for the DNL application. As an alternative, this paper proposes a continuous approach that finds the average turn (or transfer) volume over a full cycle under the prevailing link boundary conditions and traffic signal timing. This average 'continuous' volume can then be applied to any (fine or coarse) time discretization. To this end, it discusses in depth and proposes mathematical formulations for all boundary and consistency requirements that a traffic signal imposes, and the intricate interactions between stage timing and arrival patterns of vehicles and outflow opportunities (gaps). This COntinuous Signalized or COS node model and its iterative solution algorithm combine all these boundaries and interactions in a theoretically consistent way. In a case study, we show that COS is the only existing, theoretically consistent continuous signalized node model, as alternative models sometimes fail to produce holding-free solutions, and/or violate boundary conditions imposed by the connecting links (especially in more complicated combinations of boundary conditions involving congestion spillback). [ABSTRACT FROM AUTHOR]

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions. • Heavy-traffic analysis of long-term queueing behavior of fixed-cycle traffic lights. • Special limiting regime with high load and non-zero delay probability. • Sharp performance approximations for one traffic queue in heavy traffic. • Easy prescription of close-to-optimal green times for conflicting traffic flows. [ABSTRACT FROM AUTHOR]

Connected and Autonomous Vehicles is a technology that will be disruptive for all layers of traffic control. The Lagrangian, in-the-flow nature of their operation offers untapped new potentials for sensing and actuation, but also presents new fundamental challenges. In order to use these vehicles for traffic state reconstruction and control, we need suitable traffic models, which should be computationally efficient and able to represent complex traffic phenomena. To this end, we propose the Front-tracking Transition System Model, a cell-free modelling approach that can incorporate Lagrangian measurements, and has a structure that yields itself to on-line model learning and control. The model is formulated as a transition system, and based on the front-tracking method for finding entropy solutions to the Lighthill–Whitham–Richards model. We characterize the solution of this model and show that it corresponds to the solution of the underlying PDE traffic model. Algorithms for traffic state reconstruction and model learning are proposed, exploiting the model structure. The model is then used to design a prediction-based control law for stop-and-go wave dissipation using randomly arriving Connected and Autonomous Vehicles. The proposed control framework is able to estimate the traffic state and model, adapt to changes in the traffic dynamics, and achieve a reduction in vehicles' Total Time Spent. • Connected and Automated Vehicles can be used as traffic sensors and actuators. • Front-tracking Transition System Model is based on front tracking numerical methods. • The model captures stop-and-go waves and moving bottlenecks. • Algorithms are proposed for traffic state reconstruction and model learning. • Prediction-based moving bottleneck control is used to dissipate stop-and-go waves. [ABSTRACT FROM AUTHOR]

This paper presents an analysis on the convergence to a steady state for the traffic dynamics in a network of signalized intersections. The links carrying the traffic from one intersection to another in the network are partitioned into a series of cells whose dynamics is modelled as a nonlinear cell transmission model. A microscopic convergence analysis is presented for the network where the traffic lights at the intersections are controlled by pre-timed control in which the average flow rate along each link is assumed to be known accurately. A macroscopic convergence analysis is applied to the traffic network where the traffic lights are controlled by coordinated model predictive control. In coordinated model predictive control, each local agent optimizes the switching times of traffic light at one intersection online with sampled local traffic state around this intersection and exchanged information from neighbouring intersections. A unique periodic function for the microscopic steady state is proved to exist under pre-timed control while a unique macroscopic steady state is achieved under coordinated model predictive control for the traffic lights. This paper validates by simulations that the ability of coordinated model predictive control to stabilize the traffic demand is not worse than pre-timed control even though the average flow rate along each link is not assumed to be known and further no explicit cycle time for the traffic light is suggested. Moreover, the incurred delay from the steady state is lower on the average under coordinated model predictive control compared to pre-timed control. • Presenting microscopic convergence analysis on pre-timed control • Proposing distributed model predictive control for traffic signals. • Presenting macroscopic convergence analysis on distributed control. • Validating claims on convergence of traffic signal control by simulations. [ABSTRACT FROM AUTHOR]

Perimeter control is a traffic management approach aimed at regulating vehicular accumulation within urban regional networks by managing flows on all border-crossing roads. Methods based on the macroscopic fundamental diagram (MFD) fall short in providing specific metering for individual roads. Recent advancements in the cell transmission model (CTM) have attempted to address this limitation but are hindered by their reliance on centralized control, which requires the availability of full information and authority over traffic generation sites. Our study proposes an innovative decentralized, game-theoretical framework for perimeter control to address these practical challenges. It is structured around two key groups of agents: perimeter agents, tasked with managing border roads, and interior agents, focused on traffic within generation sites. The framework also incorporates mechanisms for interactions between these agents and the road network, aiming to optimize their individual utilities. Additionally, we have developed a multi-agent reinforcement learning (RL) algorithm, extending the mean-field theory concept, to address the complexity of simultaneous learning by multiple agents. • Developed a perimeter control method for heterogeneous decision-makers. • Applied the macroscopic fundamental diagram concept to simplify perimeter control. • Introduced innovative reinforcement learning techniques for problem-solving. • Demonstrated superior performance using real-world traffic data. [ABSTRACT FROM AUTHOR]

Bayesian optimization (BO) is an attractive method for tackling transportation optimization problems due to its ability to balance exploitation and exploration. However, scaling BO to solve high-dimensional problems is a major challenge which has remained unsolved. Since transportation problems can be high-dimensional, the use of BO to solve transportation problems has been limited. This paper explores the use of BO with Gaussian process (GP) models to tackle high-dimensional transportation problems. It proposes formulations of the prior mean function and covariance function of the GP that enable BO to incorporate problem-specific transportation information, while remaining computationally tractable. This is done through the use of an analytical surrogate model. We validate the method with the 1-D and 100-D Griewank functions. The impact of different forms of bias in the surrogate model was also evaluated using the 100-D Griewank function example. We then apply the method to a high-dimensional traffic signal control problem in New York City. The results indicate the added value of using the problem-specific information in the prior mean and/or the covariance function. Importantly, for surrogate models that are not accurate approximations of, but have significant (anti-)correlation with the true objective function, the better approach is to embed the information in the covariance function, rather than in the prior mean function. More generally, the use of problem-specific information in the covariance function is robust to the accuracy of the surrogate model. This opens the way for a variety of low-resolution analytical transportation models to be used to tackle high-dimensional simulation-based optimization problems. • Problem-specific information can be used for exploration and exploitation in BO. • Using the surrogate model in the GP prior mean function improves exploitation. • Using the surrogate model in the GP covariance function improves exploration. • The surrogate model-based covariance function is robust to biases in the model. [ABSTRACT FROM AUTHOR]

Two new synchronization strategies are developed for signalized grids of two-directional streets. Both strategies are found to reduce congestion significantly more than do other approaches. One of the strategies is static and the other adaptive. Both use a common timing pattern for all signals on the grid but use a different offset for each. The static strategy serves the morning rush by providing perfect forward progression on all streets in the directions that point toward a reference intersection, one that is located near the center of gravity of all workplaces. For the evening rush, perfect progression is achieved for all travel directions that point away from the reference intersection. The adaptive strategy toggles between this forward synchronization mode and a second mode suited for congestion, but only in a pre-determined district surrounding the reference intersection. Toggling is based on the district's real-time traffic density. The paper shows how to switch quickly between the two synchronization modes without resorting to unacceptably short phases. It also shows that if the grid is formed by two intersecting sets of parallel streets, even if unevenly spaced, then every street can be perfectly synchronized in one of its directions. As a result, an inbound driver in the morning, or an outbound driver in the evening, is guaranteed to encounter synchronized signals over the full length of her trip. Although this is not possible for more irregular grids, the paper shows how to modify the two strategies for this case, so that they still perform well. The strategies were benchmarked with simulations against a fixed, zero-offset strategy for many scenarios, because zero-offsets are known to work well under congestion. In one important scenario representing a severely congested morning rush, both strategies were also benchmarked against a state-of-the-practice computer program. While the state-of-the-practice program reduced the zero-offset delay by a modest 7%, the proposed strategies reduced it by 21% (static) and 32% (adaptive); i.e., improving on the state-of-the-practice program by 14% and 25%. These improvements considerably exceed the 1% to 5% reductions typically reported in the literature for other state-of-the-art methods that have been compared with state-of-the-practice programs. Similarly good results were obtained for the other scenarios, which included the morning and evening rushes, various distributions of workplaces, and both regular and irregular grids. [ABSTRACT FROM AUTHOR]

