On the stability of traffic perimeter control in two-region urban cities

In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.     

Traffic guidance–perimeter control coupled method for the congestion in a macro network

Macroscopic fundamental diagram (MFD) describes the macro relationship between a network vehicle density and a network space mean flow, without requiring the mastery of complex origin to destination data. Thus, MFD provides an opportunity for the macro control of urban road network. However, most of the existing MFD control methods ignore the active role of traffic guidance in solving congestion problems. This study presents a traffic guidance–perimeter control coupled (TGPCC) method to improve the performance of macroscopic traffic networks. The method considers the optimal cumulative volume of a network as the goal and establishes a programming function according to the network equilibrium rule of traffic flow amongst multiple MFD sub-regions, which regards the minimum delay of network, as the objective. The Logit model for the compliance rate of driver route guidance is established by the stated preference survey. Moreover, the perimeter control (PC) method is proposed for adjusting the phase split of intersections. Finally, three schemes, namely, the TGPCC, PC and the method without PC and guidance are tested on a network with four well-defined MFD sub-regions. Results show that the TGPCC addresses the issue of congestion and decreases the total delay accordingly.     

Multi-scale perimeter control approach in a connected-vehicle environment

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors).     

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.     

Cooperative traffic control of a mixed network with two urban regions and a freeway

Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.     

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

Recent research has studied the existence and the properties of a macroscopic fundamental diagram (MFD) for large urban networks. The MFD should not be universally expected as high scatter or hysteresis might appear for some type of networks, like heterogeneous networks or freeways. In this paper, we investigate if aggregated relationships can describe the performance of urban bi-modal networks with buses and cars sharing the same road infrastructure and identify how this performance is influenced by the interactions between modes and the effect of bus stops. Based on simulation data, we develop a three-dimensional vehicle MFD (3D-vMFD) relating the accumulation of cars and buses, and the total circulating vehicle flow in the network. This relation experiences low scatter and can be approximated by an exponential-family function. We also propose a parsimonious model to estimate a three-dimensional passenger MFD (3D-pMFD), which provides a different perspective of the flow characteristics in bi-modal networks, by considering that buses carry more passengers. We also show that a constant Bus–Car Unit (BCU) equivalent value cannot describe the influence of buses in the system as congestion develops. We then integrate a partitioning algorithm to cluster the network into a small number of regions with similar mode composition and level of congestion. Our results show that partitioning unveils important traffic properties of flow heterogeneity in the studied network. Interactions between buses and cars are different in the partitioned regions due to higher density of buses. Building on these results, various traffic management strategies in bi-modal multi-region urban networks can then be integrated, such as redistribution of urban space among different modes, perimeter signal control with preferential treatment of buses and bus priority.     

Agent-based network transmission model using the properties of macroscopic fundamental diagram

The field of research that has recently come to the fore is the perimeter control, which aims to control traffic demand for a large urban area prior to controlling internal flow inside the area. Such control concept needs to be tested by simulations, hence, it is necessary to develop a model that can appropriately estimate the network-wide flow dynamics. In this paper, agent-based network transmission model (ANTM) is proposed for describing the aggregated flow dynamics over an urban area of multiple large-scale networks. The proposed model is the combination of the cell transmission model (CTM), macroscopic fundamental diagram (MFD), and agent concept. The CTM-based simulation is adopted for the simplicity considering the computation requirements for real-time feasibility. The MFD concept is applied for representing the network properties, and a new approach is taken particularly for estimating network outflow affected by both demand patterns and boundary capacity. The agent concept is applied for representing drivers’ travel behaviors. The model is compared with microscopic simulations and shows reasonable accuracy for large areas. In addition, various travel direction choice behaviors are applicable to this model. Various perimeter control policies are applicable as well, thus, the proposed model can be a useful tool for testing various control methods, in terms of reducing the congestion in urban areas.     

Perimeter and boundary flow control in multi-reservoir heterogeneous networks

In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a single-reservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.     

