Estimating MFDs in simple networks with route choice

Corrigendum to “Estimating MFDs in Simple Networks with Route Choice”

Estimating MFDs in Simple Networks with Route Choice

Macroscopic Fundamental Diagram (MFD) is widely used in traffic state evaluation due to its description of the macro level of urban road network. This study focuses on the discrimination and short-term prediction of macro traffic states in urban road networks, using MFD combined with FCM clustering for state partitioning to characterize different macro states of the road network. To predict the MFD state, this paper builds two LSTMs to perform short-term predictions on two important parameters in MFD: road network weighted flow qw and road network weighted density kw. The parameters of the first three statistical intervals and the predicted time period are used as inputs to output the MFD parameters for the predicted time period. To ensure that the two LSTM structures and hyper-parameters settings can achieve the best prediction performance for MFD, the parameter optimization process of both should be included in the same search framework for hyper-parameters search. Therefore, this paper uses GA algorithm combined with multi-objective particle swarm optimization algorithm as the solving algorithm, with the accuracy of solving two MFD parameters and the accuracy of MFD point positioning as the hyper-parameters solving objectives. The study was validated using actual road network data from Hong Kong, and the results showed that the method proposed in this paper has an MRE prediction error of less than 7.8% for the two parameters of MFD, and can predict the future temporal trend of the two parameters, demonstrating the feasibility of MFD related predictions. The model's prediction of the overall shape and change trajectory trend of MFD is consistent with reality, and some test sets in MFD state prediction show high accuracy, the overall accuracy is 81.45%. To verify the effectiveness of the multi-objective search algorithm, typical LSTM models and RNN models were used for comparison. The experiment proved that the model used in this study performed better in error control and state prediction. This study explores and practices a short-term prediction method for road network MFD parameters, MFD status, and their changing trends. Provided path reference for urban road network prediction, traffic control status, and MFD related research.

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 analyze 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.

ABSTRACTThis 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.

Road network traffic management and control are the key mechanisms to alleviate urban traffic congestion. With this study, we aimed to characterize the traffic flow state of urban road networks using the Macroscopic Fundamental Diagram (MFD) to support area traffic control. The core property of an MFD is that the network flow is maximized when network traffic stays at an optimal accumulation state. The property can be used to optimize the temporal and spatial distribution of traffic flow with applications such as gating control. MFD construction is the basis of these MFD-based applications. Although many studies have been conducted to construct MFDs, few studies are dedicated to improving the accuracy considering the reliability of different sources of data. To this end, we propose an MFD construction method using multi-source data based on Dempster–Shafer evidence (DS evidence) theory considering the reliability of different data sources. First, the MFD was constructed using VTD and CSD, separately. Then, the fused MFD was derived by quantifying the reliability of different sources of data for each MFD parameter based on DS evidence theory. The results under real data and simulated data show that the accuracy of the constructed MFDs was greatly improved considering the reliability of different data sources (the maximum MFD estimation error was reduced by 22.3%). The proposed method has the potential to support the evaluation of traffic operations and the optimization of signal control schemes for urban traffic networks.

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

Equilibrium Analysis and Route Guidance in Large-scale Networks with MFD Dynamics

The design of network-wide traffic management schemes or transport policies for urban areas requires computationally efficient traffic models. The macroscopic fundamental diagram (MFD) is a promising tool for such applications. Unfortunately, empirical MFDs are not always available, and semi-analytical estimation methods require a reduction of the network to a corridor that introduces substantial inaccuracies. We propose a semi-analytical methodology to estimate the MFD for realistic urban networks without the information loss induced by the reduction of networks to corridors. The methodology is based on the method of cuts but applies to networks with irregular topologies, accounts for different spatial demand patterns, and determines the upper bound of network flow. Therefore, we consider both flow conservation and the effects of spillbacks at the network level. Our framework decomposes a given network into a set of corridors, creates a hypernetwork, including the impacts of source terms, and then treats the dependencies across corridors (e.g., because of turning flows and spillbacks). Based on this hypernetwork, we derive the free-flow and capacity branch of the MFD. The congested branch is estimated by considering gridlock characteristics and utilizing recent advancements in MFD research. We showcase the applicability of the proposed methodology in a case study with a realistic setting based on the Sioux Falls network. We then compare the results to the original method of cuts and a ground truth derived from the cell transmission model. This comparison reveals that our method is more than five times more accurate than the state of the art in estimating the network-wide capacity and jam density. Moreover, the results clearly indicate the MFD’s dependency on spatial demand patterns. Compared with simulation-based MFD estimation approaches, the potential of the proposed framework lies in the modeling flexibility, explanatory value, and reduced computational cost. Funding: G. Tilg acknowledges support from the German Federal Ministry for Digital and Transport (BMDV) for the funding of the project LSS (capacity increase of urban networks). S. F. A. Batista and M. Menéndez acknowledge support from the NYUAD Center for Interacting Urban Networks (CITIES), funded by Tamkeen under the NYUAD Research Institute Award [CG001]. L. Ambühl acknowledges support from the ETH Research Grant [ETH-27 16-1] under the project name SPEED. L. Leclercq acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program [Grant 646592 - MAGnUMproject]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0402 .