We formulate a traffic theoretic and probabilistic analytical link transmission model. The proposed model extends past work that is based on a stochastic formulation of the link transmission model, which itself is an operational formulation of Newell's simplified theory of kinematic waves. The proposed model yields a probabilistic description of the link's upstream and downstream boundary conditions. The model only tracks the transient probabilities of two of the link's boundary states. This leads to a model with a state space dimension that is constant, i.e., it does not depend on any link attributes, such as link length. In other words, the model has constant complexity, whereas past formulations have a complexity that scales linearly or cubically with link length. The gain in computational runtime is of at least one order of magnitude and it increases with link length. This makes the proposed model suitable for large-scale network optimization. The model is validated versus a simulation-based implementation of the stochastic link transmission model. Its performance is also benchmarked with other past analytical formulations. The proposed model yields estimates with comparable accuracy, while the computational efficiency is enhanced by at least one order of magnitude. It is also validated versus a microscopic traffic simulator, the results indicate that the proposed model accurately approximates the link's boundary conditions for realistic traffic situations, such as signalized links and platoon arrival patterns. The model is then used to address a city-wide traffic signal control problem. The performance of the proposed model is benchmarked versus various other models and traffic signal control approaches. It is shown to reduce optimization compute time by at least one order of magnitude, while also yielding solutions (i.e., signal plans) with improved performance. • A traffic theoretic and probabilistic analytical link transmission model. • Probabilistic description of the link's upstream and downstream boundary conditions. • Constant model complexity suitable for large-scale network optimization. • Validation versus a simulation-based implementation of a stochastic link transmission model. • Validation versus a microscopic traffic simulator for realistic scenarios. • A case study of a signal control problem for the city of Lausanne (Switzerland). [ABSTRACT FROM AUTHOR]

Urban traffic control (UTC) is inherently multiscale in both temporal and spatial domains. With the wide deployment of connected and automated vehicles (CAVs), data is increasingly available to help reveal this multiscale nature of UTC and the inter-dynamics among different scales. This paper applies the multiscale UTC framework we proposed earlier and extends it to UTC on a network of traffic signals with a mixed flow of CAVs and human-driven vehicles (HDVs). We adopt distributed control as the basic scheme for network-wide control and use information sharing to achieve cooperation among different intersections. We use CAV information to estimate HDV state and develop a "safety check" technique to control CAVs in the mixed traffic flow. Together, we propose a network-wide UTC framework with mixed traffic flow. To address the computation issue of the model-based multiscale method, we develop an imitation learning (IL) enhanced data-driven method to improve the computation efficiency. Specifically, we use a convolutional neural network (CNN) to represent the policies of the slower-scale signal control problem and use the data aggregation method as the learning framework to improve the policies. This algorithm's unique feature is that IL policies' training is based on the optimized results from the model-based multiscale control method. We test the model-based and IL-based methods in simulation, under various traffic scenarios and on multiple networks. We also test the transferability property of the IL-based method by training individual intersection control separately in small networks and applying them to larger networks with various types of intersections. [ABSTRACT FROM AUTHOR]

In public transport, e.g., railways, crowding is of major influence on passenger satisfaction and also on system performance. We study the passenger-oriented traffic control problem by means of integrated optimization, particularly considering the crowding effects on passenger route choices and on train traffic. The goal is to find the system optimum solution by adapting train schedules and rerouting passengers. A mixed-integer nonlinear programming (MINLP) model is proposed, identifying the train orders and departure and arrival times, as well as finding the best route for passengers, with the objective of minimizing passenger disutility and train delay. In the model, we allow free splits of the passengers in a group onto different routes and reasonable passenger transfers between trains. We value train crowding by using time multiplier, which is defined as a piecewise constant function of the train crowding ratio (also called load factor), indicating that passengers perceive a longer travel time on a more crowded train. Moreover, we assume variations of the minimum train dwell time, caused by the alighting and boarding passengers. The nonlinear terms in the MINLP model are linearized by using an exact reformulation method and three transformation properties, resulting in an equivalent mixed-integer linear programming (MILP) model. In the experiences, we adopt a real-world railway network, i.e., the urban railway network in Zürich city, to examine the proposed approach. The results demonstrate the effectiveness of the model. The results show that, by considering the crowding effects, some passengers are forced to choose the routes that are less crowded but have larger travel/delay times, which leads to the improved passenger comfort and makes the planned train timetable less affected (in terms of delays). We also find that flexibility in train schedules brings more possibilities to serve better the passengers. Moreover, it is observed that if the train dwell time is highly sensitive to the alighting and boarding passengers, then the transport network will become vulnerable and less reliable, which should be avoided in real operations. • We study the passenger-oriented traffic control problem, considering crowding effects. • An MINLP model is proposed and further reformulated into an equivalent MILP model. • Passengers of a group can split on different routes, depending on crowding and capacity. • In the model, we restrict train capacity by penalizing train crowding. • With passenger rerouting onto alternatives, the overall system performance is improved. [ABSTRACT FROM AUTHOR]

Understanding the resilience of transportation networks has received considerable research attention. Nevertheless in the field of network traffic flow control, few control approaches target the mitigation from hyper-congestion, and the control objective has rarely touched the system resilience requirement which focuses on system recovering from hyper-congested state. This paper sheds light on a resilience-oriented network control. We firstly define the traffic resilience as the integral of deviation against optimal state from disturbance generation moment t 0 to recovery moment t f. Then, we propose a control method under hyper-congested situations by formulating the analytical problem using a two-reservoir transportation system with parabola-shaped Macroscopic Fundamental Diagrams (MFDs), using phase diagram analysis, attraction region derivation and switched controller design. Afterwards, we evaluate the system resilience performances between two classic perimeter control schemes (constant perimeter control (CPC) and state-feedback control (SFC)) and the proposed resilient control scheme. Results show that proposed controller can ensure the system to recover from hyper-congestion to the optimal state while existing studies failed to recover. This resilience is confirmed in various case study scenarios, e.g., when the level of hyper-congestion is different. More promisingly, the proposed control shows high compatibility with the form of the MFDs, e.g., the recover can be achieved under hysteresis conditions which are common for network-level traffic dynamics. These findings will help to design an intelligent transportation system with enhanced resilience. • We propose a traffic resilience measure as a control objective. • We propose a resilient control method to recover system to the optimal state from hyper-congestion. • We extend our methodology to two typical scenarios where the shape of the MFD changes under disruptions. [ABSTRACT FROM AUTHOR]

We study the well-posedness of a class of dynamical flow network systems describing the dynamical mass balance among a finite number of cells exchanging flow of traffic between themselves and with the external environment. Dynamical systems in the considered class are described as differential inclusions whereby the routing matrix is constant and the outflow from each cell in the network is limited by a control that is a Lipschitz continuous function of the state of the network. This framework finds application in particular within traffic signal control, whereby it is common that an empty queue can be allowed to have more outflow than vehicles in the queue. While models for this scenario have previously been presented for open-loop outflow controls, our result ensures the existence and uniqueness of solutions for the network flow dynamics in the case Lipschitz continuous feedback controllers. • A queuing network model with feedback that allows service to empty queues. • Prove existence and uniqueness of solutions when the controller is Lipschitz. • Show how dynamic flow propagation can be incorporated into the model. [ABSTRACT FROM AUTHOR]

