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Macroscopic traffic flow modeling is essential for describing and forecasting the characteristics of traffic flow. However, the classic Lighthill–Whitham–Richards (LWR) model only provides equilibrium values for steady‐state conditions and fails to capture common stochastic variabilities, which are a necessary component of accurate modeling of real‐time traffic management and control. In this paper, a stochastic LWR (SLWR) model that randomizes free‐flow speed is developed to account for the stochasticity incurred by the heterogeneity of drivers, while holding individual drivers' behavior constant. The SLWR model follows a conservation law of stochastic traffic density and flow and is formulated as a time‐dependent stochastic partial differential equation. The model is solved using a dynamically bi‐orthogonal (DyBO) method based on a spatial basis and stochastic basis. Various scenarios are simulated and compared with the Monte Carlo (MC) method, and the results show that the SLWR model can effectively describe dynamic traffic evolutions and reproduce some commonly observed traffic phenomena. Furthermore, the DyBO method shows significant computational advantages over the MC method. [ABSTRACT FROM AUTHOR]

In the conventional human driving environment, due to poor traffic information transmission and the inability to actively control vehicles, variable speed limits (VSLs) and ramp metering (RM) strategies often fail to achieve the desired results when dealing with the merging zone of an expressway under high traffic demand. To improve traffic efficiency, an integrated control method for traffic flow in the merging area of expressways is proposed by combining connected and autonomous vehicle (CAV) active lane change (LC) technology with traditional VSL and entrance RM strategies. This method uses an upgraded cell transmission model (CTM) to estimate the state of the mainline and ramp input traffic volume and then uses the genetic algorithm (GA) to solve for the optimal combination of the mainline speed limit, number of mainline vehicles changing lanes, and ramp regulation under maximized flow in the merging zone. This integrated control strategy incorporating VSL, LC, and RM (VSL-LC-RM) enables synergistic control of the mainline and ramp traffic entering the merging zone in time-space. Finally, simulation experiments are conducted with the mainline two-lane and on-ramp singlelane expressway merging zone scenarios. The results show that compared with the VSL strategy and the strategy incorporating only VSL and RM (VSL-RM), the proposed VSL-LC-RM strategy can enhance the regulation of traffic flow, improve the flow of merging bottlenecks, and make full use of the road space-time resources. [ABSTRACT FROM AUTHOR]

We develop reinforcement learning (RL) boundary controllers to mitigate stop-and-go traffic congestion on a freeway segment. The traffic dynamics of the freeway segment are governed by a macroscopic Aw–Rascle–Zhang (ARZ) model, consisting of 2 $\times $ 2 quasi-linear partial differential equations (PDEs) for traffic density and velocity. The boundary stabilization of the linearized ARZ PDE model has been solved by PDE backstepping, guaranteeing spatial $L^{2}$ norm regulation of the traffic state to uniform density and velocity and ensuring that traffic oscillations are suppressed. Collocated proportional (P) and proportional–integral (PI) controllers also provide stability guarantees for allowable control gains and are always applicable as model-free control options through gain tuning by trial and error, or by model-free optimization. Although these approaches are mathematically elegant, the stabilization result only holds locally and is usually affected by the change of model parameters. Therefore, we reformulate the PDE boundary control problem as an RL problem that pursues stabilization without knowing the system dynamics, simply by observing the state values. The proximal policy optimization (PPO), a neural network-based policy gradient algorithm, is employed to obtain RL controllers by interacting with a numerical simulator of the ARZ PDE. Being stabilization-inspired, the RL state-feedback boundary controllers are compared and evaluated against the rigorously stabilizing controllers in two cases: 1) in a system with perfect knowledge of the traffic flow dynamics and then 2) in one with only partial knowledge. We obtain RL controllers that nearly recover the performance of the backstepping, P, and PI controllers with perfect knowledge and outperform them in some cases with partial knowledge. It must be noted, however, that the RL controllers are obtained by conducting about one thousand episodes of iterative training on a simulation model. This training cannot be performed in a collision-free fashion in real traffic, nor convergence guaranteed when training. Thus, we demonstrate that the RL approach has learning (i.e., adaptation) potential for traffic PDE systems under uncertain and changing conditions, but RL is neither simple nor a fully safe substitute for model-based control in real traffic systems. [ABSTRACT FROM AUTHOR]

