Macroscopic Fundamental Diagram Model Research Articles

Investigating built environment and traffic flow impact on crash frequency in urban road networks

While numerous studies have examined the factors that influence crash occurrence, there remains a gap in understanding the intricate relationship between built environment, traffic flow, and crash occurrences across different spatial units. This study explores how built environment attributes, and dynamic traffic flow characteristics affect crash frequency by focusing on proposed traffic density-based zones (TDZs). Utilizing a comprehensive dataset from Greater Melbourne, Australia, this research emphasizes on the dynamic traffic flow variables and insights from the Macroscopic Fundamental Diagram model, considering parameters such as shockwave velocity and congestion index. The association between the potential influencing factors and crash frequency is examined using a random parameter negative binomial regression model. Results indicate that the data segmentation based on TDZs is instrumental in establishing a more refined crash model compared to traditional planning-based zones, as demonstrated by improved goodness-of-fit measures. Factors including density (e.g., employment density), network design (e.g., road density and highway density), land use diversity (e.g., job-housing balance and land use mixture), and public transit accessibility (e.g., bus route density) are significantly associated with crash occurrence. Furthermore, the unobserved heterogeneity effects of the shockwave velocity and congestion index on crashes are revealed. The study highlights the significance of incorporating dynamic traffic flow variables in understanding crash frequency variations across different spatial units. These findings can inform optimal real-time traffic monitoring, environmental design, and road safety management strategies to mitigate crash risks.

A dynamic multi-region MFD model for ride-sourcing with ridesplitting

Dynamic network-level models directly addressing ride-sourcing services can support the development of efficient strategies for both congestion alleviation and promotion of more sustainable mobility. Recent developments presented models focusing on ride-hailing (solo rides) and traditional ride-sharing, but no work addressed ridesplitting (a type of ride-sourcing service with shared rides) in dynamic contexts. Here, we sought to develop a dynamic aggregated traffic network model capable of representing ride-sourcing services and background traffic in a macroscopic multi-region urban network. We combined the Macroscopic Fundamental Diagram (MFD) with detailed state-space and transition descriptions of background traffic and ride-sourcing vehicles in their activities to formulate mass conservation equations. Accumulation-based MFD models might experience additional errors due to the variation profile of trip lengths, e.g., when vehicles cruise for passengers. We integrate the so-called M-model that utilizes the total remaining distance to capture dynamics of regional and inter-regional flows and accumulations for different vehicle (private or ride-sourcing) states. This aggregated model is capable to reproduce the dynamics of complex systems without using resource-expensive simulations. We also show that the model can accurately forecast the vehicles’ conditions in near-future predictions (e.g., 30 min ahead). Later, a comparison with benchmark models shows lower errors in the proposed model in all states. Finally, we evaluate the model’s robustness to noises in its inputs, and forecast errors remain below 15% even where inputs are 20% off the actual values for ride-sourcing vehicles. The development of this model prepares the path for developing real-time feedback-based management policies such as priority-based perimeter control or repositioning strategies for idle ride-sourcing vehicles and developing regulations over ride-sourcing in congested areas.

Demand and state estimation for perimeter control in large-scale urban networks

State observability and demand estimation are two main issues in large-scale traffic networks which hinder real-world application of real-time control strategies. This study proposes a novel combined estimation and control framework (CECF) to develop perimeter control strategies based on macroscopic fundamental diagram (MFD). The proposed CECF is designed to operate with limited real-time traffic data and capture discrepancies in a priori demand estimates. The CECF is developed with a moving horizon estimator (MHE) that estimates traffic states, route choices and demand flows considering region accumulations and boundary flows observed from the network. The estimated traffic states are incorporated into a model predictive controller (MPC) scheme to derive the control decisions, which are then executed in the urban network. A novel accumulation-based MFD model is developed in this study to address the observability problem, which is incorporated into MHE and MPC schemes. The proposed CECF is implemented in a large-scale traffic network where several demand scenarios are tested. The results confirm the success of the CECF in overcoming observability issues and improving the performance of perimeter control strategies.