• Urban traffic control is achieved by optimal route guidance based on avoidance maps. • Avoidance maps define which areas vehicles should better circumvent to sustain optimal internal traffic conditions. • Avoidance maps are derived from a reactive proportional control scheme. • A thorough sensitivity analysis shows how to tune the main parameters of the new concept (region sizes, safety distance, controller time horizon). • The new concept can improve total travel time by around 15% with little harm to individual vehicles. • Privacy by design is guaranteed as vehicles are not sharing data with the control system. This paper presents a new concept for operating traffic management at a sizeable urban scale. The overall principle is to partition the network into multiple regions, where traffic conditions should remain optimal. Instead of monitoring the inflow, like for perimeter control, deviations in regional mean speed compared to a reference value are transformed into avoidance levels by a centralized controller. That information is broadcasted to vehicles through a public avoidance map. The onboard navigation systems then interpret this map to deliver individual route guidance according to the avoidance levels. In that way, the concept tends to distribute vehicles in the network optimally while preserving privacy. In addition to the controller parameters itself, three other critical parameters define the system: the safety distance, the controller time horizon, and the region sizes. Thorough sensitivity analysis leads to the optimal setting. The concept is proven effective using microsimulation for both a Manhattan and a realistic network. The total travel time is improved by about 15% when traffic is severely congested compared to the uncontrolled case. In the meantime, the mean individual travel distance increase for rerouted vehicles is kept below 10%. Those results have been obtained with a simple decentralized reactive control framework, i.e., an individual proportional feedback system independently governs each region. More advanced formulations introducing cooperation between the regions are also tested. In a nutshell, this paper is a proof of concept for a new control system that appears both practical and valuable to alleviate congestion in urban areas. © 2021 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 24th International Symposium on Transportation and Traffic Theory [ABSTRACT FROM AUTHOR]

Secondary roads often suffer from diverted traffic trying to avoid congestion on major motorways. In this paper we study the traffic problems of a small town that is located parallel to a congested motorway and suffers from such diverted traffic (high local accident risks, local congestion and other nuisances). We assume that the motorway and the secondary road through the local town are under the jurisdiction of a different authority. A local government controls local accident risks and congestion using non-price measures such as speed bumps, traffic lights and explicit access restrictions for through traffic. A 'federal' government can control traffic levels on the motorway using tolls. We show the following results. First, competition between the federal and local authority leads to a Nash equilibrium where the toll is too high and there is too much traffic calming compared to the second-best social optimum. Second, if the local government uses traffic calming measures, imposing a federal toll on the main road is welfare-reducing, unless congestion on the main road is severe and accident risks and other traffic nuisances in the small town are unimportant. Third, traffic diverted from the main road to the local community gives the latter strong incentives to close the local road for through traffic, even when it is socially undesirable to do so. Fourth, if the access restriction only applies to through traffic by trucks, the conflict between federal and local authorities disappears: both will agree on restricting truck access. A numerical application using a two-link network between Leuven and Brussels (the highway and an alternative road passing through local communities) illustrates the theoretical results. [ABSTRACT FROM AUTHOR]

• There is a need for a secure-by-design tool for transportation systems. • Attack models made based on the link queue model and double ring road network model. • Attacks target control response time, traffic flow performance, and/or stability. • System states are analytically identified as vulnerable to attacks. • Analysis and simulations demonstrate effectiveness of attacks on vulnerable states. Wireless communication is being used as an enabling technology with traditional fixed traffic control systems in this transitional era toward Intelligent Transportation Systems (ITS). Unfortunately, major security concerns have arisen with respect to ever-increasing complexity and interconnectivity, and a noticeable lack of attention for security in these systems. Addressing concerns is a colossal challenge as it requires thorough development and formal analysis of a system model with respect to security. To tackle this challenge, we present a novel formal attack modeling and impact analysis methodology based on the Link Queue Model (LQM) of traffic flow inside a double ring road network, which is equivalent to a grid network with homogeneous links. We develop attack models as functions of tampered traffic control settings (e.g., green time ratios, cycle length, retaining ratios) with outputs equivalent to mobility impacts on the traffic network (e.g., time until system reaches state convergence, asymptotic average network flow). Further, for a given attack model, we define and identify vulnerable states: states that are critical to protect because they lead to negative impacts under the given attack model. Using our methodology we found that for certain vulnerable states, after only a few cycles of tampered control settings an attacker could cause a real impact of 1.5x speed-up in gridlock state convergence or 37%-99% drop in the asymptotic average flow rate. These results imply potentially drastic financial costs for cities and all involved drivers if similar attacks were performed on a real traffic control system. [ABSTRACT FROM AUTHOR]

• Identify, formulate, and solve optimal location problem for VSL application areas. Formulation and solution for lane-drop, sag, and tunnel bottlenecks. • Lighthill-Whitham Richards model with bounded acceleration (BA-LWR) is used. • Capacity drop formation depends on speed limits and VSL locations. • Define admissible conditions for congested and uncongested stationary states. • Optimal distances of VSL application areas from bottlenecks increase in speed limits. Some studies consider variable speed limit (VSL) control as a viable option to prevent traffic breakdown at bottlenecks by limiting the mainline flow with reduced speed limits. However, few studies consider the location of the application area as a design variable of the problem. This paper explains why the location of a VSL control area is crucial to prevent the capacity drop phenomenon at lane drop bottlenecks. We first define two types of stationary states, congested and uncongested, inside a lane drop bottleneck assuming the Lighthill-Whitham Richards model with bounded acceleration. In particular, the characteristics of these stationary states and their admissible conditions are discussed thoroughly. If the speed limit imposed is low enough, the location of the VSL application area is irrelevant to ensure an uncongested stationary state inside the bottleneck. However, for a given range of speed limits, the location of the VSL application area should be designed carefully to allow for uncongested stationary states and prevent the occurrence of the capacity drop. We formulate an optimization problem and show that, contrary to the general belief, the larger the speed limit, the farther the VSL application area should be from the bottleneck. Finally, the results are extended to other types of bottlenecks, such as sag or tunnel bottlenecks. To the best of our knowledge, this is the first study to analytically identify, formulate, and solve the optimal location problem for variable speed limit application areas. It makes fundamental contributions to both traffic flow theory (by analyzing the stationary states for VSL-controlled bottlenecks) and traffic control (by determining the optimal location of a VSL application area). Moreover, the results presented are of practical relevance because they can help to establish some guidelines for practitioners to implement VSL control strategies. [ABSTRACT FROM AUTHOR]

• We eliminate delay by coordinating the approach of CAV platoons at smart intersections. • We formulate the synchronization success probability for a general distribution of error. • We maximize the network capacity by optimizing the platoon size and marginal gap length. • We present the ANFD as a macro-level analytical tool for modeling the traffic dynamics. • We evaluate the accuracy of the analytical model using our simulation results. Recent advances in artificial intelligence and wireless communication technologies have created great potential to reduce congestion in urban networks. In this research, we develop a stochastic analytical model for optimal control of communicant autonomous vehicles (CAVs) at smart intersections. We present the automated network fundamental diagram (ANFD) as a macro-level modeling tool for urban networks with smart intersections. In the proposed cooperative control strategy, we make use of the headway between the CAV platoons in each direction for consecutive passage of the platoons in the crossing direction through non-signalized intersections with no delay. For this to happen, the arrival and departure of platoons in crossing directions need to be synchronized. To improve system robustness (synchronization success probability), we allow a marginal gap between arrival and departure of the consecutive platoons in crossing directions to make up for operational error in the synchronization process. We then develop a stochastic traffic model for the smart intersections. Our results show that the effects of increasing the platoon size and the marginal gap length on the network capacity are not always positive. In fact, the capacity can be maximized by optimizing these cooperative control variables. We analytically solve the traffic optimization problem for the platoon size and marginal gap length and derive a closed-form solution for a normal distribution of the operational error. The performance of the network with smart intersections is presented by a stochastic ANFD, derived analytically and verified numerically using the results of a simulation model. The simulation results show that optimizing the control variables increases the capacity by 138% when the error standard deviation is 0.1 s. [ABSTRACT FROM AUTHOR]