Recent advances in traffic flow theory at the network level, namely the Macroscopic Fundamental Diagram (MFD), reveals the existence of well-defined laws of congestion dynamics at aggregated levels. The same knowledge for multimodal networks however is limited. It is critical to understand how urban space can be allocated and managed for multimodality. The objective is to develop aggregated modeling and optimization approaches, which will contribute on the knowledge of congestion dynamics in cities of different structures and mode usages, and ultimately facilitate the design of efficient and equitable urban transport policies. Building on the knowledge of the single-mode MFD theory, a bi-modal MFD model considering the effect of mode conflict is proposed for mixed networks of buses and cars. A system-level model is developed for multiple-region city network. The flow dynamics among regions are described by a regional level flow conservation law. A non-linear optimization framework is performed to optimize space allocation, minimizing the total passenger cost, given certain demand, city structure and road facility. Then, parking limitation is integrated in the proposed multi-modal system model, where vehicles cruising for parking are also integrated. The extra delay of cruising is captured by a geometric distribution related to the time-dependent parking availability and estimated at the aggregated level. The delay cost to other users is also estimated via the bi-modal MFD, and it shows the effect of cruising on all travelers who do not require parking. Optimal parking pricing policies for on-street and garage parking are obtained through the optimization framework, as well. The existence of a three-dimensional MFD (3D-MFD) for mixed bi-modal networks is investigated and analyzed via micro-traffic simulation studies. A 3D-MFD relates vehicular production of a network (flow, travel distance) to the density of cars and buses, where the impact of each mode on network performance can be directly observed. To further compare the modal impact on performance, the Bus-Car Unit equivalent value is estimated, indicating that this value is state- and mode-composition dependent rather than deterministic. In addition to the conventional vehicle-flow-based analysis, a passenger 3D-MFD is derived which provides a different perspective of the flow characteristics in bi-modal networks. Simulation study on 3D-MFD based perimeter-control shows promising performance in real-time control. The final part of the thesis concerns the MFD-controlled congestion pricing. Feedback-type control mechanisms are proposed to determine and adjust the time-dependent tolls, based on congestion level as expressed by the MFD. One pricing scheme also considers userâ s adaptation to the toll cost, allowing a great flexibility in toll adjustment, and deals with the promotion of public transport usage. The performance of the pricing schemes is investigated in an existing agent-based model where the complex travel behavior in real-life is reasonably reproduced. Results demonstrate that the pricing schemes are effective in congestion reduction. Remarkably, smooth behavioral equilibrium in long-term operation is found under such pricing schemes. Furthermore, user heterogeneity with respect to value-of-time is introduced in the agent-based model. By realizing and treating this heterogeneity, pricing strategies can achieve even higher efficiency and equitable benefit.

Calibration and validation of multi-reservoir MFD models: A case study in Lyon

Macroscopic fundamental diagram (MFD) has been used for aggregate modeling of urban traffic network dynamics under stationary traffic assumption for dynamic taxi dispatching, vehicle relocation and dynamic pricing schemes to tackle the dimensionality problem of microscopic approaches. A city is assumed to be partitioned into several regions with each admits a well-defined MFD. Integrating state-dependent regional travel time function as an endogenous time-varying delay, the MFD model with time delay, is adopted to describe the traffic dynamics within a region. On the other hand, it is necessary to enable simultaneous route choice and departure time choice under the MFD framework for various applications such as vehicle dispatching and relocation. This paper presents an optimal control framework to model dynamic user equilibria (DUE) with simultaneous route choice behavior and departure time choice for general urban networks. Necessary conditions for the DUE are analytically derived through the lens of Pontryagin minimum principle. In contrast to existing analytical methods, the proposed method is applicable for general MFD systems without approximation schemes of the equilibrium solution. Numerical examples by time discretization are conducted to illustrate the characteristics of DUE and corresponding dynamic external costs.

