Macroscopic Fundamental Diagram: measuring flow and density

Macroscopic Fundamental Diagram
Zhimai Zhang on Unsplash

This research presents a novel, network-wide approach to identify critical links and estimate average traffic flow and density. The proposed model estimates the Macroscopic Fundamental Diagram (MFD) using flow and density measurements from those critical links, which constitute only a small subset of all the links in the network.

The MFD, which exhibits the relationship between average flow and average density of an urban network, is a promising framework for monitoring and controlling urban traffic networks.

Given that monitoring resources (e.g. loop detectors, probe vehicle data, etc.) are limited in real-world networks, acquiring adequate data to estimate an MFD is of crucial importance.

Applying the same method to identify the critical links, the second aim of this research is to combine the loop detector and probe vehicle data, and use this simultaneously to estimate the MFD.

Furthermore, it may be possible to examine new traffic data sources (i.e. vehicle spacing data) in MFD estimation alongside with traditional traffic data.


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Project background

Traffic congestion has been increasing due to population growth and rapid development of metropolitan areas. It has been proven that increasing the supply (e.g. constructing new infrastructure) will not necessarily alleviate traffic congestion.

Additionally, urban space is often limited and does not allow more roadway infrastructure to be built around the cities. Therefore, the efficient use of existing infrastructures seems to be the only way forward to confront increasing urban traffic congestion. Traffic control methods such as road pricing, adaptive signal controls, etc. are essential to alleviate traffic congestion in urban areas and improve mobility at the network level. The first stage towards this final goal is to properly monitor or estimate traffic dynamics.

Large-scale traffic control remains a big challenge due to the complexity and unpredictability of transportation networks. Current traffic control strategies focus on individual intersections or arterial corridors, and they are considered less efficient in over-saturated traffic conditions, as the modelling of traffic underlying these strategies breaks down under such conditions. Given accurate inputs, detailed traffic models (e.g. microscopic simulation models) can provide substantial traffic predictions at the link level.

However, network management based on these models can be quite inefficient due to:

  1. Exhaustive number of required inputs (e.g. detailed OD tables, signal settings, etc.)
  2. Inaccuracy of behavioural models (e.g. car following, route choice models, etc.)
  3. Chaotic behaviour of traffic in over-saturated networks. Hence, efficient management of transportation systems requires parsimonious modelling of traffic. Therefore, the Macroscopic Fundamental Diagram (MFD) is introduced to simplify the complexity of micro-modelling by capturing the average traffic flow dynamics in a large urban network. MFD is a useful tool for designing and implementing monitoring and management strategies.

A non-biased MFD arises only when all the vehicle trajectories are available. However, in practice, for large urban networks, it is unlikely that such data is available. Therefore, researchers have developed mathematical approaches to identify the most important traffic sensors to collect traffic data. Given that most of the previous studies require a priori knowledge of the ground-truth MFD, our aim is to develop a method for estimating the MFD which does not require such information. We use the ground-truth data only to evaluate our estimations.

The proposed method is focusing on finding a subset of links (i.e., critical links) that we assume they are the links that represent average traffic conditions in the network. Therefore, we aim at identifying the different traffic patterns and selecting the critical links out of important patterns. Critical links are the links where loop detectors are supposed to be installed to estimate the MFD and minimise the estimation error between the MFD that is estimated by limited measurements and the true MFD which is estimated from all the network links measurements.

Project objectives

1. Address limited budget constraints

Usually in large-scale urban networks, collecting adequate traffic data is not straightforward since our budget is limited. For instance, it is not efficient to install loop detectors on all the links in the network as they are expensive to implement and maintain. Therefore, we are aiming to find the most important links to install loop detectors on.

2. Incorporate disparate data sources

In the first part of this study, we assume that only loop detector data is available. In the second part; however, we assume that we have access to another source of traffic data (e.g. probe vehicle GPS data). The goal is to combine these two sources of data to estimate a more accurate MFD.