• New functional form with a physical meaning for the MFD. • Function allows curve fitting, but can also be combined with analytical MFD approaches. • One parameter quantifies average network flow reducing factors, e.g. vehicle interactions, heterogeneity, etc. The macroscopic fundamental diagram (MFD) relates vehicle accumulation and production of travel in an urban network with a well-defined and reproducible curve. Thanks to this relationship, the MFD offers a wide range of applications, most notably for traffic control. Recently, more and more empirical MFDs have been documented, providing further insights and facilitating their application in real urban networks. So far, however, no generally accepted functional form has been identified. This paper proposes a functional form for the MFD that is based on the smooth approximation of an upper bound of technologically feasible traffic states (uMFD). In this functional form, the uMFD can be either estimated from MFD measurements or defined a-priori, either analytically or with additional measurements in the network, while the smoothing to the uMFD is quantified with a single parameter λ. The uMFD can in principle be any multi-regime function, but we find that a trapezoidal shape with only four parameters, all physically meaningful, models the familiar shape of the MFD very well as shown with empirical data from Marseille, London, Lucerne, Yokohama, and Zurich. Further, we point to novel applications and analyses based on the interpretation of λ that would otherwise not be possible without this new functional form. [ABSTRACT FROM AUTHOR]

• Point-queue model is applied to model vehicle queuing at the boundary of two regions. • MFD-based efficient-range control determines the inflow rate to a region at the boundary. • Travelers choose routes to minimize their instantaneous travel times. • Efficient range control and instantaneous route choice can be modeled as a differential game. • The differential game modeled can be mathematically formulated as a DCS. •. Macroscopic fundamental diagram (MFD) has been receiving increasing attention recently due to its potential to describe traffic dynamics and guide the design of traffic control schemes at the network level. Perimeter control and route guidance are two main MFD-based traffic control approaches. However, current MFD-based perimeter control seldom considers travelers' route choice behavior, while MFD-based route guidance studies usually assume directly that travelers would follow the guidance and neglect the effects of traffic control. This paper aims to integrate the MFD-based perimeter control (i.e., the behavior of a system manager) and the dynamic user equilibrium based route choice behavior (i.e., the behavior of travelers) into one rigorous mathematical framework. Given a traffic network that has been divided into multiple homogeneous regions, we use MFD to describe the dynamics of each region, and use point queue model to capture the dynamics of queues formed at the boundaries. Besides, we model travelers' route choice behavior by the instantaneous dynamic user equilibrium (IDUE) principle, and design an efficient range perimeter control method from the system perspective. We model the interactions between the system manager and the travelers as a non-zero sum, non-cooperative differential game, where the system manager aims to improve the system performance while travelers try to minimize their own travel times. Meanwhile, they share the common constraints (i.e., MFD dynamics and point queue dynamics at boundaries). Mathematically, this leads to a differential complementarity system (DCS). We propose a time-stepping approach to discretize and solve the DCS model, based on which the solution existence and convergence are also established. Numerical results show that the proposed method can limit the vehicle accumulations within the efficient range of each region, which helps improve the network performance. Compared with the condition without perimeter control, the proposed control method can improve network-wide traffic performance up to 14.18%. [ABSTRACT FROM AUTHOR]

• A mixed linear integer programming formulation for synchronized vehicle trajectories and multi-intersection traffic control optimization • Modeling additional constraints for implementations, such as the effective capacities for permissive phases and during yellow and all-red clearance. • Propose a Lagrangian decomposition approach with subproblem approximation. • The proposed framework is suitable for high-performance-computing (HPC) techniques. Thanks to the development of mobile computing, novel traffic data sources are emerging as the promising building blocks for more effective traffic control strategies. It is expected that the vehicle space-time trajectories will become ubiquitously available in foreseeable future. Real-time trajectory data will provide full-spectrum pattern of traffic dynamics among multiple intersections. In this paper, we present a new traffic control representation for multiple intersections. A new multi-intersection phase (MI-phase) is proposed to represent safe vehicle movements across a few tightly connected intersections. All the intersections are also viewed as one integral "super intersection" within which vehicles move according to their planned paths. Through scheduling the sequence and durations of MI-phases over time, the vehicles will be crossing intersections with minimal delays. This approach can provide more flexibilities for traffic control coordination than the traditional Cycle-Split-Offset approach. A linear integer programming formulation is presented for joint optimization of vehicle space-time trajectories and traffic control. We also design a scalable optimization frame for real-world traffic control optimization, referred to as "Lagrangian decomposition with subproblem approximation" approaches. In this new framework, we construct the dynamic network loading based lower bound estimator (DNL-LBE) in which the relaxed constraints and sensitivity to the Lagrangian multiplier prices are explicitly considered while vehicular flows are being loaded. By doing so, the complex controlled dynamic network loading process can be represented through Lagrangian multipliers interfacing with the MI-phase optimization module (then solved by Dynamic Programming). This approach can facilitate price-based search heuristics to find high quality solutions for both vehicular space-time trajectories and traffic control plans without increasing the overall computing complexity. The efficiency of the proposed optimization framework is further improved through multiple advanced computing techniques. In the end, one demonstrative and one real-world example are provided to show the performance of the new approach. [ABSTRACT FROM AUTHOR]

• A robust counterpart of the Freeway Network Control problem is proposed. • We take uncertainty in the fundamental diagram and future traffic demand into account. • Under certain conditions, the robust problem admits a tractable, convex reformulation. • We also propose a receding horizon control approach with robustness guarantees. In the freeway network control (FNC) problem, the operation of a traffic network is optimized using only flow control. For special cases of the FNC problem, in particular the case when all merging junctions are controlled, there exist tight convex relaxations of the corresponding optimization problem. In practice, many parameters of this optimization problem are not known with certainty, in particular the fundamental diagram and predictions of future traffic demand. This uncertainty poses a challenge for control approaches that pursue a model- and optimization-based strategy. In this work, we propose a robust counterpart to the FNC problem, where we introduce uncertainty sets for both the fundamental diagram and future, external traffic demands and seek to optimize the system operation, minimizing the worst-case cost. For a network with controlled merging junctions, and assuming that certain technical conditions on the uncertainty sets are satisfied, we show that the robust counterpart of the FNC problem can be reduced to a convex, finite-dimensional and deterministic optimization problem, whose numerical solution is tractable. [ABSTRACT FROM AUTHOR]

The perimeter control concept based on macroscopic fundamental diagram (MFD) modeling is now well-established in various literature. Recent research efforts are devoted to develop perimeter control schemes, which can be eventually applied to urban traffic control systems. Modern urban traffic control systems increasingly rely on information technology infrastructure, combining various network and physical facilities and use of communication technologies, which increases the vulnerability for cyberattacks. As witnessed in recent real-life events, modern urban traffic control systems are vulnerable and not protected from internal and external, malicious and accidental threats. Hence, applicable perimeter control algorithms should be robust not only against dynamic uncertainties, but in addition, it should be resilient against cyberattack issues for real future implementations. In this paper, a resilient perimeter control scheme is developed for a modified multi-region MFD system model. The developed perimeter control is a fully decentralized scheme, which operates based on online local regional information only. It achieves an a priori desired tracking performance with simultaneous compensation of (i) cyberattacks in the channels of control signals transmission, (ii) model parameter uncertainties, (iii) unknown but bounded disturbances, and (iv) control input constraints. A framework of adaptive control techniques is utilized to design the perimeter control. The proposed fault-tolerant perimeter control does not require on-line fault detection, as the fault effects caused by cyberattacks are continuously and adaptively compensated by the developed algorithm. Stability proof of the closed-loop system in terms of the tracking and parameter errors are introduced, and simulation results for three aggregate urban traffic regions are presented. [ABSTRACT FROM AUTHOR]