Analytical model for information flow propagation wave under an information relay control strategy in a congested vehicle-to-vehicle communication environment

Vehicular traffic congestion in a vehicle-to-vehicle (V2V) communication environment can lead to congestion effects for information flow propagation. Such congestion effects can impact whether a specific information packet of interest can reach a desired location, and if so, in a timely manner to influence the traffic system performance. Motivated by the usefulness and timeliness of information propagation, this paper aims to characterize the information flow propagation wave (IFPW) for an information packet in a congested V2V communication environment under an information relay control strategy. This strategy seeks to exclude information that is dated in the communication buffer under a first-in, first-out queue discipline, from being relayed if the information flow regime is congested. It trades off the need to enable the dissemination of every information packet as far as possible, against the congestion effects that accrue because of the presence of multiple information packets. A macroscopic two-layer model is proposed to characterize the IFPW. The upper layer is formulated as integro-differential equations to characterize the information dissemination in space and time under this control strategy. The lower layer adopts the Lighthill-Whitham-Richards model to capture the traffic flow dynamics. Based on the upper layer model, a necessary condition is derived which quantifies the expected time length that needs to be reserved for broadcasting the information packet of interest so as to ensure the formation of an IFPW under a given density of V2V-equipped vehicles. When the necessary condition is satisfied under homogeneous conditions, it is shown that the information packet can be propagated at an asymptotic speed whose value can be derived analytically. Besides, under the proposed control strategy, only a proportion of vehicles (labeled asymptotic density of informed vehicles) can receive the specific information packet, which can be estimated by solving a nonlinear equation. The asymptotic IFPW speed, the asymptotic density of informed vehicles, and the necessary condition for the IFPW, help in evaluating the timeliness of information propagation and the influence of traffic dynamics on information propagation. In addition, the proposed model can be used to numerically estimate the IFPW speed for heterogeneous conditions, which can aid in the design of traffic management strategies built upon the timely propagation of information through V2V communication.     

Model based urban traffic control,part II: Coordinated model predictive controllers

The present paper describes how to use coordination between neighbouring intersections in order to improve the performance of urban traffic controllers. Both the local MPC (LMPC) introduced in the companion paper (Hao et al., 2018) and the coordinated MPC (CMPC) introduced in this paper use the urban cell transmission model (UCTM) (Hao et al., 2018) in order to predict the average delay of vehicles in the upstream links of each intersection, for different scenarios of switching times of the traffic lights at that intersection. The feedback controller selects the next switching times of the traffic light corresponding to the shortest predicted average delay. While the local MPC (Hao et al., 2018) only uses local measurements of traffic in the links connected to the intersection in comparing the performance of different scenarios, the CMPC approach improves the accuracy of the performance predictions by allowing a control agent to exchange information about planned switching times with control agents at all neighbouring intersections. Compared to local MPC the offline information on average flow rates from neighbouring intersections is replaced in coordinated MPC by additional online information on when the neighbouring intersections plan to send vehicles to the intersection under control. To achieve good coordination planned switching times should not change too often, hence a cost for changing planned schedules from one decision time to the next decision time is added to the cost function. In order to improve the stability properties of CMPC a prediction of the sum of squared queue sizes is used whenever some downstream queues of an intersection become too long. Only scenarios that decrease this sum of squares of local queues are considered for possible implementation. This stabilization criterion is shown experimentally to further improve the performance of our controller. In particular it leads to a significant reduction of the queues that build up at the edges of the traffic region under control. We compare via simulation the average delay of vehicles travelling on a simple 4 by 4 Manhattan grid, for traffic lights with pre-timed control, traffic lights using the local MPC controller (Hao et al., 2018), and coordinated MPC (with and without the stabilizing condition). These simulations show that the proposed CMPC achieves a significant reduction in delay for different traffic conditions in comparison to these other strategies.     

