Published online 3 June 1999 | Nature | doi:10.1038/news990603-1

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Traffic goes with the flow

Regular users of a motorway or highway soon get to know the problem spots. My heart always sinks at Junction 3 of the M4 motorway into London, beyond which a tailback is assured as three lanes converge into two. Basically,anything that perturbs the steady-state flow of traffic is likely to set up a jam when the traffic is heavy. But some perturbations are worse than others, and in the 24 May issue of Physical Review Letters, Dirk Helbing and colleagues from the Institute of Theoretical Physics at the University of Stuttgart, Germany, provide the ‘big picture’ of exactly how different kinds of disturbance will affect traffic flow.

They consider the effect of an ‘on-ramp’ - a conduit that feeds new traffic onto the highway at a certain point, like the entry junctions in motorways. But this perturbation can stand in for several others, such as an uphill gradient that causes some vehicles to slow, or a change in the number of lanes - anything, really, that reduces the through-flow on a given stretch of highway.

The researchers observe that disturbances of this sort can cause several different kinds of traffic jam, ranging from localized clusters of slower vehicles that move upstream (that is, the cluster appears to move ‘backwards’ as the vehicles themselves move forwards) over time; to ‘stop-and-go’ waves of blockages; to perhaps the most depressing of all - a long block of slowly moving traffic called ‘synchronized’ congested flow.

All of this falls out from a simple computer model of the traffic flow, in which each vehicle is represented by a particle that travels along the highway. Each driver wants to achieve a certain desired ‘cruise’ speed, but adjusts his or her actual speed to maintain a safe distance from the vehicle in front. The model contains a range of desired speeds and driver estimates of safe distances, just as a trip down any busy highway reveals differing perceptions of what is desirable and safe. The progress of each vehicle is therefore sensitive to what is happening ahead, and downstream effects can be transmitted back upstream as vehicles successively adjust their speeds according to what is happening in front of them.

Helbing and colleagues show that changes in just two model parameters are sufficient to bring about a variety of different flow states: the density of traffic inflow onto the highway and the density of additional inflow at the entry ramp. If both of these are small, the traffic flows freely, which means that each of the drivers can more or less do as they please. But as the traffic either on the main highway or on the ramp gets heavier, there is an abrupt change at some critical density to a cluster of localized congestion around the ramp’s entry point. Further increases cause switches to such well-known phenomena as stop-and-go flow, that exhausting state in which one is constantly accelerating and braking, or to moving clusters of slow traffic, like shock waves that pass upstream from the entry point. If both the highway and ramp inflows are large enough, everyone behind the ramp is slowed to a crawl.

The researchers suggest that this kind of mapping-out of the different flow regimes might be useful for highway design or for traffic control. For example, regulating the inflow onto the start of the highway might help to avoid snarl-ups downstream. And because some properties of the flow (such as the outflow from a tailback) depend on the dimensions of the highway (such as the length of the entry ramp), the predictions might guide civil engineers to the best design.