• We propose a new, max-pressure based network traffic control policy for legacy and autonomous vehicles. • We introduce an autonomous vehicle-restricted phase, named the blue phase, to coordinate autonomous vehicles at network intersections. • We formulate a green signal phase model wherein movement capacities are endogenous to the choice of the activation matrix and lane FIFO blocking effects are accounted for. • We show that the proposed hybrid network traffic control policy is stable, i.e. maximizes throughout. • Our numerical experiments reveal considerable trade-offs in terms of vehicle-class travel time based on the level of congestion and the proportion of autonomous vehicles in the network. With the forecasted emergence of autonomous vehicles in urban traffic networks, new control policies are needed to leverage their potential for reducing congestion. While several efforts have studied the fully autonomous traffic control problem, there is a lack of models addressing the more imminent transitional stage wherein legacy and autonomous vehicles share the urban infrastructure. We address this gap by introducing a new policy for stochastic network traffic control involving both classes of vehicles. We conjecture that network links will have dedicated lanes for autonomous vehicles which provide access to traffic intersections and combine traditional green signal phases with autonomous vehicle-restricted signal phases named blue phases. We propose a new pressure-based, decentralized, hybrid network control policy that activates selected movements at intersections based on the solution of mixed-integer linear programs. We prove that the proposed policy is stable, i.e. maximizes network throughput, under conventional travel demand conditions. We conduct numerical experiments to test the proposed policy under varying proportions of autonomous vehicles. Our experiments reveal that considerable trade-offs exist in terms of vehicle-class travel time based on the level of market penetration of autonomous vehicles. Further, we find that the proposed hybrid network control policy improves on traditional green phase traffic signal control for high levels of congestion, thus helping in quantifying the potential benefits of autonomous vehicles in urban networks. [ABSTRACT FROM AUTHOR]

• Develop an effective queuing stratgy to control the spatiotemporal propagation of multiclass information. • Develop a new nonlinear integro-differential equations (IDE) system to characterize the information dissemination wave under the designed queuing strategy. • Develop an analytical soution for the proposed IDE system. • Consider multiple performance measures to address application needs involving multiple information classes. • Calibrate the communication kernel using NS-3 simulation. Most existing models for information flow propagation in a vehicle-to-vehicle (V2V) communications environment are descriptive. They lack capabilities to control information flow, which may preclude their ability to meet application needs, including the need to propagate different information types simultaneously to different target locations within corresponding time delay bounds. This study proposes a queuing-based modeling approach to control the propagation of information flow of multiple classes. Two control parameters associated with a vehicle, the number of communication servers and the mean communication service rate, are leveraged to control the propagation performance of different information classes. A two-layer model is developed to characterize the information flow propagation wave (IFPW) under the designed queuing strategy. The upper layer is formulated as integro-differential equations to characterize the spatiotemporal information dissemination due to V2V communication. The lower layer characterizes the traffic flow dynamics using the Lighthill–Whitham–Richards model. The analytical solution of the asymptotic density of informed vehicles and the necessary condition for existence of the IFPW are derived for homogeneous traffic conditions. Numerical experiments provide insights on the impact of the mean communication service rate on information spread and its spatial coverage. Further, a numerical solution method is developed to solve the two-layer model, which aids in estimating the impacts of the control parameters in the queuing strategy on the IFPW speed under homogenous and heterogeneous conditions. The proposed modeling approach enables controlling the propagation of information of different information classes to meet application needs, which can assist traffic managers to design effective and efficient traffic management and control strategies under V2V communications. [ABSTRACT FROM AUTHOR]

• A stochastic dynamic network loading model for the mixed traffic with autonomous vehicles and human-driven vehicles is developed. • The probabilistic link model captures the boundary conditions of a link and approximates the evolution of link state distribution. • The probabilistic node model reflects the between-link dependency by evaluating the expected transmission flow through an iterative algorithm. • Two applications of the proposed model, including a traffic signal control problem and a class-based ramp metering problem, are presented. In this study, we develop a stochastic dynamic network loading (DNL) model for the mixed traffic with autonomous vehicles (AVs) and human-driven vehicles (HVs). The source of stochasticity is the uncertainty inherent in the arrival process of the two classes of vehicular flow. The developed model captures both within-link and between-link traffic flow dependencies and evaluates the network state distribution in an analytical manner. The model has two main components, a probabilistic link model and a probabilistic node model. The link model is a stochastic formulation of the link transmission model (LTM), which captures the boundary conditions of a link and approximates the evolution of link state distribution. The node model, on the other hand, characterizes the flow transmissions across a network node. It reflects the between-link dependency by evaluating the expected transmission flow through an iterative algorithm, with an explicit consideration of the interactions between supply and demand constraints associated with a node. The developed model is validated versus replicated running of the deterministic LTM as well as microscopic traffic simulations, and the results reveal that it yields relatively accurate estimations. We also present two applications of the proposed model, including a traffic signal control problem and a class-based ramp metering problem, to demonstrate its practical value. [ABSTRACT FROM AUTHOR]

The emerging connected autonomous vehicle (CAV) technology offers a significant opportunity to address the congestion problem caused by the selfish routing behavior of human drivers. If the transportation management center (TMC) can control the routing of all vehicles on the network, they could easily reverse this effect. However, during the transition period, CAVs will share roads with human-piloted vehicles (HVs). In the era of mixed autonomy, a more realistic scenario is to route the CAVs to lead the traffic state towards the desired equilibrium. We first consider a repeated routing game in which the TMC can control the routes of CAVs to minimize the system travel time, i.e., CAVs follow the system optimal (SO) routing principle. In this manner, we can influence the travel time traversing each link, which indirectly influences HV users' route choices. As a consequence, HV users may adjust their routes dynamically through day-to-day (DTD) learning to minimize individual travel cost. On the other hand, the SO routing strategy may induce higher travel time for CAVs than HVs within the same origin–destination (OD) pair. To address such inherent unfairness, road pricing is used to influence route choices of HVs to achieve specific supply regulation targets, e.g., traffic restraint. We present qualitative analysis on the stability of the controlled DTD dynamics and the effect of road pricing regarding the unfairness. To the best of our knowledge, this paper is one of the first to design dynamic pricing schemes for a mixed autonomy system under DTD learning dynamics. We carry out numerical experiments to demonstrate the effectiveness of the control schemes. The cooperative CAVs could reduce the total travel time when the market penetration rate of CAVs reaches the lower minimum control ratio that the network could escape the user equilibrium (UE) condition. When the market penetration rate of CAVs reaches the upper minimum control ratio, the network would achieve SO condition even though there are non-cooperative HVs. On the other hand, the pricing scheme can reduce the unfairness index and total travel time of the network when the market penetration rate of CAVs is low. • Day-to-day evolution of the mixed autonomy system. • Routing the CAVs to SO paths to mitigate the impact of selfish routing of HVs. • Tolling the HVs to address the unfairness and to improve the network performance. • Qualitative analysis on the effects of road pricing regarding the unfairness. • Stability guarantee of the day-to-day traffic dynamics under the control schemes. [ABSTRACT FROM AUTHOR]

• A three-link quasi-dynamic spatial queueing assignment/control network model is specified. • It is proved that control policy P 0 does not maximise the capacity of this network even if queue storage capacities are very large. The local responsive traffic signal control policy P 0 was designed to maximise network capacity under certain conditions and it has been shown, in Smith (1979a, b, 1980) and Smith et al. (2019a, 2022), that the P 0 policy and related policies do indeed maximise the capacity of many steady state networks or quasi-dynamic networks with vertical and spatial queues under various conditions. This current paper shows, by giving an example, that if queueing is spatial then the original policy P0 itself may not maximise network capacity, even if the queue storage capacity of each link is very large. [ABSTRACT FROM AUTHOR]