Perimeter Control and Route Guidance of Multi-Region MFD Systems With Boundary Queues Using Colored Petri Nets

Perimeter control based on Macroscopic Fundamental Diagram (MFD) aims to meter the number of transferring vehicles at the periphery of the protected urban region in order to obtain the desired number of vehicles in that region. The advantage of perimeter control is less computational effort, while its drawback is that it may create long queues and delays at the perimeter of the controlled area. For capturing boundary queue dynamics, an enhanced accumulation-based MFD model is proposed using colored Petri Nets by considering transfer flows, boundary queues and travel delays simultaneously. The gated intersections and related road segments on the border of a protected region are modeled as so-called boundary buffers. Based on the enhanced MFD model, anintegrated perimeter control framework is proposed with consideration of travel time and queuing time in buffers. In this framework, the controllers between peripheral and protected region are optimized using model predictive control theory. Then, internal flow controllers are adopted to homogenize traffic density among subregions, and route guidance is also used to balance the number of queuing vehicles among boundary buffers. Simulation results verify the effectiveness of the proposed integrated perimeter control. Furthermore, the impacts of buffer storage capacity on region heterogeneity and trip completion rates are also investigated in this paper. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —It is challenging to manage traffic congestion in large-scale urban network. Perimeter control provides an accumulation-based methodology with consideration of the existing correlation between traffic density and flow, which is known as MFD. For practical application, the efficiency as well asweakness of potential perimeter control strategies need to be evaluated and improved using customized traffic simulations. Accumulation-based traffic model using Petri Nets is introduced to serve for perimeter control, in which the intersections and road segments on the boundary of each pair of adjacent subregions are modeled as a boundary buffer. Both perimeter control and route guidance are integrated in the proposed control framework considering the queuing vehicles in the boundary buffers. Moreover, the effect of buffer storage capacity on network performances is tested, which is the essential for traffic engineers to design and implement management measures in practice.

Research on carbon emission measurement of Shanghai expressway under the vision of peaking carbon emissions

ABSTRACT Generally, the carbon emissions of road transportation have substantial negative effects on biological ecosystem and sustainable development. Thus, to achieve the strategy of peaking carbon emissions before 2030, research on measuring vehicle emissions in large metropolitan road networks is indispensable. With that in mind, a carbon emission macroscopic fundamental diagram model (CE-MFD) is presented to assess network-wide road emissions, and an indicator, carbon emission intensity (CEI), is quantified to capture the influence of traffic dynamics on emissions. Further, the results of CE-MFD show a positive correlation between road congestion and emissions. Based on the CEI indicator, the corresponding network-wide traffic controls are proposed for effectively reducing the emissions. In addition, the effects of electric vehicle (EV) penetration are explored. This study suggests that by 2030, even if the traffic becomes more congested, the CE-MFD of the urban expressway network will reach a peak with an EV penetration of 73%.

Schedule-Constrained Demand Management in Two-Region Urban Networks

Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.

Robust perimeter control with cordon queues and heterogeneous transfer flows

Accumulation-based Macroscopic Fundamental Diagram (MFD) model is widely employed to design perimeter control methods to improve traffic operation in urban networks. While the accumulation-based MFD assumes a low-scatter, non-linear relationship between region production and accumulation, the outflow relationship in formulating dynamics of multi-region networks requires simplifying assumptions. The existing perimeter control methods are grounded on accumulation-based MFD models where the number of transferring vehicles is approximated by the ratio of the instantaneous number of vehicles based on their destinations. Moreover, perimeter control may lead to more vehicles queuing at the region boundary (i.e. cordon queues) which add local impediments on traveling vehicles and impact the accuracy of well-defined MFDs. To address these shortcomings under time-varying conditions, this paper develops a robust perimeter control method based on the Sliding Mode Control to minimize total travel time in the entire network. To test the performance of the proposed control method, a trip-based MFD model is developed that accounts for cordon queues and various trip lengths of individual travelers. In this paper, two-region accumulation-based and trip-based MFD models are compared through numerical experiments. The results pinpoint the proposed robust perimeter control method can effectively alleviate congestion and improve network efficiency during traffic rush hours.

Resilient multivariable perimeter control of urban road networks under cyberattacks

