Modified Cell Transmission Model Research Articles

Enhancing reinforcement learning‐based ramp metering performance at freeway uncertain bottlenecks using curriculum learning

AbstractMost current RM approaches are developed for fixed bottlenecks. However, the number and locations of bottlenecks are usually uncertain and even time‐varying due to some unexpected phenomena, such as severe accidents and temporal lane closures. Thus, the RM approach should be able to enhance traffic flow stability by effectively handling the time‐delay effect and fluctuations in traffic flow rate caused by uncertain bottlenecks. This study proposed a novel approach called deep reinforcement learning with curriculum learning (DRLCL) to improve ramp metering efficacy under uncertain bottleneck conditions. The curriculum learning method transfers an optimal control policy from a simple on‐ramp bottleneck case to more challenging bottleneck tasks, while DRLCL agents explore and learn from the tasks gradually. Four RM control tasks were developed in the modified cell transmission model, including typical on‐ramp bottleneck, fixed downstream bottleneck, random‐location bottleneck, and multiple bottlenecks. With curriculum learning, the entire training process was reduced by 45.1% to 64.5%, while maintaining a similar maximum reward level compared to DRL‐based RM control with full learning from scratch. Specifically, the results also demonstrated that the proposed DRLCL‐based RM outperformed the feedback‐based RM due to its stronger predictive ability, faster response, and higher action precision.

Coordinated Variable Speed Limit Control for Consecutive Bottlenecks on Freeways Using Multiagent Reinforcement Learning

Most of the current variable speed limit (VSL) strategies are designed to alleviate congestion in relatively short freeway segments with a single bottleneck. However, in reality, consecutive bottlenecks can occur simultaneously due to the merging flow from multiple ramps. In such situations, the existing strategies use multiple VSL controllers that operate independently, without considering the traffic flow interactions and speed limit differences. In this research, we introduced a multiagent reinforcement learning-based VSL (MARL-VSL) approach to enhance collaboration among VSL controllers. The MARL-VSL approach employed a centralized training with decentralized execution structure to achieve a joint optimal solution for a series of VSL controllers. The consecutive bottleneck scenarios were simulated in the modified cell transmission model to validate the effectiveness of the proposed strategy. An independent single-agent reinforcement learning-based VSL (ISARL-VSL) and a feedback-based VSL (feedback-VSL) were also applied for comparison. Time-varying heterogeneous traffic flow stemming from the mainline and ramps was loaded into the freeway network. The results demonstrated that the proposed MARL-VSL achieved superior performance compared to the baseline methods. The proposed approach reduced the total time spent by the vehicles by 18.01% and 17.07% in static and dynamic traffic scenarios, respectively. The control actions of the MARL-VSL were more appropriate in maintaining a smooth freeway traffic flow due to its superior collaboration performance. More specifically, the MARL-VSL significantly improved the average driving speed and speed homogeneity across the entire freeway.

A modified cell transmission model considering queuing characteristics for channelized zone at signalized intersections

This paper focuses on traffic flow modeling of signalized intersections with entrance widening lanes and shared lanes. The link of the signalized intersection is divided into the upstream mixed zone, the transition zone, and the downstream channelized zone. The development of the modeling framework is motivated by the need to model realistic flow dynamics, especially regarding the complex interactions in the channelized zone. To describe the evolution of traffic flow, a modified cell transmission model is developed, which jointly captures features of the queue discharge process, diverge process, optional lane-changing, and shared lanes. Furthermore, a queue length calculation method based on cell densities is proposed to obtain the queue profile. Finally, the performance of the proposed modified CTM is tested using both VISSIM simulation data and empirical data on actual intersections. Numerical experiments are conducted to illustrate the importance of capturing each of these realistic queuing features for queue estimation. It is observed that our modified CTM can estimate the lane-group based queue length, and it has good estimation accuracy on both under-saturated and over-saturated traffic conditions. With the increase of the proportion of through vehicles, the estimation error decreases. The mean values of the weighted mean absolute percentage error (WMAPE) of the link maximum queue length estimation in all cases are less than 13.73%. Compared with the benchmark method, the proposed method shows better accuracy. The improvement of the modified CTM is more significant under heavy traffic conditions.