• A backpressure approach built on macroscopic traffic theory. • A decentralized approach suitable for implementation in large urban networks. • Theoretical proof of network-wide traffic stability properties. • Very low computational costs. • Extensive experiments and comparisons that highlight the superiority of the proposed approach. Decentralized intersection control techniques have received recent attention in the literature as means to overcome scalability issues associated with network-wide intersection control. Chief among these techniques are backpressure (BP) control algorithms, which were originally developed of for large wireless networks. In addition to being light-weight computationally, they come with guarantees of performance at the network level, specifically in terms of network-wide stability. The dynamics in backpressure control are represented using networks of point queues and this also applies to all of the applications to traffic control. As such, BP in traffic fail to capture the spatial distribution of vehicles along the intersection links and, consequently, spill-back dynamics. This paper derives a position weighted backpressure (PWBP) control policy for network traffic applying continuum modeling principles of traffic dynamics and thus capture the spatial distribution of vehicles along network roads and spill-back dynamics. PWBP inherits the computational advantages of traditional BP. To prove stability of PWBP, (i) a Lyapunov functional that captures the spatial distribution of vehicles is developed; (ii) the capacity region of the network is formally defined in the context of macroscopic network traffic; and (iii) it is proved, when exogenous arrival rates are within the capacity region, that PWBP control is network stabilizing. We conduct comparisons against a real-world adaptive control implementation for an isolated intersection. Comparisons are also performed against other BP approaches in addition to optimized fixed timing control at the network level. These experiments demonstrate the superiority of PWBP over the other control policies in terms of capacity region, network-wide delay, congestion propagation speed, recoverability from heavy congestion (outside of the capacity region), and response to incidents. [ABSTRACT FROM AUTHOR]

• A Macroscopic Fundamental Diagram for a general network with one-to-many OD demands is analyzed. • A new inverse problem of dynamic user equilibrium with a periodic boundary condition is presented. • An analytical formula for the network throughput is derived by solving the inverse problem. • A sensitivity analysis reveals conditions of decreasing in the network throughput. • A distributed signal control for improving network performance is presented based on the sensitivity analysis. This study aims to analyze the relationship between a macroscopic fundamental diagram (MFD), which relates vehicle accumulation with throughput at the network level, and the spatial distribution of congestion (congestion pattern) in a general network with one-to-many origin-destination demands. In particular, we clarify the causes of a decreasing branch of MFDs and the influence of local signal controls on the (global) network throughput. For this aim, we present a new inverse problem of the dynamic user equilibrium assignment by using a periodic boundary condition, and an analytical formula of the network throughput for a fixed accumulation is derived by solving it. This enables us to incorporate the effects of network configurations and route choice behaviors into the analysis of the network throughput. By conducting a sensitivity analysis of this formula, we identify the types of congestion patterns that cause the decrease in the network throughput and examine a network signal control for improving network performance. [ABSTRACT FROM AUTHOR]

Highlights • Study freeway evacuation problems with limited inputs. • Establish the optimal conditions for InFO strategy. • Develop a combined evacuation strategy based on simple rules. Abstract In this paper, we propose an intuitive, non-anticipative, partially decentralized, and adaptive combined strategy for managing evacuation routes with limited inputs so as to minimize the system clearance time. This strategy is intuitive due to the use of simple and transparent rules, non-anticipative because it relies on readily available information only, partially decentralized because only the upstream ramps are coordinately optimized, and adaptive due to the self-renewal with traffic condition. It is a combined strategy because it may include priority control strategy or proportional control strategy. Our approach is robust in the sense that it can be easily implemented, and can deal with not only real-time data but also predictive information. Numerical results show that the proposed strategy works effectively and can serve as a simple evacuation tool for regulating ramp discharge flows. [ABSTRACT FROM AUTHOR]

Highlights • A bi-objective stochastic simulation-based optimization (BOSSO) method is proposed. • Equitable and efficient signal timing stochastic SO problem is solved well. • Network-wide microscopic traffic simulation model is well calibrated from two aspects. • The proposed BOSSO method can address other similar problems. Abstract The equity of right-of-way is an important topic in traffic management and control. With the balance consideration of traffic equity and efficiency, which are respectively evaluated by the Atkinson index and average travel time, this study proposes a bi-objective signal timing simulation-based optimization (SO) model under uncertainties, and solve it by a bi-objective stochastic simulation-based optimization (BOSSO) method. In this method, two types of surrogate models (i.e., regressing Kriging model and quadratic regression model) are used to capture the complicated mapping relationship between decision variables and bi-objectives, respectively in the whole variable domain and in the local trust-region. Meanwhile, the incorporation of the global regressing Kriging model and an adaptive selector helps to predict bi-objective values of untested samples and re-estimate simulated samples in the local trust-region, which can save great computational costs and smooth stochastic noises. Moreover, the non-interactive role of a decision maker is taken to generate more Pareto optimal solutions around his/her desired bi-objective values. Through the algorithm comparison for a benchmark bi-objective stochastic optimization problem, the proposed BOSSO method is validated to outperform three other counterparts (i.e., NSGA-II, BOTR and BOEGO) under the same simulation costs. In real-field experiments, an urban road network with 15 signalized and five non-signalized intersections in Changsha, China is modeled by VISSIM. After the well calibration of the microscopic traffic simulation model, the network-wide bi-objective signal timing stochastic SO problems with and without coordination are solved by BOSSO. Numerical results indicate that compared with the real-field case, the average travel time and Atkinson index are reduced respectively by at most 13.48% and 23.49% for optimized non-coordinated signal plans, and respectively by at most 25.58% and 2.83% for optimized coordinated ones. It is further validated that under variable traffic volumes, the non-coordinated signal plan can well improve both traffic efficiency and equity, and the coordinated one is capable to improve traffic efficiency at a larger degree but sacrifice traffic equity. Moreover, the balance analyses show the existence of competing relationship between bi-objectives, and BOSSO is confirmed to outperform NSGA-II, BOTR and BOEGO in searching the better Pareto optimal signal plans under the same budged simulations. In conclusion, BOSSO is promising to address bi-objective optimization problems characterized by costly evaluation, high dimensions and stochastic noises. [ABSTRACT FROM AUTHOR]

Highlights • We introduce a spatial queueing link model to consider the effects of spatial queueing and blocking back. • We develop a novel equilibrium model with capacity constraints, queueing delays and blocking back. • The modelling framework is further integrated in a traffic assignment and control problem. • We prove existence of equilibrium results under a variety of scenarios and compare different control policies. • With blocking back, existence of an equilibrium depends on the adopted merge models. Abstract This paper introduces a steady-state, fixed (or inelastic) demand equilibrium model with explicit link-exit capacities, explicit bottleneck or queueing delays and explicit bounds on queue storage capacities. The model is a quasi-dynamic model. The link model at the heart of this quasi-dynamic equilibrium model is a spatial queueing model, which takes account of the space taken up by queues both when there is no blocking back and also when there is blocking back. The paper shows that if this quasi-dynamic model is utilised then for any feasible demand there is an equilibrium solution, provided (i) queue storage capacities are large or (ii) prices are used to help impose capacity restrictions; the prices either remove queueing delays entirely or just reduce spatial queues sufficiently to ensure that blocking back does not occur at equilibrium. Similar results, but now involving the P 0 control policy (introduced in Smith (1979a, 1987)) and two new variations of this policy (i.e., the spatial P 0 control policy, and the biased spatial P 0 control policy) are obtained. In these results, the control policies allow green-times to vary in response to prices as well as spatial queueing delays. These three policies are also tested on a small simple network. In these tests, the biased spatial version of P 0 is much the best in reducing equilibrium delays (on this simple network). The paper further illustrates how the spatial queueing model works on simple networks with different merge models; it is demonstrated that equilibrium may be prevented by certain (fixed ratio) merge models. It is also shown in this case that equilibrium may be imposed on just the controlled area itself by a variety of (merge model, gating strategy) combinations. Opportunities for developing such combined gating and merging control strategies are finally discussed. [ABSTRACT FROM AUTHOR]