The Macroscopic Fundamental Diagram (MFD) concept has become a very valuable tool for modeling the aggregated dynamic of large-scale urban traffic networks. This advance in traffic modeling has fueled the development of many urban traffic control (UTC) policies based on the MFD concept. In particular, perimeter control policies with the aim of maintaining a large-scale urban traffic network operating at its maximum capacity by manipulating the transfer flow of vehicles between adjacent homogeneous regions. In addition to achieve a satisfactory performance level, it is desirable that the control system would maintain a reliable operation under unanticipated events such as cyberattacks. It is important to note that modern UTC systems extensively rely on information technology infrastructures making them vulnerable to cyberattacks. Due to the occurrence of real-world cyberattacks affecting controlled physical systems in different fields, the threat of cyberattacks is becoming a serious and increasing concern for the proper operation of UTC. This paper presents a resilient multivariable control framework for large-scale urban traffic networks subject to several types of cyberattacks such as deception attacks and denial of service (DoS) attacks. Additionally, a feedforward–feedback control scheme combining a time-optimal controller with the resilient multivariable controller is also proposed. The aim of this feedforward–feedback controller is to steer the accumulations to their desired values after a large deviation. Finally, the performance of the proposed resilient controller is demonstrated by means of some realistic simulations of urban traffic networks, including stochastic errors in the traffic demands and in the MFD model, in addition to cyberattacks.

Traffic Speed Forecast in Adjacent Region between Highway and Urban Expressway: Based on MFD and GRU Model

Traffic congestion in the adjacent region between the highway and urban expressway is becoming more and more serious. This paper proposes a traffic speed forecast method based on the Macroscopic Fundamental Diagram (MFD) and Gated Recurrent Unit (GRU) model to provide the necessary traffic guidance information for travelers in this region. Firstly, considering that the road traffic speed is affected by the macroscopic traffic state, the adjacent region between the highway and expressway is divided into subareas based on the MFD. Secondly, the spatial-temporal correlation coefficient is proposed to measure the correlation between subareas. Then, the matrix of regional traffic speed data is constructed. Thirdly, the matrix is input into the GRU prediction model to get the predicted traffic speed. The proposed algorithm’s prediction performance is verified based on the GPS data collected from the adjacent region between Beijing Highways and Expressway.

Perimeter traffic control for single urban congested region with macroscopic fundamental diagram and boundary conditions

Macroscopic fundamental diagram (MFD) characterizes a unimodal and low-scatter relationship between traffic accumulation and trip completion rate for homogenous urban network, providing a new perspective for the development of regional congestion control strategies. This paper contributes to the state-of-the-art by proposing a perimeter traffic control strategy for single urban congested region with MFD model and boundary conditions. For an urban protected region, the MFD is introduced to capture network traffic dynamics and optimal capacity. When regional accumulation exceeds the optimal capacity, the restricted inflow distribution considering boundary condition constraints of real-time traffic flows and queue dynamics is used to formulate a perimeter traffic flow control strategy for adjusting traffic signal timing on the periphery of region. To proactively reduce the possibility of queue spillbacks at border links, the dynamic queue-dependent border gated points are also integrated into the proposed control method. The simulation experiment was performed using part of urban network in Jinan, China. The results demonstrate the proposed perimeter control method alleviates the issue of congestion and improves traffic performance in the protected region and at the boundaries.

Perimeter gating control and citywide dynamic user equilibrium: A macroscopic modeling framework

In recent years, several perimeter control strategies have been proposed for traffic management in cities. The common factor found in these works is the use of Macroscopic Fundamental Diagram (MFD) models to describe the dynamics of the network and optimize traffic inside the perimeter by manipulating perimeter inflows. Perimeter gating control strategies are attractive for traffic management inside the inner city. However, it inevitably creates a negative impact on the traffic outside. Most of the works in this research area have neglected vehicle re-routing outside the controlled perimeter, i.e., they do not consider demand elasticity to the central region resulting from gating and the related queues. In this paper, we propose a global modeling framework capable of assessing the effect of perimeter gating control (in terms of queue, emission, and total time spent) on the full network, considering demand elasticity resulting from Dynamic User Equilibrium (DUE). Classical Proportional-Integral (PI) control scheme is used to control traffic congestion inside a central region (reservoir). The modeling framework is comprised of: (i) an accumulation-based MFD model to reproduce traffic dynamics inside the reservoir, (ii) point-queue model to represent queuing vehicles on inbound links to the gating points, and (iii) a time-dependent travel time profile based on a steady-state approximation of MFD dynamics to characterize the alternative road network (bypass). DUE is then implemented, considering instantaneous predicted travel time. This determines how the demand to the inner region is affected by the gating. The functioning of the global system is assessed by total time spent and NOx and CO2 emissions inside the reservoir and for the full network. The presented simulation results show that the perimeter gating control helps to maintain congestion at the desired level with significant improvements in the total time spent and the mean speed in the network. However, it shows a slight increase in the queues. As expected, deviation to the bypass alternative is significant and should not be neglected when carrying out a global assessment of gating system performance.

