Simulating The Effect of Dynamic Tolling on Traffic Flows
John Swanson, Steer Davies Gleave
A simulation of dynamic tolling and traffic flows, showing how easily instability can occur, but showing how this can be overcome. It implies that road user charging on networks could be very risky.
This paper describes work carried out to investigate the effect of dynamic tolling on traffic flows, using Managed Lanes as an example. These are highway lanes that offer restricted access, in this case by paying a toll, in return for reduced congestion and/or more reliable speeds and drive times.
The project tested a fully dynamic tolling system in which traffic speeds are constantly monitored, and tolls adjusted dynamically to moderate the traffic flow and maintain target speeds.
A simulation was constructed to model this system. It assumed traffic arrives at a toll booth where current tolls are clearly advertised, and drivers can make a decision: either to pay and drive in an uncongested lane or not to pay but travel by an alternative, slower, route. The tolled lane was assumed to be 10km long. The simulation could test how the provision of data to drivers affected results, either showing only the toll, or the toll and the time saving that would be achieved.
A series of tests were made to ensure that the simulation was performing realistically. It was then used to test a number of scenarios under different assumptions about the traffic flows arriving at the booth, the capacity of the booth, the target speeds, and the algorithm used for setting the entry toll.
A persistent result, under nearly every policy, was that the system quickly becomes unstable, falling into a pattern of oscillation. This happens even if the vehicle arrival rate is constant. The reason is that once the tolls have been increased and the speeds brought back up to their target, it is not obvious when to reduce them again. In fact with an essentially inward-looking system of the type described here, meaning that the only information used to adjust the toll is the state of flow on the tolled lane, this oscillation is virtually guaranteed.
The problem can be fixed by using additional ‘external’ information when setting the tolls. The model showed that if tolls are set in anticipation of increases – or decreases - in the flows, the problem disappears. In other words, the oscillation stops when the tolls are set using forecasts of vehicle arrival rates, perhaps by monitoring flows upstream. The simplest method is to use a semi-dynamic system, in which tolls are set using predetermined information about flows through the day.
This result is of some importance. It suggests that using dynamic tolling to regulate traffic conditions could be very dangerous unless the algorithms are very carefully designed to avoid their inherent instability. Purely reactive algorithms are to be avoided. This is likely to apply also to road user charging more generally.
An earlier version of this abstract was presented and accepted for a previous ETC Conference, but was withdrawn due to illness.
Association for European Transport