Perimeter Flow Control Research Articles

Multi-gated perimeter flow control for monocentric cities: Efficiency and equity

A control scheme for the multi-gated perimeter traffic flow control problem of monocentric cities is presented. The proposed scheme determines feasible and optimally distributed input flows for various gates located at the periphery of a protected network area. A parsimonious model is employed to describe the traffic dynamics of the protected network. To describe traffic dynamics outside of the protected area, the basic state-space model is augmented with additional state variables to account for vehicle queues at store-and-forward origin links at the periphery. The multi-gated perimeter flow control problem is formulated as a convex optimisation problem with finite horizon, and constrained control and state variables. This scheme aims to equalise the relative queues at origin links and to maintain the vehicle accumulation in the protected network around a desired set point, while the system’s throughput is maximised. For real-time control, the optimal control problem is embedded in a rolling-horizon scheme using the current state of the whole system as the initial state as well as predicted demand flows at origin/entrance links. Furthermore, practical flow allocation policies for single-region perimeter control strategies without explicitly considering entrance link dynamics are presented. These policies allocate a global perimeter-ordered flow to a number of candidate gates at the periphery of a protected network area by taking into account the different geometric characteristics of origin links. The proposed flow allocation policies are then benchmarked against the multi-gated perimeter flow control. A meticulous study is carried out for a 2.5 square mile protected network area of San Francisco, CA, including fifteen gates of different geometric characteristics. The results showed that the proposed approach is able to manage excessive queues outside of the protected network area and to optimally distribute the input flows, which confirms its efficiency and equity properties. Similar policies are expected to be utilised for dynamic routing and road pricing.

A Linear-Parameter-Varying Formulation for Model Predictive Perimeter Control in Multi-Region MFD Urban Networks

An alternative approach for real-time network-wide traffic control in cities that has recently gained attention is perimeter flow control. Many studies have shown that this method is more efficient than state-of-the-art adaptive signal control strategies for heterogeneously congested urban networks. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the interregional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of current work is the mathematical formulation of the original nonlinear problem in a linear parameter-varying (LPV) form so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Numerical simulation results for the case of a macroscopic environment (plant) are presented in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark,” as well as the linear case. Furthermore, the developed scheme is applied to a large-scale microsimulation of a European city with more than 500 signalized intersections in order to better investigate its applicability to real-life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared with fixed-time control because all of the performance indicators are significantly improved. Funding: This work was supported by Dit4Tram “Distributed Intelligence & Technology for Traffic & Mobility Management” project from the European Union’s Horizon 2020 research and innovation programme under [Grant agreement 953783].

Coordinated Perimeter Flow and Variable Speed Limit Control for Mixed Freeway and Urban Networks

Recent studies have leveraged the existence of network macroscopic fundamental diagrams (MFD) to develop regional control strategies for urban traffic networks. Existing MFD-based control strategies focus on vehicle movement within and across regions of an urban network and do not consider how freeway traffic can be controlled to improve overall traffic operations in mixed freeway and urban networks. The purpose of this study is to develop a coordinated traffic management scheme that simultaneously implements perimeter flow control on an urban network and variable speed limits (VSL) on a freeway to reduce total travel time in such a mixed network. By slowing down vehicles traveling along the freeway, VSL can effectively meter traffic exiting the freeway into the urban network. This can be particularly useful since freeways often have large storage capacities and vehicles accumulating on freeways might be less disruptive to overall system operations than on urban streets. VSL can also be used to change where freeway vehicles enter the urban network to benefit the entire system. The combined control strategy is implemented in a model predictive control framework with several realistic constraints, such as gradual reductions in freeway speed limit. Numerical tests suggest that the combined implementation of VSL and perimeter metering control can improve traffic operations compared with perimeter metering alone.

Perimeter control with real-time location-varying cordon

With unbalanced travel demand distribution over time and space, a stationary cordon location hinders the full potential of perimeter flow control based on network Macroscopic Fundamental Diagram (MFD). This paper introduces a perimeter control method wherein the region boundaries alter in real-time to tackle propagation of local pockets of congestion. The nonlinear dynamics of the heterogeneous traffic network are modelled as a switching system. The linearization of the derived switching nonlinear dynamics is conducted considering the accumulation heterogeneity. A Linear Quadratic Regulator (LQR) is employed for gating the flow exchange between regions to minimize network congestion. Several scenarios are examined comparing perimeter control schemes with static and dynamic cordons. Results pinpoint the proposed LQR control with location-varying cordon strategy and a moderate switching interval significantly reduces the vehicles total time spent in the network.

H∞ robust perimeter flow control in urban networks with partial information feedback

Perimeter control is an effective city-scale solution to tackle congestion problems in urban networks. To accommodate the unpredictable dynamics of congestion propagation, it is essential to incorporate real-time robustness against travel demand fluctuations into a pragmatic perimeter control strategy. This paper proposes robust perimeter control algorithms based on partial information feedback from the network. The network dynamics are modeled using the concept of the Macroscopic Fundamental Diagram (MFD), where a heterogeneously congested network is assumed to be partitioned into two homogeneously congested regions, and an outer region that acts as demand origin and destination. The desired operating condition of the network is obtained by solving an optimization program. Observer-based H∞ proportional (P) and proportional-integral (PI) controllers are designed based on Lyapunov theory, to robustly regulate the accumulation of each region and consequently to maximize the network outflow. The controller design algorithms further accommodate operational constraints by guarantying: (i) the boundedness of the perimeter control signals and (ii) a bounded offset between the perimeter control signals. Control parameters are designed off-line by solving a set of linear matrix inequalities (LMI), which can be solved efficiently. Comprehensive numerical studies conducted on the nonlinear model of the network highlight the effectiveness of the proposed robust control algorithms in improving the congestion in the presence of time-varying disturbance in travel demand.