Purpose The expected benefits of newly developed transportation infrastructures are the saving of travel time and further promoted transport economics. There is a need for a methodology of travel time estimation with acceptable robustness and practicability. Macroscopic fundamental diagram (MFD) represents the overall traffic performance at a network level by linking average flow, speed and density. MFD can be used to estimate network state and to describe various traffic management strategies. This study aims to describe the effect of new infrastructure development on the network performance using the MFD framework. Design/methodology/approach The scenarios of Islamabad Road network before and after the infrastructure construction were simulated, in which the floating car data set (FCD) for multiple modes was extracted. MFD has been formed for the whole region and partitioned region, which was divided on the basis of infrastructural changes. Moreover, this study has been extended to calculate travel time for multiple modes using the MFD results and the Bureau of Public Roads (BPR) function at a neighborhood level. Findings MFD results for the whole network showed that the speed of traffic improves after the construction of new infrastructure. The travel time estimates using MFD results were dependent on the speed estimates, whereas the estimates obtained using the BPR function were found to be dependent on the traffic volume variation during different intervals of the day. By using the FCD for multiple modes, travel time estimates for multiple modes were obtained. The BPR function method was found valid for estimating travel time of traffic stream only. Originality/value This paper innovatively investigates the change in network performance for pre-construction and post-construction scenarios using the MFD framework. In practice, the approach presented can be used by transportation agencies to evaluate the effect of different traffic management strategies and infrastructural changes.

A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems

Today, the development and evaluation of traffic management strategies heavily relies on microscopic traffic simulation models. In case detailed input (i.e. od matrix, signal timings, etc.) is extracted and incorporated in these simulators, they can provide valuable traffic state predictions. However, as this type of information is almost never available at the large-scale and traffic represents chaotic behavior in saturated networks, microscopic simulation models remain intractable and unstable. An alternative is a recently discovered network traffic model; macroscopic fundamental diagram (MFD). Nevertheless, large-scale traffic management strategies remain a big challenge partly due to unpredictability of choices of travelers (e.g. route, departure time and mode choice). Part I of the thesis is an attempt to fill this gap. Chapter 2, 3 and 4 elaborate new aspects of large-scale traffic modeling, and integrate route choice behavior into the modeling. Chapter 2 proposes a dynamic traffic assignment (DTA) model to establish equilibrium conditions in multi-region urban networks where the modeling is done through MFD dynamics. The method handles the stochastic components of the aggregated model through a sampling approach. In addition, the assignment model enables us to consider the response of drivers to changing traffic conditions in an aggregated modeling framework. Chapter 3 extends the DTA model presented in Chapter 2 to a route guidance system, where drivers are given a sequence of subregions to follow. Two aggregated models, region- and subregion-based models, are introduced to develop the guidance scheme and to test its effect, respectively. Notably, the challenge here is to translate certain variables across the traffic models without a loss of significance and assure certain degree of consistency. Chapter 4 extracts and reconstructs aggregated route choice patterns through an extensive GPS data set from taxis in a mega city. Observed GPS trajectories are first grouped together to provide a physical evidence for consistent route patterns. Second, in order to investigate the consistency of equilibrium assumptions considered in Chapter 2, observed trajectories are replaced with shortest path trajectories, and aggregated route choice patterns are reconstructed. Part II introduces novel travel time prediction and variability models. Travel time is a crucial performance measure in assessing the efficiency of transportation systems, and it provides a common index for both practitioners and travelers. Chapter 5 develops a travel time prediction model that jointly exploits traffic flow fundamentals and advanced data mining techniques. The prediction method detects the congestion patterns through the identification of active bottlenecks, and clusters the days with similar traffic patterns. This approach basically allows the model to train its predictions with relevant historical data sets. The method is applicable in oversaturated conditions and consistent with physics of traffic flow. Nevertheless, travelers not only consider travel time on average, but also value its variation. Day-to-day travel time variability, addressing the travel time variations of vehicles crossing the same route at the same period of time on different days, reveals interesting patterns. Departure time periods with similar mean travel times in the onset and offset of congestion exhibit quite different variance values. This phenomenon causes counter-clockwise hysteresis loops on the mean-variance curves. Chapter 6 investigates the empirical implications of hysteresis shape within the context of day-to-day travel time variability.