Purpose. To increase output of traffic network while deriving new dependencies of transport flow characteristics upon control law parameters and using them to develop an algorithm to automate a process of the transport flow coordinated regulation within towns and cities. Methodology. The aggregated simulation model, describing processes of road traffic formation within a local section of urban traffic system, is used for the analysis of dependencies to assess quality of transport flow control upon correcting conditions being parameters of traffic cycles within intersections. The abovementioned should involve a PID controller as well as a negative feedback idea to automate control of the road traffi c process. In this context, control criterion is applied to determine critical flow intensity if a traffic jam occurs. The criterion makes it possible to identify changes in the road traffic nature. To determine the optimal settings of the PID controller for diff erent stocks of the stability control system, the standard deviation of the controlled variable from the set value and the mean static control error are defined. The derived dependencies of control quality criteria upon a law of flow regulation have helped develop a new algorithm of the coordinated automated road traffi c control within a local section of urban traffic section using standard control action. Simulation experiments made it possible to assess efficiency of the proposed algorithm of control compared with available ones applied in terms of different road conditions. Findings. As a part of the studies, algorithm of the coordinated automated road traffic has been developed. It helps support maximum output of road systems while monitoring changes in the traffic environment characteristics. Originality. For the first time, dependencies of assessment criteria of traffic flow control upon the parameters of a law of flow intensity regulation have been identified if maximum output of road systems is provided. The dependencies have helped substantiate optimum control criteria for different road conditions while automating a process of coordinated traffic flow regulation within local section of urban traffic network. Practical value. The proposed dependencies of assessment criteria of traffic flow control upon the parameters of a law of flow intensity regulation as well as the algorithm of automated coordinated control are the theoretical foundations to solve such an important applied scientific problem as automation of a process of urban traffic flow regulation. [ABSTRACT FROM AUTHOR]

With rapid development of the urbanization, how to improve the traffic lights efficiency has become an urgent issue. The traditional traffic light control is a method that calculates a series of corresponding timing parameters by optimizing the cycle length. However, fixing sequence and duration of traffic lights is inefficient for dynamic traffic flow regulation. In order to solve the above problem, this study proposes a traffic light timing optimization scheme based on deep reinforcement learning (DRL). In this scheme, the traffic lights can output an appropriate phase according to the traffic flow state of each direction at the intersection and dynamically adjust the phase length. Specifically, we first adopt Proximal Policy Optimization (PPO) to improve the convergence speed of the model. Then, we elaborate the design of state, action, and reward, with the vehicle state defined by Discrete Traffic State Encoding (DTSE) method. Finally, we conduct experiments on real traffic data via the traffic simulation platform SUMO. The results show that, compared to the traditional timing control, the proposed scheme can effectively reduce the waiting time of vehicles and queue length in various traffic flow modes. [ABSTRACT FROM AUTHOR]