Highlights • Formulating a signal timing optimization program with explicit representation of the cell transmission model flow-density diagram to avoid the flow holding-back problem. • Developing an algorithm based on the Benders decomposition technique to convert the original MINLP to an IP and several CTM simulation runs. • Proving the optimality, convergence, and feasibility properties of the solution technique. • Developing a dual estimation algorithm for the MINLP to generate Benders cuts with a simulation-based approach. Abstract This paper formulates the network-level traffic signal timing optimization problem as a Mixed-Integer Non-Linear Program (MINLP) and presents a customized methodology to solve it with a tight optimality gap. The MINLP is based on the Cell Transmission Model (CTM) network loading concept and captures the fundamental flow-density diagram of the CTM explicitly by considering closed-form constraints in the model and thus, eliminates the flow holding-back problem. The proposed solution algorithm is based on the Benders decomposition technique and decomposes the original MINLP to an equivalent Integer Program (IP) (Master problem), and a new MINLP (Primal problem). We will show that the new MINLP has only one optimal non-holding-back solution that can be found by a CTM simulation run. We will prove that the proposed solution technique guarantees convergence to optimal solutions with a finite number of iterations. Furthermore, we propose a dual estimation algorithm for the new MINLP (the Primal problem), which utilizes a simulation-based approach to generate Benders cuts instead of solving a complex optimization program. We applied the proposed solution technique to a simulated network of 20 intersections under various demand patterns and observed an optimality gap of at most 2% under all tested conditions. We compared the solutions of the proposed algorithm with two benchmark algorithms and found reductions in total travel time ranging from 7.0% to 35.7%. [ABSTRACT FROM AUTHOR]

Highlights • A trajectory-based traffic management model is proposed for an exclusive AV zone. • The base model can be easily extended to include the scheduling and entry decisions. • The model is further extended to accommodate side constraints such as enforcing equity. • The model is solved by a solver and a specialized rolling horizon algorithm. • Numerical experiments validate the proposed model and algorithm. Abstract This paper studies a trajectory-based traffic management (TTM) problem for the purpose of managing traffic in a road facility reserved exclusively for autonomous vehicles (AV). The base TTM model aims to find optimal trajectories for multiple AVs while resolving inter-vehicle conflicts in the most generic way. The model is formulated as a mixed integer program (MIP) that can be solved using off-the-shelf solvers. To improve computational efficiency, a specialized algorithm based on the rolling horizon approach is also developed. We then show that the base TTM model can be easily extended to first accommodate scheduling decisions (the TTMS model) and to further impose equity constraints (the TTMSE model). For the simplest network and homogeneous users, solutions to TTMS and TTMSE are similar, respectively, to system optimal (SO) and user equilibrium (UE) solutions of Vickrey's bottleneck model. Numerical experiments highlight TTM's ability to simultaneously generate optimal trajectories for multiple vehicles. They also show that, while solving TTM exactly is computationally demanding, obtaining good approximate solutions can be accomplished efficiently by the rolling horizon algorithm. [ABSTRACT FROM AUTHOR]

Highlights • We propose valid inequalities for a MILP model for the rtRTMP. • They allow a reformulation and a reduction of the number of binary variables. • They may represent all facets of the convex hull in the subspace of binary variables. • Experiments show that the reformulation improves significantly the performance. Abstract The real-time Railway Traffic Management problem consists in finding suitable train routes and schedules to minimize delay propagation due to traffic perturbations. RECIFE-MILP is a mixed integer linear programming based heuristic for this problem which has proven to be effective in various contexts. However, when instances are very large or difficult, the performance of the algorithm may worsen. In this paper, we propose valid inequalities to boost the performance of RECIFE-MILP. These valid inequalities link the routing and scheduling binary variables. We also provide an instance in which they are able to represent all the facets of the projection of the convex hull of the problem in the subspace of the binary variables. Moreover, they allow reformulating the model based on a reduced number of scheduling binary variables. In an experimental analysis based on realistic instances representing traffic in four French infrastructures, we observe that the merit of addition of valid inequalities depends on the specific case-study at hand, and that the reduction of the number of binary variables in general boosts the performance of RECIFE-MILP significantly. [ABSTRACT FROM AUTHOR]

Highlights • Developing a hierarchical traffic control scheme of route guidance. • Building consistent models of different granularity levels. • Developing decentralized integer linear programming (ILP) based path assignment mechanism. • Incorporating heterogeneity coefficient and variable trip lengths into regional route guidance formulation. Abstract High level of detail renders microscopic traffic models impractical for control purposes and local control schemes cannot coordinate actions over large scale heterogeneously congested urban networks. Developing efficient models and control methods for large-scale urban road networks is, therefore, an important research challenge. Alleviating congestion via manipulation of traffic flows or assignment of vehicles to specific paths has a great potential in achieving efficient network usage. Motivated by this fact, this paper proposes a hierarchical traffic management system. The upper-level route guidance scheme builds a model predictive control (MPC) scheme and optimizes network performance based on actuation via regional split ratios, whereas the lower-level path assignment mechanism develops an integer linear programming (ILP) formulation and recommends subregional paths for vehicles to follow, satisfying the regional split ratios in order to achieve said performance. Simulation results from a 49-subregion or 7-region network shows a great potential of the proposed scheme in achieving coordination and efficient use of network capacity, leading to increased mobility. [ABSTRACT FROM AUTHOR]

Abstract Uniqueness of the dynamic user-equilibrium assignment is still an important issue. This paper proves uniqueness with a milder condition compared to past studies and shows another counterexample to the uniqueness. A unidirectional network , in which any node on any shortest route has a unique node potential, is introduced. Orders of vehicles are determined by this node potential so that, given any two vehicles passing through the same node, the lower potential vehicle arrives at the node before the higher potential vehicle. It is shown that, for a unidirectional network in equilibrium, the link travel times and traffic volumes of congested links are uniquely determined. Moreover, a simple non-unidirectional network having multiple equilibria is introduced. This example exhibits importance of unidirectional-network structure to prove uniqueness. [ABSTRACT FROM AUTHOR]

Abstract We study a parsimonious theory that synthesizes short-term traffic demand management (TDM) policies with long-term endogenous heterogeneities of demand. In a corridor network with multiple discrete bottlenecks, we study a model of system optimal assignment that integrates the short-term problem (departure time choice with tolling) and the long-term problem (job and residential location choice). For the short-term departure-time-choice equilibrium, under mild assumptions on schedule delay function, we derive analytical solutions under a first-best TDM scheme. Investigating properties of long-term equilibria, we found that the overall equilibrium pattern exhibits remarkable spatio-temporal sorting properties. It is further shown that a lack of integration of the short- and the long-term policy results in excessive investments for long-term road construction. [ABSTRACT FROM AUTHOR]

Abstract This paper shows that severe congestion on streets controlled by traffic signals can be reduced by dynamically adapting the signal offsets to the prevailing density with a simple rule that keeps the signals' green-red ratios invariant. Invariant ratios reduce a control policy's impact on the crossing streets, so a policy can be optimized and evaluated by focusing on the street itself without the confounding factors present in networks. Designed for heavy traffic with spillovers, the proposed policies are adaptive and need little data – they only require average traffic density readings and no demand forecasts. A battery of numerical experiments simulating the dynamics of rush hour traffic on a congested, homogeneous circular street reveals that the proposed form of adaptation reduces the duration of the rush and overall congestion compared with pre-timed control strategies. Eighteen different adaptation policies were considered. All inspect the street densities periodically and simultaneously, and retime the signals immediately thereafter. The period is a fixed multiple of the cycle. The street is evenly divided into sections that contain a set number of consecutive blocks and signals. The offset is the same for all blocks in a section. Three inspection intervals and six section sizes were tested. The latter ranged from a single block/signal to the whole street. It was found that adaptation worked best when sections were large and adaptation frequent. The effects were considerable across all scenarios. For a short street with a short rush and high input flows the probabilistic incidence of gridlock was reduced from 10 to 0%, and the average duration of a trip from 216 to 181 s. For a long street with a long rush and high input flows the gridlock probability was reduced from 23 to 0% and the average trip duration from 2037 to 1143s. [ABSTRACT FROM AUTHOR]