Robust constrained control of uncertain macroscopic fundamental diagram networks

This paper considers modeling and control of uncertain Macroscopic Fundamental Diagram (MFD) systems for multiple-region networks. First, the nonlinear vehicle conservation equations based on MFD dynamics, presented in earlier publications, are transformed to linear equations with parameter uncertainties. The parameter uncertainties include the destination decomposition fractions, that are difficult to estimate in reality. Then, the uncertain linear model is utilized to design a robust feedback controller by an interpolation-based approach. This approach (i) guarantees robustness against all parameter uncertainties, (ii) handle control and state constraints, and (iii) present a computationally cheap solution. The main idea is to interpolate between (i) a stabilizing outer controller that respects the control and state constraints and (ii) an inner robustly stable controller designed by any method. The robust control is further challenged to deal with different relative locations of reference accumulation points on the MFD diagrams. Numerical results for a two-region system show that the uncertain linear model can replace the nonlinear model for modeling and control. Moreover, the robust control law is presented as implicit and explicit solutions, where in the implicit case one linear programming (LP) problem is solved at each time instant, while in the explicit case, the control law is shown as a piecewise affine function of state. Finally, a comparison between the interpolating controller and other controllers in the literature is carried out. The results demonstrate the performance advantages from applying the robust interpolating controller.     

Clustering of heterogeneous networks with directional flows based on “Snake” similarities

Aggregated network level modeling and control of traffic in urban networks have recently gained a lot of interest due to unpredictability of travel behaviors and high complexity of physical modeling in microscopic level. Recent research has shown the existence of well-defined Macroscopic Fundamental Diagrams (MFDs) relating average flow and density in homogeneous networks. The concept of MFD allows to design real-time traffic control schemes specifically hierarchical perimeter control approaches to alleviate or postpone congestion. Considering the fact that congestion is spatially correlated in adjacent roads and it propagates spatiotemporaly with finite speed, describing the main pockets of congestion in a heterogeneous city with small number of clusters is conceivable. In this paper, we propose a three-step clustering algorithm to partition heterogeneous networks into connected homogeneous regions, which makes the application of perimeter control feasible. The advantages of the proposed method compared to the existing ones are the ability of finding directional congestion within a cluster, robustness with respect to parameters calibration, and its good performance for networks with low connectivity and missing data. Firstly, we start to find a connected homogeneous area around each road of the network in an iterative way (i.e. it forms a sequence of roads). Each sequence of roads, defined as ‘snake’, is built by starting from a single road and iteratively adding one adjacent road based on its similarity to join previously added roads in that sequence. Secondly, based on the obtained sequences from the first step, a similarity measure is defined between each pair of the roads in the network. The similarities are computed in a way that put more weight on neighboring roads and facilitate connectivity of the clusters. Finally, Symmetric Non-negative Matrix Factorization (SNMF) framework is utilized to assign roads to proper clusters with high intra-similarity and low inter-similarity. SNMF partitions the data by providing a lower rank approximation of the similarity matrix. The proposed clustering framework is applied in medium and large-size networks based on micro-simulation and empirical data from probe vehicles. In addition, the extension of the algorithm is proposed to deal with the networks with sparse measurements where information of some links is missing. The results show the effectiveness and robustness of the extended algorithm applied to simulated network under different penetration rates (percentage of links with data).     

Equilibrium analysis and route guidance in large-scale networks with MFD dynamics

Recent studies have demonstrated that Macroscopic Fundamental Diagram (MFD), which provides an aggregated model of urban traffic dynamics linking network production and density, offers a new generation of real-time traffic management strategies to improve the network performance. However, the effect of route choice behavior on MFD modeling in case of heterogeneous urban networks is still unexplored. The paper advances in this direction by firstly extending two MFD-based traffic models with different granularity of vehicle accumulation state and route choice behavior aggregation. This configuration enables us to address limited traffic state observability and to scrutinize implications of drivers’ route choice in MFD modeling. We consider a city that is partitioned in a small number of large-size regions (aggregated model) where each region consists of medium-size sub-regions (more detailed model) exhibiting a well-defined MFD. This paper proposes a route guidance advisory control system based on the aggregated model as a large-scale traffic management strategy that utilizes aggregated traffic states while sub-regional information is partially known. In addition, we investigate the effect of equilibrium conditions (i.e. user equilibrium and system optimum) on the overall network performance, in particular MFD functions.     