Perimeter control for urban traffic system based on macroscopic fundamental diagram

In this paper, we study the application of perimeter flow control by simulation of cellular automaton model on urban traffic system. We find that the relation of traffic flow and vehicle density (Macroscopic Fundamental Diagram, MFD) will have different shapes for the core area and the peripheral area. The MFD shows free-flow state, saturate flow state and congestion state. But the magnitude of maximal flow and the position for congestion transition are different for the whole system and the core area. We suggest to realize the perimeter control strategy by assigning a special prohibiting phase to the perimeter traffic lights for the roads entering the core area. The strategy is controlled by two critical densities ρ1 and ρ2, which are determined by the MFD of the core area. Simulations show that both the average arrival rate and the average flow will be greatly improved with the perimeter flow control strategy. In addition, the perimeter flow control strategy can increase the critical density of traffic congestion. The probability of system-wide gridlock will decrease, and the system can perform well under both close and open boundary conditions. All the results indicate that the perimeter flow control strategy can effectively improve the performance of the traffic system.

Robust perimeter control for two urban regions with macroscopic fundamental diagrams: A control-Lyapunov function approach

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.

Hierarchical perimeter control with guaranteed stability for dynamically coupled heterogeneous urban traffic

Perimeter control based on the Macroscopic Fundamental Diagram (MFD) is widely developed for alleviating or postponing congestion in a protected region. Recent studies reveal that traffic conditions might not be improved if the perimeter control strategies are applied to unstable systems where high demand generates heavy and heterogeneously distributed traffic congestion. Therefore, considering stability of the targeted traffic system is essential, for the sake of developing a feasible and then optimal control strategy. This paper sheds light on this direction. It integrates a stability characterization algorithm of MFD system equations into the Model Predictive Control (MPC) scheme, and features respectively an upper and a lower bound of the feasible control inputs, to guarantee system stability. Firstly, the dynamics of traffic heterogeneity and its effect on the MFD are analyzed, using real data from Guangzhou in China. Piecewise affine functions of average flow are proposed to capture traffic heterogeneity in both regional and subregional MFDs. Secondly, stability of a three-state two-region system is investigated via stable equilibrium and surface boundaries analysis. Finally, a three-layer hierarchical control strategy is introduced for the studied two-region heterogeneous urban networks. The first layer of the controller calculates the stable surface boundaries for the given traffic demands and then determines the bounds of control input (split rate). An MPC approach in the second layer is used to solve an optimization problem with two objectives of minimizing total network delay and maximizing network throughput. Heterogeneity among the subregions is minimized in the last layer by implementing simultaneously a subregional perimeter flow control and an internal flow control. The effectiveness and stability of the proposed control approach are verified by comparison with four existing perimeter control strategies.

A Linear Formulation for Model Predictive Perimeter Traffic Control in Cities

An alternative approach for real-time network-wide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The basic concept of such an approach is to partition heterogeneous cities into a small number of homogeneous regions (zones) and apply perimeter control to the inter-regional flows along the boundaries between regions. The transferring flows are controlled at the traffic intersections located at the borders between regions, so as to distribute the congestion in an optimal way and minimize the total delay of the system. The focus of the current work is to study three aspects that are not covered in the perimeter control literature, which are: (a) the treatment of some model parameters that are not measurable in real life implementations and can affect the performance of the controller (e.g. advanced online estimation schemes can be developed for this purpose), (b) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (c) mathematical formulation of the original nonlinear problem in a linear form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. Preliminary simulation results for the case of a macroscopic environment (plant) are presented, in order to demonstrate the efficiency of the proposed approach. Results for the closed-loop model predictive control scheme are presented for the nonlinear case, which is used as “benchmark”, as well as the linear case.

Robust Perimeter Control for Two Urban Regions with Macroscopic Fundamental Diagrams: A Control-Lyapunov Function Approach

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.

Intersection Control and MFD Shape: Vehicle-Actuated versus Back-Pressure Control

Various studies have demonstrated that the state and dynamics of an urban network can be described by Macroscopic Fundamental Diagrams (MFD) and that MFDs can be used for perimeter flow control. Perimeter flow control aims at a higher throughput in an urban network by controlling the flow at the boundaries of sub-networks. For perimeter flow control it is desirable that the MFD has a favourable and consistent shape, independent of fluctuations in traffic demand and of intersection signal variations. From literature it is known that a consistent shape is related to the homogeneity of vehicle accumulation in the sub-network. However, also the signal controller type may influence homogeneity and the MFD shape. In this paper we investigate the relationship between the type of intersection control and the shape and scatter of the MFD, and the homogeneity of the sub-network, for Vehicle-Actuated (VA) and Back-Pressure (BP) control. The comparison of the two control methods is performed by means of microsimulation. The results show that for both control methods the free-flow branch of the MFD has a low scatter with an average relative deviation around 2%. The congested branch shows a much larger deviation, 15% for the Vehicle-Actuated control, 16% for the Back-Pressure control. Furthermore, there is a distinct difference in the shape of the MFDs: for VA control the production increases faster as function of the accumulation than for BP control, but the network breakdown starts at a lower accumulation. So, based on the simulation results, VA control is better in undersaturated situations, and BP is better at higher accumulation levels.

Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.