Macroscopic Traffic Dynamics Under Fast-Varying Demand

Aggregated dynamic traffic models based on the network macroscopic fundamental diagram (MFD) have been founded on stationary or steady-state approximations. Theoretically, they are only qualified with slow-varying demand profiles as inputs. In practice, MFD models are often fed with fast-varying demand patterns classically observed during peak hours. This paper investigates the accuracy of existing MFD model outputs in such a case. It also provides a fresh look at hysteresis loops that may arise on MFD shapes and shows how they are connected to the demand profile. First derived are the exact solutions of the Lighthill, Whitham, and Richards (LWR) model for a simple but meaningful test case corresponding to the loading and the recovery of an arterial with a single bottleneck. The spatial integration of these solutions permits to derive the average flow- and outflow-MFD patterns. The average flow-MFD exhibits a clockwise hysteresis loop with higher flows during the network loading than during the recovery. The outflow MFD shows an opposite trend with a counterclockwise hysteresis loop. The detailed analysis of the LWR solution highlights that these patterns are fully driven by the congestion dynamics and different wave propagation during both periods. This complements existing studies that tend to explain hysteresis by heterogeneous network loading due to unbalanced flows at intersections. It should be noted that the size of the production-MFD hysteresis loop is influenced by the demand loading profile, which means that the MFD is more sensitive to the demand than initially expected. The second part of the paper is about the implications of these observations on the MFD simulation. The main conclusion is that the accumulation-based formulation captures properly the aggregate dynamics of the LWR model during saturation but not in free-flow. It should be calibrated with an average flow-MFD that does not account for the hysteresis pattern to properly estimate the outflow. On the contrary, the original formulation of the trip-based model is only valid in free-flow. During saturation, it should be patched to modify the outflow values. The best approach is a hybrid model that combines the trip-based model in free-flow and the accumulation-based model during saturation. Note that in free-flow the trip-based model is better fed by the average flow-MFD with hysteresis as it gives better estimation for the mean speed. Finally, some evidences are presented and tend to confirm that all the conclusions remain valid for more complex urban settings.

Regional Dynamic Traffic Assignment Framework for Macroscopic Fundamental Diagram Multi-regions Models

In this paper, we propose a regional dynamic traffic assignment framework for macroscopic fundamental diagram (MFD) models that explicitly accounts for trip length distributions. The proposed framework considers stochasticity on both the trip lengths and the regional mean speed. Consequently, we can define utility functions to assess the cost on alternatives, depending on which terms are considered stochastic. We propose a numerical resolution scheme based on Monte Carlo simulations and use the method of successive averages to solve the network equilibrium. Based on our test scenarios, we show that the variability of trip lengths inside the regions cannot be neglected. Moreover, it is also important to consider the stochasticity on the regional mean speeds to account for correlation between regional paths. We also discuss an implementation of the proposed dynamic traffic assignment framework on the sixth district of the Lyon network, where trip lengths are explicitly calculated. The traffic states are modeled by considering the accumulation-based MFD model. The results highlight the influence of the variability of trip lengths on the predicted traffic states.

Heterogeneous perimeter flow distributions and MFD-based traffic simulation

This paper investigates how network and traffic heterogeneities influence the accuracy of a simulation based on the Macroscopic Fundamental Diagram (MFD). To this end, the MFD modeling of a simple grid network is compared to the outputs of a mesoscopic kinematic wave model simulating traffic in the same network. Heterogeneous distributions of demand and supply at the boundaries are set to the local entries and exits of the mesoscopic model to generate heterogeneous network loadings. These boundary conditions challenge the MFD simulation, as significant discrepancies are observed between both modeling approaches in steady state. While the accurate calibration of the MFD and the average trip length can reduce the discrepancies for heterogeneous demand settings, no simple solution exists for heterogeneous supply settings, because they may drive very different internal congestion patterns in the network. We propose a correction method to adjust the MFD model outputs in such a case.

Demand management with limited cooperation among travellers: A doubly dynamic approach

This paper proposes a demand management method that optimizes the network performance by manipulating departure times within limited cooperation settings. The framework builds on the restricted flexibility of travellers’ departure times and exposes the impact of minimal changes in travellers’ schedule on the overall network performance. The test-bed (the plant) is based on the trip-based Macroscopic Fundamental Diagram (MFD) that relates the network space-mean speed to the vehicle accumulation. Travellers in the trip-based MFD model are characterized by their specific desired arrival times, heterogeneous trip lengths, and earliness and lateness scheduling penalties. The optimization problem, on the other hand, is formulated based on the accumulation-based MFD model that relates the network production (i.e. length-weighted aggregated link flows) to the vehicle accumulation. The accumulation-based MFD is an aggregated parsimonious model and does not consider individual traveller attributes, which enables it to remain analytically tractable and makes it suitable for optimization purposes. The proposed demand management method is also incorporated into a day-to-day evolution model where travellers adapt based on their historical departure times, experienced travel costs, and individual characteristics. The results highlight that the accumulation-based MFD can be efficiently used to develop travel demand management methods with realistic representation of traffic congestion within and across days.