Recent developments in traffic flow modeling using macroscopic fundamental diagram

ABSTRACT

This paper presents an overview of the recent developments in traffic flow modelling and analysis using macroscopic fundamental diagram (MFD) as well as their applications. In recent literature, various aggregated traffic models have been proposed and studied to analyse traffic flow while enhancing network efficiency. Many of these studies have focused on models based on MFD that describes the relationship between aggregated flow and aggregated density of transport networks. The analysis of MFD has been carried out based on experimental data collected from sensors and GPS, as well as simulation models. Several factors are found to influence the existence and shape of MFD, including traffic demand, network and signal settings, and route choices. As MFD can well express the traffic dynamics of large urban transport networks, it has been extensively applied to traffic studies, including the development of network-wide control strategies, network partitioning, performance evaluation, and road pricing. This work also presents future extensions and research directions for MFD-based traffic modelling and applications.     

Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing

Cruising-for-parking constraints mobility in urban networks. Car-users may have to cruise for on-street parking before reaching their destinations. The accessibility and the cost of parking significantly influence people's travel behavior (such as mode choice, or parking facility choice between on-street and garage). The cruising flow causes delays eventually to everyone, even users with destinations outside limited parking areas. It is therefore important to understand the impact of parking limitation on mobility, and to identify efficient parking policies for travel cost reduction. Most existing studies on parking fall short in reproducing the dynamic spatiotemporal features of traffic congestion in general, lack the treatment of dynamics of the cruising-for-parking phenomenon, or require detailed input data that are typically costly and difficult to collect. In this paper, we propose an aggregated and dynamic approach for modeling multimodal traffic with the treatment on parking, and utilize the approach to design dynamic parking pricing strategies. The proposed approach is based on the Macroscopic Fundamental Diagram (MFD), which can capture congestion dynamics at network-level for single-mode and bi-modal (car and bus) systems. A parsimonious parking model is integrated into the MFD-based multimodal modeling framework, where the dynamics of vehicular and passenger flows are considered with a change in the aggregated behavior (e.g. mode choice and parking facility choice) caused by cruising and congestion. Pricing strategies are developed with the objective of reducing congestion, as well as lowering the total travel cost of all users. A case study is carried out for a bi-modal city network with a congested downtown region. An elegant feedback dynamic parking pricing strategy can effectively reduce travel delay of cruising and the generic congestion. Remarkably, such strategy, which is applicable in real-time management with limited available data, is fairly as efficient as a dynamic pricing scheme obtained from system optimum conditions and a global optimization with full information about the future states of the system. Stackelberg equilibrium is also investigated in a competitive behavior between different parking facility operators. Policy indications on on-street storage capacity management and pricing are provided.     

Dynamic modeling and control of taxi services in large-scale urban networks: A macroscopic approach

Taxis are increasingly becoming a prominent mobility mode in many major cities due to their accessibility and convenience. The growing number of taxi trips and the increasing contribution of taxis to traffic congestion are cause for concern when vacant taxis are not distributed optimally within the city and are unable to find unserved passengers effectively. A way of improving taxi operations is to deploy a taxi dispatch system that matches the vacant taxis and waiting passengers while considering the search friction dynamics. This paper presents a network-scale taxi dispatch model that takes into account the interrelated impact of normal traffic flows and taxi dynamics while optimizing for an effective dispatching system. The proposed model builds on the concept of the macroscopic fundamental diagram (MFD) to represent the dynamic evolution of traffic conditions. The model considers multiple taxi service firms operating in a heterogeneously congested city, where the city is assumed to be partitioned into multiple regions each represented with a well-defined MFD. A model predictive control approach is devised to control the taxi dispatch system. The results show that lack of the taxi dispatching system leads to severe accumulation of unserved taxi passengers and vacant taxis in different regions whereas the dispatch system improves the taxi service performance and reduces traffic congestion by regulating the network towards the undersaturated condition. The proposed framework demonstrates sound potential management schemes for emerging mobility solutions such as fleet of automated vehicles and demand-responsive transit services.     

On the distribution of urban road space for multimodal congested networks

Transport systems in real cities are complex with many modes of transport sharing and competing for limited road space. This work intends to understand how space distributions for modes and interactions among modes affect network traffic performance. While the connection between performance of transport systems and general land allocation is the subject of extensive research, space allocation for interacting modes of transport is an open research question. Quantifying the impact of road space distribution on the performance of a congested multimodal transport system with a dynamic aggregated model remains a challenge. In this paper, a multimodal macroscopic fundamental diagram (MFD) is developed to represent the traffic dynamics of a multimodal transport system. Optimization is performed with the objective of minimizing the total passenger hours traveled (PHT) to serve the total demand by redistributing road space among modes. Pricing strategies are also investigated to provide a higher demand shift to more efficient modes. We find by an application to a bi-modal two-region city that (i) the proposed model captures the operational characteristics of each mode, and (ii) optimal dynamic space distribution strategies can be developed. In practice, the approach can serve as a physical dynamic model to inform space distribution strategies for policy makers with different goals of mobility.     