Dynamic Assessment of Road Network Vulnerability Based on Cell Transmission Model

The road network maintaining stability is critical for guaranteeing urban traffic function. Therefore, the vulnerable links need to be identified accurately. Previous vulnerability research under static condition compared the operating states of the old equilibrium before the event and the new equilibrium after the event to assess vulnerability ignoring the dynamic variation process. Does road network vulnerability change over time? This paper combines the vulnerability assessment with the traffic flow evolution process, exploring the road network vulnerability evaluation from the perspective of time dimension. More accurate identification and evaluation of vulnerable nodes and links can help to strengthen the ability of road network resisting disturbances. A modified dynamic traffic assignment (DTA) model is established for dynamic path selection (reselect the shortest path at the end of each link) based on the dynamic user optimal (DUO) principle. A modified cell transmission model is established to simulate the traffic flow evolution processes. The cumulative and time-varying index of vulnerability assessment is established from the viewpoint of traveler’s time loss. Then the road network vulnerability assessment combined the traffic flow model with the vulnerability index. The road network vulnerability assessment of Bao’an Central District of Shenzhen, China, reveals that road network vulnerability does contain a dynamic process, and vulnerable links in each phase can be exactly identified by the model. Results showed that the road network would have a large vulnerability during the disordered phase when the main road fails. Therefore, prioritizing the smooth flow of main roads can weaken the impact of road network vulnerability exposure.

Modeling Traffic Flows on Urban Arterials Considering the Downstream Influence

Arterials are important transportation facilities, undertaking the two functions of mobility and accessibility. In the urban area, signalized intersections along arterials are usually closely spaced and bear heavy traffic pressure. Capacities of intersections can be reduced by downstream intersections even without having spillback. This effect will be accumulated and amplified back along the traffic direction and may lead to severe congestion in the upstream intersection which can be frequently observed, especially during peak hours. However, existing traffic simulators cannot capture this phenomenon accurately because they ignore the capacity drop before spillback happens. In this study, downstream influence is quantified by a virtual optimal speed ( vop). vop is the speed by which the upstream platoon reaches the endpoint of the queue ahead when the last vehicle in the downstream queue just starts. Based on that, two piecewise regression models, for start-up lost time and saturation flow rate, are formulated to estimate the capacity reduction. These regression models are further introduced to improve the modified cell transmission model (CTM). The result of the simulation experiment shows that the proposed CTM model has better performance in simulating traffic flow on signalized arterials than the existing CTM, especially in reproducing the traffic congestion in upstream. The analysis emphasized the importance of considering the downstream influence when simulating the traffic on signalized arterials. Finally, a sensitivity analysis is designed to further reveal the causes of upstream congestion.

Effects of Variable Speed Limit on Energy Consumption with Autonomous Vehicles on Urban Roads Using Modified Cell-Transmission Model

AbstractAutonomous vehicles create new opportunities for innovative intelligent traffic systems. Variable speed limit (VSL), which is a speed management system that can adjust the speed limit accor...

A Wireless Charging Facilities Deployment Problem Considering Optimal Traffic Delay and Energy Consumption on Signalized Arterial

With the looming promise of wireless recharging technology, electric vehicles (EVs) are going to be able to acquire energy while still in motion. This paper focuses on the optimal deployment of wireless recharging facilities on signalized arterials for EVs. To address this issue, a bi-objective model considering both traffic operation efficiency (i.e., traffic delay saving) and charging infrastructure utilization rate (i.e., electricity gain from charging) has been formulated. A modified cell transmission model (CTM) is used as a base to simulate traffic flow on an arterial with traffic signals. The cells in the CTM also serve as a potential installation site for wireless recharging facilities. The essential goal of this model is to maximize the recharging electricity for EVs traveling on arterials while maintaining low travel delay. Due to the complexity in solving the bi-objective model, heuristic approaches, such as genetic algorithm and particle swarm optimization, are employed. The numerical experiments based on real day-to-day traffic demand are executed. A Pareto set is obtained and a sensitivity analysis regarding recharging rate, investment, and minimum recharging region length is provided.