Demand management with limited cooperation among travellers: A doubly dynamic approach

Abstract This paper proposes a demand management method that optimizes the network performance by manipulating departure times within limited cooperation settings. The framework builds on the restricted flexibility of travellers’ departure times and exposes the impact of minimal changes in travellers’ schedule on the overall network performance. The test-bed (the plant) is based on the trip-based Macroscopic Fundamental Diagram (MFD) that relates the network space-mean speed to the vehicle accumulation. Travellers in the trip-based MFD model are characterized by their specific desired arrival times, heterogeneous trip lengths, and earliness and lateness scheduling penalties. The optimization problem, on the other hand, is formulated based on the accumulation-based MFD model that relates the network production (i.e. length-weighted aggregated link flows) to the vehicle accumulation. The accumulation-based MFD is an aggregated parsimonious model and does not consider individual traveller attributes, which enables it to remain analytically tractable and makes it suitable for optimization purposes. The proposed demand management method is also incorporated into a day-to-day evolution model where travellers adapt based on their historical departure times, experienced travel costs, and individual characteristics. The results highlight that the accumulation-based MFD can be efficiently used to develop travel demand management methods with realistic representation of traffic congestion within and across days.

Economic Model Predictive Control of Large-Scale Urban Road Networks via Perimeter Control and Regional Route Guidance

Local traffic control schemes fall short of achieving coordination with other parts of the urban road network, whereas a centralized controller based on the detailed traffic models would suffer from excessive computational burden. State estimation for detailed traffic models with limited observations and unpredictability of individual driver behavior create additional complications in the applicability of these models for large-scale traffic control. This point toward the need for designing network-level controllers building on aggregated traffic models, which have recently attracted attention through the macroscopic fundamental diagram (MFD) of urban traffic. Under some conditions, the MFD provides a unimodal, low-scatter, and demand-insensitive relationship between vehicle accumulation and travel production inside an urban region. In this paper, we propose MFD-based economic model predictive control (MPC) schemes to improve mobility in heterogeneously congested large-scale urban road networks. For more realistic simulations of urban networks with route guidance actuation-based control, a new model with cyclic behavior prohibition is developed. This paper extends upon earlier works on perimeter control-based MPC schemes with MFD modeling by integrating route guidance type actuation, which distributes flows exiting a region over its neighboring regions. Performance of the proposed schemes is evaluated via simulations of congested scenarios with noise in demand estimation and measurement errors. Results show the possibility of substantial improvements in urban network performance, in terms of network delays and traveled distance, even for low levels of driver compliance to route guidance.

Dynamic macroscopic simulation of on-street parking search: A trip-based approach

This paper extends a trip-based aggregate dynamic traffic model to account for on-street parking search. The trip-based approach for a road network defined as a reservoir characterizes the internal traffic states by a macroscopic fundamental diagram (MFD) in speed while individualizing all vehicle travel distances. This paper first investigates distances to park for on-street parking based on real data in Lyon (France) and stochastic numerical experiments. An updated formulation compared to the existing literature is proposed for the relation between such distances and the parking occupancy. This new formulation is then incorporated into an event-based numerical scheme that solves the trip-based MFD model. The complete framework is able to account for different vehicle categories with respect to their parking strategies and to finely tune the related travel distances. Finally, the capabilities of the full framework are illustrated based on three different scenarios. The first two correspond to strategies with static and dynamic (reactive) switch of the demand from on- to off-street parking. While being very classical, they permit to demonstrate that the proposed model reacts as expected in such cases. The third scenario assesses the effect of a smart-parking technology that informs the users when a free parking spot is available on one of the downstream links at each intersection. In such a case, the model permits to estimate the benefit for the equipped users but also the impacts on all other vehicle categories. The three scenarios highlight that the proposed framework is versatile and can quickly provide a first assessment with a low calibration burden of different parking strategies or policies.

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.

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.