Network operation reliability in a Manhattan-like urban system with adaptive traffic lights

Traffic breakdown to global gridlock occurring in congested traffic network makes the serious traffic congestion even much worse. This paper has proposed to use Network Operation Reliability (NOR) to quantitatively depict the probabilistic feature of traffic breakdown to global gridlock. The Nagel–Schreckenberg cellular automaton model has been used to simulate the traffic flow in a Manhattan-like urban network. A simple adaptive traffic light strategy has been proposed. It has been shown that if vehicles choose to use geometric shortest path, the adaptive traffic signals are able to remarkably enhance the NOR and sometimes the average velocity and the arrival rate as well. The vehicle distribution has been investigated, which has heuristically explained the enhancement of the NOR. A simple perimeter control strategy has been shown to fail to enhance the NOR. Finally, we show that if the time shortest path information could be provided and updated timely, then the NOR can be remarkably enhanced but the adaptive traffic signals have only trivial effect on NOR.     

A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model

Pricing is considered an effective management policy to reduce traffic congestion in transportation networks. In this paper we combine a macroscopic model of traffic congestion in urban networks with an agent-based simulator to study congestion pricing schemes. The macroscopic model, which has been tested with real data in previous studies, represents an accurate and robust approach to model the dynamics of congestion. The agent-based simulator can reproduce the complexity of travel behavior in terms of travelers’ choices and heterogeneity. This integrated approach is superior to traditional pricing schemes. On one hand, traffic simulators (including car-following, lane-changing and route choice models) consider travel behavior, i.e. departure time choice, inelastic to the level of congestion. On the other hand, most congestion pricing models utilize supply models insensitive to demand fluctuations and non-stationary conditions. This is not consistent with the physics of traffic and the dynamics of congestion. Furthermore, works that integrate the above features in pricing models are assuming deterministic and homogeneous population characteristics. In this paper, we first demonstrate by case studies in Zurich urban road network, that the output of a agent-based simulator is consistent with the physics of traffic flow dynamics, as defined by a Macroscopic Fundamental Diagram (MFD). We then develop and apply a dynamic cordon-based congestion pricing scheme, in which tolls are controlled by an MFD. And we investigate the effectiveness of the proposed pricing scheme. Results show that by applying such a congestion pricing, (i) the savings of travel time at both aggregated and disaggregated level outweigh the costs of tolling, (ii) the congestion inside the cordon area is eased while no extra congestion is generated in the neighbor area outside the cordon, (iii) tolling has stronger impact on leisure-related activities than on work-related activities, as fewer agents who perform work-related activities changed their time plans. Future work can apply the same methodology to other network-based pricing schemes, such as area-based or distance-traveled-based pricing. Equity issues can be investigated more carefully, if provided with data such as income of agents. Value-of-time-dependent pricing schemes then can also be determined.     

Exploring the effects of cooperative adaptive cruise control on highway traffic flow using microscopic traffic simulation

This paper examines the impact of having cooperative adaptive cruise control (CACC) embedded vehicles on traffic flow characteristics of a multilane highway system. The study identifies how CACC vehicles affect the dynamics of traffic flow on a complex network and reduce traffic congestion resulting from the acceleration/deceleration of the operating vehicles. An agent-based microscopic traffic simulation model (Flexible Agent-based Simulator of Traffic) is designed specifically to examine the impact of these intelligent vehicles on traffic flow. The flow rate of cars, the travel time spent, and other metrics indicating the evolution of traffic congestion throughout the lifecycle of the model are analyzed. Different CACC penetration levels are studied. The results indicate a better traffic flow performance and higher capacity in the case of CACC penetration compared to the scenario without CACC-embedded vehicles.