Highlights • Presents a Continuum Percolation based approach to determine the effects of the vehicular density and communication range on the connectivity level. • Investigates string stability under different communication ranges and market penetration rates of connected and autonomous vehicles. Abstract Connectivity and automation are expected to enhance safety and efficiency in transportation systems. Connectivity will provide information to drivers/autonomous vehicles to enhance decision-making reliability at the operational and tactical levels. Consequently, drivers are more likely to execute safe and efficient maneuvers and autonomous vehicles will have a more accurate perception of the traffic condition and an "error-free" execution of the driving maneuvers. At the operational level, ensuring string stability is a key consideration since unstable traffic flow results in shockwave propagation and possibly crashes. While several studies have examined the effects of information availability on string stability in a connected environment, most of the approaches are focused on automated driving (e.g., Cooperative Adaptive Cruise Control systems) and do not consider a mixed environment with regular, connected, and autonomous vehicles. To ensure connectivity in such a mixed environment, the correlation between communication range and connected vehicles density should be considered. To capture the effects of this correlation, this study uses the Continuum Percolation theory to determine the effects of the vehicular density and communication range on the connectivity level in telecommunications network and consequently, on the string stability of traffic flow. Based on the Continuum Percolation theory, there is a critical density of connected vehicles above which the entire system is connected. This critical density also depends on the communication range. This study presents an analytical derivation of this critical density. Moreover, this study evaluates the string stability under different communication ranges and market penetration rates of connected and autonomous vehicles. Results revealed that as communication range increases, the system becomes more stable and at high communication ranges, the system performs similar to the system with full connectivity. Moreover, results indicated the existence of an optimal communication range to maximize stability and ensure information delivery. [ABSTRACT FROM AUTHOR]

Abstract The Macroscopic Fundamental Diagram (MFD) framework has been widely utilized to describe traffic dynamics in urban networks as well as to design perimeter flow control strategies under stationary (constant) demand and deterministic settings. In real world, both the MFD and demand however suffer from various intrinsic uncertainties while travel demand is of time-varying nature. Hence, robust control for traffic networks with uncertain MFDs and demand is much appealing and of greater interest in practice. In literature, there would be a lack of robust control strategies for the problem. One major hurdle is of requirement on model linearization that is actually a basis of most existing results. The main objective of this paper is to explore a new robust perimeter control framework for dynamic traffic networks with parameter uncertainty (on the MFD) and exogenous disturbance induced by travel demand. The disturbance in question is in general time-varying and stochastic. Our main contribution focuses on developing a control-Lyapunov function (CLF) based approach to establishing a couple of universal control laws, one is almost smooth and the other is Bang-bang like, for different implementation scenarios. Moreover, it is indicated that the almost smooth control is more suited for road pricing while the Bang-bang like control for signal timing. In sharp contrast to existing methods, in which adjusting extensive design parameters are usually needed, the proposed methods can determine the control in an automatic manner. Furthermore, numerical results demonstrate that the control can drive the system dynamics towards a desired equilibrium under various scenarios with uncertain MFDs and travel demand. Both stability and robustness can be substantially observed. As a major consequence, the proposed methods achieve not only global asymptotic stability but also appealing robustness for the closed-loop traffic system. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the dynamic user equilibrium (DUE) on a single origin-destination pair with two alternative routes, a freeway with a fixed capacity and the surrounding city-streets network, modeled with a network macroscopic fundamental diagram (NMFD). We find using suitable transformations that only a single network parameter is required to characterize the DUE solution, the freeway to NMFD capacity ratio. We also show that the stability and convergence properties of this system are captured by the constant demand case, which corresponds to an autonomous dynamical system that admits analytical solutions. This solution is characterized by two critical accumulation values that determine if the steady state is in free-flow or gridlock, depending on the initial accumulation. Additionally, we also propose a continuum approximation to account for the spatial evolution of congestion, by including variable trip length and variable NMFD coverage area in the model. It is found that gridlock cannot happen and that the steady-state solution is independent of surface network parameters. These parameters do affect the rate of convergence to the steady-state solution, but convergence rates appear virtually identical when time is expressed in units of the NMFD free-flow travel time. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the equilibrium properties of the morning commute problem at the network level with heterogeneous trip lengths. Congestion is modeled with a Macroscopic Fundamental Diagram relating the space-mean speed of a network to the vehicular accumulation. It is shown for a large class of scheduling preferences that if users have continuously distributed characteristics, the network accumulation at equilibrium is a continuous function of time. With α − β − γ preferences and under certain conditions, a partial First-In, First-Out (FIFO) pattern emerges at equilibrium among early and late users. This FIFO pattern is strict only within families of users having heterogeneous trip lengths and identical preferences, or vice versa. Simulation results confirmed that an attracting steady-state exists for a wide range of demands and that the predicted patterns are indeed observed. [ABSTRACT FROM AUTHOR]

Highlights • Consider coordinated traffic signal controls under both deterministic and stochastic demands. • A new mixed integer linear programming (MILP) for deterministic optimization is proposed. • The MILP has a network structure and its size is smaller than the existing formulations. • The problem is extended to treat the stochastic fluctuations in traffic demand. • An accurate and efficient approximation method of expected delays is developed. • Optimal control parameters for deterministic and stochastic controls are examined. Abstract This study considers an optimal coordinated traffic signal control under both deterministic and stochastic demands. We first present a new mixed integer linear programming (MILP) for the deterministic signal optimization wherein traffic flow is modeled based on the variational theory and the constraints on a signal control pattern are linearly formulated. The resulting MILP has a clear network structure and requires fewer binary variables and constraints as compared with those in the existing formulations. We then extend the problem so as to treat the stochastic fluctuations in traffic demand. We here develop an accurate and efficient approximation method of expected delays and a solution method for the stochastic version of the signal optimization by exploiting the network structure of the problem. Using a set of proposed methods, we finally examine the optimal control parameters for deterministic and stochastic coordinated signal controls and discuss their characteristics. [ABSTRACT FROM AUTHOR]

Abstract In transportation and traffic analysis count data arises frequently, collectively emerging from individual traveler choices from a choice set of alternatives. Examples include network origin-destination (OD) flow rates and visitor counts at sites, for example transit stations and public parks. From a modeling perspective, these data are aggregate counts at the top level, but are comprised of individual discrete choices at the lower level. Models of count data are widely applied in the transportation and traffic fields. However, only a moderate level of applications jointly model count observations at the top level with discrete choice models at the bottom level under a random utility maximization (RUM) framework. This paper considers modeling count data with an underlying choice process as a joint model that merges an observed event count process with a discrete choice process, where the count level is Poisson distributed. This model captures both processes within a single random utility framework that preserves a direct mapping between the count intensity and the utility of the chosen alternative, including unobserved variables and latent factors. The decision-making context examines discretionary activity type choice for activities completed within a one-day period. The results show that a model of count with endogenous choices can account for the mapping of impacts of choice attributes from the lower level towards the observed count at the top level emerging from choices, including the idiosyncratic term associated with the utility of choice alternatives. Furthermore, since this model preserves the linkage between the maximizing utility and rate parameter in the joint model, identifying the contribution of attributes between the two levels is possible. [ABSTRACT FROM AUTHOR]