Mathematics of
Transportation Networks

19 - 21 June, 2013

This workshop will bring together researchers from multiple academic disciplines, including mathematics, engineering and computer science, as well as stakeholders from government and industry, to discuss the application of mathematics to the design and operation of transportation networks. Understanding the inherently multi-scale nature of such networks will be a central focus. Topics covered will include traffic flow theory and simulation, optimisation and control, data mining, intelligent transport systems, logistics, and infrastructure planning.

Public Lecture

• Prof Mark Wallace, Monash University and Opturion

Cheap Solutions to The Transport Problem

The term “rush hour” is out-of-date: morning traffic congestion in Melbourne lasts from 6:30 until 9:30am. ...

The term “rush hour” is out-of-date: morning traffic congestion in Melbourne lasts from 6:30 until 9:30am. The annual cost of congestion to Victoria is estimated to rise from $3 billion to $6 billion by 2020. It is estimated that more than 20,000 trucks move through Melbourne's inner west each day, but the East-West Link project - an 18-kilometre inner urban road connecting the Eastern Freeway and the Western Ring Road - would help reduce this traffic. It will cost $13 billion (so far $15M for writing the business case). Eddington’s 2008 rail and road recommendations cost $18 billion.

Mathematicians in Melbourne are exploring another way to keep traffic flowing on the existing roads and rails. Mathematical control of new traffic lights at the M1 freeway entrances, has already increased the M1 capacity by 3000 vehicles per hour. This is merely a small improvement compared with the traffic revolution currently taking place.

The new generation of vehicle communication systems will enable vehicles to drive faster and closer together with lower risk. This could increase traffic throughput by a factor of four. A broader vision is to schedule all transport. Suppose you notified the transport system each time you started a journey, then it could schedule your road use to balance out traffic across the road system and minimise congestion. Simulations show that even with a small percentage of drivers using the system, users could reach their destination in half the time.

The majority of freight in Melbourne goes on small vans. Just by introducing a small number of transfer points, so that vans are used more efficiently, simulations indicate an immediate 25% reduction in van road usage. Public transport take-up in Melbourne is limited because buses are too few and far between, so mathematicians are developing adaptable bus schemes using communication devices and scheduling algorithms to make sure there’s a bus where and when you need it.

Mathematics will make it possible to solve Melbourne’s transport problem without spending tens of billions of dollars on new infrastructure. The costs will be closer to just writing the business case for the infrastructure investment!

Keynote Speakers

• Prof Serge Hoogendoorn, Delft University of Technology

A primer in traffic flow modeling and management

Traffic flow theory finds its roots in the work of Bruce Greenshields, who in 1934 published his seminar paper on the so-called fundamental diagram, ...

Traffic flow theory finds its roots in the work of Bruce Greenshields, who in 1934 published his seminar paper on the so-called fundamental diagram, a relation between traffic density and volume, which turned out to be pivotal in modeling traffic flows.
Since then, the field has been infused by contributions from various fields, such as physics, psychology, engineering, informatics, and mathematics, showing its truly multidisciplinary nature.
This talk deals with quantitative methods in the modeling and control of traffic flows in networks, ranging from predicting freeway traffic operations, to the management of huge crowds during the Hajj.
In particular, the talk focuses on the various fascinating phenomena that are observed in traffic flow (self-organization, capacity drop, wide moving jams), the various approaches to the mathematical modeling of these phenomena (microscopic models, continuum models), and the use of these models for state estimation, prediction and control. In doing so, the lecture will pinpoint the key mathematical challenges that either have been or need to be resolved. This will be done by showing several theoretical examples and practical applications in road traffic and crowd management, and evacuation planning.

• Prof Travis Waller, The University of New South Wales

Transport network equilibrium models incorporating adaptivity and volatility

The goal of this talk is to summarize certain classes of network modelling tools in the transport domain and provide an insight into emerging techniques. ...

