21 December 2011
Reducing traffic congestion on our roads is a real possibility with new research supported by an ARC Linkage Grant suggesting that mathematics might hold the answer to our traffic woes.
Dr Tim Garoni from the School of Mathematical Sciences at Monash University teamed up with fellow mathematician Associate Professor Jan de Gier from the University of Melbourne in 2008, to develop a new model of traffic flow on road networks.
Although the current traffic signal system used in Melbourne is adaptive to traffic conditions, it may be possible to use it in ways not previously considered,” Dr Garoni said.
“What we’ve been testing is the possibility that improvements could be obtained if we had more vehicle detectors on our roads, or if we used the existing vehicle detectors so that more information could be gathered, to inform signal decisions in a more intelligent way. These studies are relevant not just to private vehicles, but also to public transport such as buses and trams.”
Critically, the model provides a view of the interactive effects from making changes in one part of the road network, and seeing how it affects other parts, and the performance of the overall network.
The project, performed in collaboration with VicRoads, started through the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). The team was joined by Dr Joyce (Lele) Zhang, MASCOS, in April 2011.
The trio have designed a mathematical model of urban traffic flow, which can be used to study road networks comprising hundreds of intersections. This means that they can quickly and easily test different traffic light systems and analyse their impact on traffic conditions, as well as simulate issues such as accidents and assess how traffic conditions respond to such scenarios.
Dr Garoni and Dr de Gier are specialists in an area of mathematical physics called ‘statistical mechanics’, which applies methods from probability theory to try to understand complex physical systems.
“The main idea behind our approach was to model road networks in the same way that physicists model other large complex systems. It may not seem obvious, but traffic flow in networks has a lot of similarities to other more fundamental physics systems,” Dr Garoni said.
“In a mathematical sense, there is quite a lot of similarity between the phase transition that turns water into ice and the phase transition that occurs when a road network changes from being freely flowing to being gridlocked.”
Working with traffic has been an opportunity for Dr Garoni and Dr de Gier to apply their work to a real-world problem.
“Urban traffic congestion is a major social, economic and environmental problem. Many would think the most obvious way to think of increasing the capacity of road networks is to build new roads,” Dr Garoni said.
“However, if we can design novel algorithms for running traffic signals more efficiently, then we can basically reduce traffic congestion for free, because it doesn’t involve building new infrastructure.”