The study of traffic flow bifurcation control analysis is of great significance for understanding the essential evolution law of traffic flow, controlling traffic flow with practical means and alleviating traffic congestion. This paper describes the influence of lateral distance compensation in the process of lane change, and adjusts the traffic flow from the perspective of bifurcation control, which can capture the characteristics of traffic flow better, so as to describe the practical significance of the actual traffic phenomenon better. For example, the green ratio of traffic lights in the road, the planning and design of traffic signs, and the guidance of traffic condition prediction in ITS. In addition, the traffic flow is introduced and applied to the traffic model from the perspective of random function, and the bifurcation control is carried out according to the bifurcation behavior in traffic. That is, the bifurcation characteristics of the system are modified by the designed feedback controller, and the appearance of the equilibrium point of the system is adjusted to make it move forward, backward or disappear, so as to prevent or alleviate traffic congestion. There are few researches on bifurcation control of traffic flow model with lateral distance compensation. This paper introduces stochastic function based on lateral compensation model to study Hopf bifurcation phenomenon and Hopf bifurcation control. Firstly, the existence condition of Hopf bifurcation at the equilibrium point in the model is proved theoretically. Then, a feedback controller is designed to control the amplitudes of the Hopf bifurcation and the limit cycles formed by the Hopf bifurcation. Finally, the theoretical results are verified by numerical simulation. The research shows that by adjusting the control parameters in the feedback controller, the influence of boundary conditions on the stability of the traffic system is fully described, the effect of unstable focus and saddle point on the system is inhibited, and the traffic flow is slowed down. In addition, the unstable bifurcation points can be eliminated, and the amplitude of the limit cycle formed by Hopf bifurcation can be adjusted, so as to achieve the stability of the control system. • A new continuum model is proposed taking into account the lateral offset compensation. • Introducing the traffic flow into the traffic model from the perspective of the random function. • The designed feedback controller corrects the bifurcation characteristics of the system and adjusts the appearance of the balance point of the system to make it forward, backward or disappear, so as to prevent or reduce traffic jams. [ABSTRACT FROM AUTHOR]

• Propose a cooperative signal-free intersection control framework under V2X communications. • Proposed framework integrates virtual platooning control and traffic flow regulation. • Virtual platooning controller mitigates effects of parametric inaccuracies and unparameterized disturbances. • Virtual platooning controller guarantees string stability. • Traffic flow regulation alleviates traffic spillbacks and travel delays. The emerging technologies of connectivity and automation enable the potential for signal-free intersection control. In this context, virtual platooning is posited to be an innovative, decentralized control strategy that maps two-dimensional vehicle movements onto a one-dimension virtual platoon to enable intersection operations. However, the effectiveness of virtual platooning-based control can be limited or degraded by parametric inaccuracies and unparameterized disturbances in vehicle dynamics, heavy traffic congestion, and/or uncoordinated platoons in multi-lane intersections. To explicitly address these limitations, this study proposes a hybrid cooperative intersection control framework consisting of microscopic-level virtual platooning control and macroscopic-level traffic flow regulation for traffic environments with connected autonomous vehicles. In virtual platooning control, vehicles approaching an intersection are organized into coordinated independent virtual platoons to avoid potential conflicts triggered by platoon formation changes. Through coordination, vehicles in a platoon are grouped into compatible passing sets to maintain desired safe spacing when proceeding through the intersection. We propose a distributed adaptive sliding mode controller (DASMC) which uses the backstepping control method and model reference adaptive control method to address parametric inaccuracies, and the sliding mode control method to consistently suppress the negative effects of the unparameterized disturbances. Each vehicle approaching the intersection utilizes the kinematic information from neighboring vehicles to implement the DASMC in a distributed manner such that vehicles within the same virtual platoon can achieve consensus safely. However, virtual platooning control cannot preclude excessive traffic from approaching the intersection, which can cause undesired spillbacks and degrade intersection control performance. To address this issue, traffic flow regulation is integrated with the virtual platooning control using an iterative feedback loop mechanism. In each iteration of the iterative feedback loop, a constrained finite-time optimal control (CFTOC) problem is solved to determine the optimal input flow permitted to proceed through the intersection, and the virtual platooning control provides feedback on the queue status to the CFTOC to initiate the next iteration. The effectiveness of the proposed intersection control framework is evaluated through numerical experiments. The results indicate that the proposed virtual platooning DASMC controller can mitigate the effects of parametric inaccuracies and unparameterized disturbances to achieve consensus for approaching vehicles, as well as guarantee string stability. Further, the proposed framework can alleviate traffic spillbacks and travel delays effectively through traffic flow regulation. [ABSTRACT FROM AUTHOR]