The goal of this talk is to summarize certain classes of network modelling tools in the transport domain and provide an insight into emerging techniques. To begin, a broad summary of multiple recent and ongoing research topics conducted by the speaker in the transport network modelling sub-field will be provided including dynamic network assignment, mesoscopic traffic modelling and dynamic network routing. Critical domain considerations and applicability will be noted as they relate to the underlying methodological development. Then, recent research developments related to stochastic routing and adaptive equilibria will be presented in the context of real-time traffic behaviour in the presence of information. New algorithms for the online shortest path problem form the core methodological contribution for the new models as well as a resulting set of convex mathematical programs which provide novel insights not previously obtainable with previous modelling tools.

• Prof Pascal van Hentenryck, NICTA

Optimization over Transportation Networks

This talk reviews how to apply modern optimization techniques to a number of applications in disaster management and large-scale supply chains. ...

This talk reviews how to apply modern optimization techniques to a number of applications in disaster management and large-scale supply chains. Their impact on the practice in field is also discussed.

• Dr Jürg von Känel, IBM

Large scale traffic modelling from city planning to emergency evacuations

As more and more people life in cities, planning for the handling of increasing traffic volumes becomes a crucial capability. ...

As more and more people live in cities, planning for the handling of increasing traffic volumes becomes a crucial capability. Determining whether or not a new road will deliver the desired relieve to congestion is one of the crucial questions in that space. Using a large scale, agent based traffic simulator allows to explore the outcomes of such changes. We have such a simulator, capable of simulating millions of cars and their drivers behaviours. For regular city planning purposes - assumptions such as most people are driving from an origin with a given destination in mind are common, and people only make detours if they have to - but still want to reach their given destination. This simulator was built by our Tokyo Research lab with city planning in mind and has been used for Tokyo, Hiroshima, Beijing, Rio and some other city planning. With appropriate adaptations such a simulator can also be applied for emergency evacuations. The work done in the traffic modelling area fits into IBM Research's broader endeavour of building a system of systems which combines different models, data, and algorithms for faster and more efficient decision support. This goal aligns with the Australian Disaster Management Platform (ADMP), a collaboration between the University of Melbourne, NICTA, and IBM Research Australia.

• Prof Katsuhiro Nishinari, The University of Tokyo

Jamology - traffic jams of self-driven particles

Jamming phenomena are seen in various transportation system including cars, buses, pedestrians, ants and molecular motors, which are considered as “self-driven particles”. ...

Jamming phenomena are seen in various transportation system including cars, buses, pedestrians, ants and molecular motors, which are considered as “self-driven particles”. There is universality of jam formation among various sorts of flows. We recently call this interdisciplinary research on jamming of self-driven particles as “jamology”. This is based on mathematics and theoretical physics, and includes engineering applications as well. In the talk, starting from the backgroud of this research, a simple mathematical model, called the asymmetric simple exclusion process (ASEP), is introduced as basis of all kinds of traffic flow. Applications to the vehicle and pedestrian flow are discussed based on extended models of the ASEP. Comparisons between theory and our various experiments are also given with jam solution ideas.

• Dr Majid Sarvi, Monash University

A quantitative measure for the lifetime analysis of transport networks

A new measure is introduced to analyse and evaluate the performance of transport networks. It is a measure of growth and shift in traffic load that a network can sustain. ...

A new measure is introduced to analyse and evaluate the performance of transport networks. It is a measure of growth and shift in traffic load that a network can sustain. The traffic growths considered are linear traffic growth and traffic shift in the network towards more attractive traffic zones. The benchmark for network performance/reliability assessment is based on a metric such as travel time, level of service or amount of transport emission. The proposed measure is applied to a large network to demonstrate its scalability and capability in identifying the weakest elements (links) in the network. Various strategies such as road pricing and capacity enhancement were examined and the results were analysed to demonstrate the capability of the proposed methodology. It is believed that this measure is useful both in the planning phase of new transport networks and in the performance and reliability analysis of the existing networks.

Sponsors

		Monash Academy for Cross & Interdisciplinary Mathematical Applications (MAXIMA)
		Melbourne Advanced Transportation Research Initiative (MATRIx)
		Australian Mathematical Sciences Institute (AMSI) This event is sponsored by the Australian Mathematical Sciences Institute (AMSI). AMSI allocates a travel allowance annually to each of its member universities. Students or early career researchers from AMSI member universities without access to a suitable research grant or other source of funding may apply to their Head of Mathematical Sciences for subsidy of travel, accommodation and registration fee for out of the departmental travel allowance.