Procedure for Determining the Deployment Locations of Variable Speed Limit Signs to Reduce Crash Risks at Freeway Recurrent Bottlenecks

The effectiveness of the variable speed limit (VSL) control is affected by the deployment locations of VSL signs. In this paper, a procedure was proposed to help determine the deployment location of VSL signs to reduce collision risks at freeway recurrent bottlenecks. The procedure is started from determining the hazardous recurrent bottleneck section by constructing the profile of the collision risks. The length of the hazardous section was determined according to the pre-selected threshold of crash risks. Various scenarios were considered for different lengths of VSL controlled sections with various densities of VSL signs. A modified cell transmission model (CTM) was used for modeling the traffic flow at the freeway bottlenecks under the VSL control. The VSL control factors were optimized by using the genetic algorithm. The safety effects of VSL were greatly affected by the placement of VSL signs. In general, the scenario with a longer VSL controlled section and more speed limit signs was more effective in reducing rear-end collision risks. The cost-benefit analyses showed that the placement of VSL signs in scenario C2 with the controlled section length of 11.7 mi and average VSL density of 1.0 mi had the best benefit/cost effect. Using 12 VSL signs, the collision risks were reduced by 69.16% and the total travel time was increased slightly by 7.73%. The procedure can help determine the optimal deployment of VSL signs on freeways, considering both the safety benefits and the cost.

Network Flow Dynamics Modeling and Analysis of Arrival Traffic in Terminal Airspace

This paper reveals and explores the flow dynamics of arrival traffic in a terminal airspace network on both mesoscopic and macroscopic levels in a systematic way from empirical data to dynamics modeling. The existence of link-based typical fundamental diagram (FD) that expresses the fundamental relations of newly defined flow-density-speed and network-based arrival macroscopic fundamental diagram (MFD-A) that represents aggregate demand-supply dynamics is demonstrated using empirical data collected in Guangzhou Terminal Airspace. After establishing heterogeneous FDs for flows along a different route segments using piecewise approximation, a density-speed-based modified cell transmission model (MCTM) is developed to simulate the spatio-temporal evolution of flow and congestion in arrival network for the enhancement of the adaption to non-uniform cell length and unique speed profile in terminal airspace. To further improve the simulation accuracy without compromising computational time, hybrid simulation is designed by deploying a queuing inspector (QI) to MCTM. The proposed network flow model is shown to be an efficient and accurate method capable of capturing the flow evolution at mesoscopic and macroscopic levels and supporting air traffic flow prediction and control. In the end, characteristics of arrival flow dynamics, including hysteresis, critical steady state (CSS), critical unsteady state (CUS), and its acceptable duration are discussed in depth as crucial theoretical parameters for air traffic flow management. This study provides a novel perspective method to model and understand the evolution of air traffic flow, and underpins advanced technical potentials for future air traffic management.

Reinforcement Learning-Based Variable Speed Limit Control Strategy to Reduce Traffic Congestion at Freeway Recurrent Bottlenecks

The primary objective of this paper was to incorporate the reinforcement learning technique in variable speed limit (VSL) control strategies to reduce system travel time at freeway bottlenecks. A Q-learning (QL)-based VSL control strategy was proposed. The controller included two components: a QL-based offline agent and an online VSL controller. The VSL controller was trained to learn the optimal speed limits for various traffic states to achieve a long-term goal of system optimization. The control effects of the VSL were evaluated using a modified cell transmission model for a freeway recurrent bottleneck. A new parameter was introduced in the cell transmission model to account for the overspeed of drivers in unsaturated traffic conditions. Two scenarios that considered both stable and fluctuating traffic demands were evaluated. The effects of the proposed strategy were compared with those of the feedback-based VSL strategy. The results showed that the proposed QL-based VSL strategy outperformed the feedback-based VSL strategy. More specifically, the proposed VSL control strategy reduced the system travel time by 49.34% in the stable demand scenario and 21.84% in the fluctuating demand scenario.

The Simulation Model of Expressway Based on Modified Cell Transmission Model

In order to realize the reasonable planning, design and management of expressway, the modified cell transmission model is proposed considering the limitation of equal cell length of traditional cell transmission model, improving the mode of traffic transmission on expressway. The capacity and jam density is calculated and the relationship between traffic speed and density is calibrated by using the vehicle detector data. Meanwhile, the traffic speed-density relationship is refined by adopting the weighted least square method, enhancing the practicality of the model. When the modified cell transmission model is applied in the expressway, the mean percentage error of cell traffic flow can be controlled at around 12 percent, which shows that the simulation result is satisfactory.