3. Exploit new vehicle technologies

While in the first and second parts of this study we exploit conventional traffic data sources (loop detector and probe vehicle), in this part we are aiming to take advantage of new vehicle technologies and the particular data that they can provide.

For instance, Driver Assistance Systems (DAS) has been becoming more popular. Such technologies can refer to Adaptive Cruise Control (ACC) which is a substitution for conventional cruise control. This new technology controls both speed of the ACC-equipped vehicle and its distance from the leading vehicle. Hence, spacing and headway data are provided using this technology which can be later applied to measure flow and density of a link, and eventually estimate the MFD.

Project background

Traffic congestion is the result of traffic demand exceeding the roadway supply capacity, which could be identified by low speeds, longer travel times and lengthy vehicle queues. The economic and population growth, enhancement in communal needs and lifestyles are major factors which contribute to high travel demands and traffic congestion.

Even though economic activities influence the traffic congestion, the growth and stability of an economy are at the mercy of traffic congestion. Department of Infrastructure and Regional Development identified that the congestion cost of Australia was $16.5 billion in 2015 and expected to reach between $ 27.7 -37.3 billion by 2030 if major policy changes were not introduced, which will be a higher burden for the Australian economy. Further, Australian Automobile Association finds that major cities in Australia such as Sydney, Melbourne, and Brisbane are facing rapid population booms due to urban sprawl, which may result to increase congestion and may cause traffic gridlock in the near future unless decisive action is taken.

The introduction of novel traffic monitoring and management techniques are an attractive avenue to manage the traffic congestion as building new infrastructure is not a justifiable solution. Demand management strategies and traffic control strategies are the broader categories of methods to reduce traffic congestion found in the literature. Although there are numerous traffic control strategies in literature, less work has been focused on demand management strategies.

After a careful review of the existing literature, we break down traffic demand management strategies into two categories:

  1. Strategies focused on reducing demand or shifting the travellers to other transport modes such as public transport, ridesharing, parking restrictions etc.
  2. The strategies focused on redistribution of demand over space and time such as route guidance, congestion pricing, peak-hour pricing, flexible working hours, etc.

We see that a vast number of studies were focused on spatial redistribution of demand and less attention was given to temporal redistribution of demand although such strategies have a very high potential in mitigating traffic congestion. At the same time, we see that the successful implementation of any demand management strategy often relies on accurate demand estimates. Nevertheless, existing demand estimation techniques face challenges in scalability to large scale networks.

Given the above research gaps, this study will focus on developing demand management and demand estimation techniques for large scale traffic networks. Our study will build upon macroscopic traffic models based on the macroscopic fundamental diagram (MFD) to understand the complex interaction of large-scale traffic networks. MFD enables analytically tractable approaches for complex problems in demand management and estimation.

The aim of this study is set to develop demand management and demand estimation tools for large-scale traffic networks. Two objectives are accomplished in this project where we focus on developing demand management and demand estimation strategies for large-scale traffic networks by incorporating the MFD-based traffic dynamics.

A thorough review of the literature shows that there are no promising methods to demand management and demand estimation in large scale traffic networks. The existing traffic demand management (TDM) strategies often face incompliance problems as they require substantial schedule changes. Hence, there is a need for developing TDM strategies which target to achieve system optimum conditions by limited schedule changes to travellers.

On the other hand, there exist demand uncertainties due to technology penetration of advanced traveller information systems and incompliance of travellers to TDM strategies. The existing demand estimation methods suffer challenges in scalability to large-scale networks and reliability in estimates. Thus, there is a need to develop computationally feasible methods to estimate demand using analytically tractable macroscopic traffic models.

Project objectives

Two objectives are formulated to bridge the research gap.

Objective 1

Develop a method to manage the demand in a large-scale traffic network by limited schedule changes.

Objective 2

Develop a robust demand estimation method applicable to large-scale and complex traffic networks

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