Flow formula

A mathematical framework for forecasting traffic flow on motorways to help manage congestion is being developed at

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and the Knowledge Transfer Network for Industrial Mathematics are partners in the project, which aims to create a system that can use real-time information to predict traffic jams.

The CBI says congestion costs UK businesses up to £20bn a year and road traffic is forecast to rise 30 per cent between 2000 and 2015.

'Congestion is here to stay and it's going to get worse,' said Dr Eddie Wilson, principal investigator. 'But we should at least give drivers some idea of how long their journey will take, by closing the gap between telling them what the speeds are at the moment and what the speed will be in a few hours time.'

'The big problem is stop-and-go patterns. You drive along and everything seems to be fine, then you grind to a halt for no apparent reason, before accelerating away. The resulting queues are like waves, which move upstream against the traffic flow, and this is why you don't usually see what caused them because it may be many kilometres downstream.

'To do forecasting, we need a better understanding of how the waves develop and propagate, and to do this we are looking at the microscopic level — individual cars — and the macroscopic level, where we think of traffic as being a bit like a compressible gas.'

The project will use existing data collected from the Motorway Incident Detection and Automatic Signalling (Midas) system. This uses inductance loops embedded in the road surface, usually about 500m apart, to measure the speed, volume and composition of traffic. The information is sent back to a control centre where an operator sets temporary speed limits and variable message warning signs.

The Bristol team is analysing this data to build new mathematical models of traffic and, in the long term, these models might be used by an automatic traffic control system.

'You can see that compressible gas models are fundamentally wrong if you look at the Midas data,' said Wilson.

'However, if you are using inductance loops that are close enough together, you can identify the driving patterns of individual vehicles and, with such data from the millions of vehicles on the motorway, you can build up really quite detailed models of driver behaviour.'

'There is a big argument in the scientific community about what sparks off stop-and-go waves. One camp says they are caused by large amplitude random events. The other school says that one shouldn't look for causes, since they are just an emergent property of an unstable, non-linear system where, at certain densities, something as small as a single bad lane change will magnify and cause a traffic jam. Using our individual vehicle data, we should be able to resolve this argument definitively in the next couple of years.'

Wilson said in future it will be possible to tap into a web page at home for advice on how long a planned journey will take. 'We want to do traffic forecasting rather like we do weather forecasting already,' he said. 'The big difference is that in traffic you always have to take account of the complexity of human behaviour whereas in weather the underlying physics is completely understood.'