Extension of Traffic Flow Pattern Dynamic Classification by a Macroscopic Model Using Multivariate Clustering

In this paper, we evaluate the performance of a dynamic approach to classifying flow patterns reconstructed by a switching-mode macroscopic flow model considering a multivariate clustering method. To remove noise and tolerate a wide scatter of traffic data, filters are applied before the overall modeling process. Filtered data are dynamically and simultaneously input to the density estimation and traffic flow modeling processes. A modified cell transmission model simulates traffic flow to explicitly account for flow condition transitions considering wave propagations throughout a freeway test stretch. We use flow dynamics specific to each of the cells to determine the mode of prevailing traffic conditions. Flow dynamics are then reconstructed by neural methods. By using two methods in part, i.e., dynamic classification and nonhierarchical clustering, classification of flow patterns over the fundamental diagram is obtained by considering traffic density as a pattern indicator. The fundamental diagram of speed-flow is dynamically updated to specify the current corresponding flow pattern. The dynamic classification approach returned promising results in capturing sudden changes on test stretch flow patterns as well as performance compared to multivariate clustering. The dynamic methods applied here are open to use in practice within intelligent management strategies, including incident detection and control and variable speed management.

Level-of-Service Based Hierarchical Feedback Control Method of Network-Wide Pedestrian Flow

Pedestrian flow control is usually used to manage the crowd motion in public facilities to avoid congestion. We propose a network-wide pedestrian flow model based on the modified cell transmission model which describes the link flow as ordinary differential equations. The network flow control model (NFCM) is proposed to limit the number of pedestrians in a network according to the level-of-service requirements; however, the NFCM cannot ensure the uniform link density which is a premise of using NFCM. As a solution, the link flow control model (LFCM) is proposed to adjust the walking speed of pedestrians to realize the uniform link density. The NFCM provides the inputs for the LFCM and the LFCM compensates the deficiency of NFCM. Both NFCM and LFCM control the pedestrian flow in a cooperative way, and thus they form the hierarchical feedback control model (HFCM) of network-wide pedestrian flow. At last, the proposed HFCM is applied to control the crowd of a hall and the comparison of the simulation results in the controlled and uncontrolled scenarios shows that the proposed HFCM has the capability to suggest the optimal link inflows and walking speeds in real time to meet the LOS requirement.

Linear complementarity system approach to macroscopic freeway traffic modelling: uniqueness and convexity

The modified cell transmission model (MCTM) is formulated as a linear complementarity system (LCS) in this paper. The LCS formulation presented here consists of a discrete time linear system and a set of complementarity conditions. The discrete time linear system corresponds to the flow conservation equations while the complementarity conditions govern the sending and receiving functions defined by a series of ‘min’ operations in the MCTM. Technical difficulties encountered in application of the CTM and its extensions such as the hard nonlinearity caused by the ‘min’ operator can be avoided by the proposed LCS model. Several basic properties of the proposed LCS formulation, for example, existence and uniqueness of solution, are analysed based on the theory of linear complementarity problem. By this formulation, the theory of LCS developed in control and mathematical programming communities can be applied to the qualitative analysis of the CTM/MCTM. It is shown that the CTM/MCTM is equivalent to a convex programme which can be converted into a constrained linear quadratic control problem. It is found that these results are irrelevant to the cell partition, that is, different cell partitions will not change the uniqueness and convexity of solution. This property is essential for stability analysis and control synthesis. The proposed LCS formulation makes the CTM/MCTM convenient for the design of traffic state estimators, ramp metering controllers.

Optimal Mainline Variable Speed Limit Control to Improve Safety on Large‐Scale Freeway Segments

AbstractThe primary objective of this study was to develop a procedure for determining the optimal variable speed limit (VSL) control strategy that aims at reducing both collision risks and injury severity on large‐scale freeway segments. The achieved reduction in collision risks and injury severity were evaluated using real‐time crash risk and severity prediction models. A modified cell transmission model (CTM) that took into consideration the capacity drop and the stop‐and‐go traffic was used to simulate the traffic operations with the VSL control. A computational procedure that incorporated the genetic algorithm and the CTM was proposed for the optimization of critical VSL control factors. Three scenarios with various placements of VSL signs on freeway mainlines were evaluated. The results showed that the optimal VSL control successfully decreased the collision risks by 22.62% and reduced the injury severity of crashes by 14.67%. We also evaluated how drivers’ compliance to speed limits affected the effectiveness of VSL control. The safety effects decreased as drivers’ compliance rate to the VSL control decreased. The finding suggests the use of speed enforcement techniques together with the VSL control to achieve the optimum control effects.

A modified Cell Transmission Model with realistic queue discharge features at signalized intersections

Modeling realistic discharge flow-rate and headway features at signalized intersections is critical to the design of traffic signals, since they play a critical role in determining the startup lost times and intersection capacity. Traditional queue discharge models are either microscopic or stochastic, and macroscopic traffic flow models for signalized intersections are based on overly simplistic assumptions. They are incapable of modeling traffic dynamics at signalized intersections as well as capturing realistic queue discharge features.In this study we propose a modified Cell Transmission Model (CTM) by substituting the traditional demand function, which is constant under over-saturated conditions, with a linearly decreasing function. The new demand function is defined through a combination of conventional macroscopic parameters, including critical density, free-flow speed, jam density, and an additional parameter, jam demand. Analytically we show that the new model reproduces observed features in the discharge flow-rate and headway. We further present a new definition of lost times at the macroscopic level based on the modified CTM. Calibration with observations in existing studies, as well as new observations, further suggest that the model can reasonably capture all traffic queue discharge features. We also discuss solutions to the new model under various Riemann problem scenarios and show that they produce realistic results while offering observable improvements in the modeling of traffic dynamics under certain scenarios.

Temporal-Spatial Analysis of Traffic Congestion Based on Modified CTM

A modified cell transmission model (CTM) is proposed to depict the temporal-spatial evolution of traffic congestion on urban freeways. Specifically, drivers’ adaptive behaviors and the corresponding influence on traffic flows are emphasized. Two piecewise linear regression models are proposed to describe the relationship of flow and density (occupancy). Several types of cellular connections are designed to depict urban rapid roads with on/off-ramps and junctions. Based on the data collected on freeway of Queen Elizabeth, Ontario, Canada, we show that the new model provides a relatively higher accuracy of temporal-spatial evolution of traffic congestions.

An Approach to Modeling the Impact of Traffic Incident on Urban Expressway

To identify network bottlenecks of urban expressway effectively is a foundational work for improving network traffic condition and preventing traffic congestion. This study proposes a methodology to estimate the impact of traffic incident on urban expressway on the basis of modified cell transmission model. The metastable state was taken into account in the proposed method to reflect the actual operating state of traffic flow on urban expressway as much as possible. Regarding the location of traffic incident, the method of cell restructuring settings was discussed. We then proceed to introduce a new concept of the effected length in a given time period as the evaluation indicator to directly depict the influence of traffic incident. The proposed method was tested on a 6516-meter urban expressway section of west second ring road in Beijing. The simulation results indicated that the proposed methodology performs well to predict the impact of traffic incident on urban expressway.

Dynamic penalty function approach for ramp metering with equity constraints

This study proposes a non-linear programming optimization model that could simultaneously consider the ramp metering efficiency and equity issue. Equity indexes are defined to capture the degree of equity of the ramp metering, which are formulated as constraints in the model. Dynamic penalty method is adopted to deal with the constraints since they are soft in nature in which solutions with small violations could be acceptable. A modified cell transmission model (MCTM) is chosen to simulate the traffic flow propagation in the network where the objective function value is derived from it. The results of the case study show that the proposed methodology could give better solutions compared to initial solutions. However, the equity indexes obtained are low. It is anticipated that the results for equity indexes can be improved if the penalty coefficients could be fine tuned properly.

Collection, spillback, and dissipation in pedestrian evacuation: A network-based method

We present a method of predicting pedestrian route choice behavior and physical congestion during the evacuation of indoor areas with internal obstacles. Under the proposed method, a network is first constructed by discretizing the space into regular hexagonal cells and giving these cells potentials before a modified cell transmission model is employed to predict the evolution of pedestrian flow in the network over time and space. Several properties of this cell transmission model are explored. The method can be used to predict the evolution of pedestrian flow over time and space in indoor areas with internal obstacles and to investigate the collection, spillback, and dissipation behavior of pedestrians passing through a bottleneck. The cell transmission model is further extended to imitate the movements of multiple flows of pedestrians with different destinations. An algorithm based on generalized cell potential is also developed to assign the pedestrian flow.