Designing and Testing Effective Algorithms for Dynamic Tolling on Highways
J Swanson, J Wang, Steer Davies Gleave, UK
Shows how dynamic tolling for highays, where tolls are varied in response to congestion, can be highly unstable. This instability is a structural property of such tolling system. An alternative is proposed and shown to be solve the problem.
Dynamic tolling is increasingly being proposed and used to manage flows on toll and HOV lanes in North America. The idea is simple: under dynamic tolling, traffic flows and speeds are constantly monitored, and if they fall below pre-set standards the tolls are raised to reduce the traffic in-flows. This reduces congestion and maintains the desired level of service (speeds and flows) on the toll road.
The question is: how should the tolls be varied? This paper will show that dynamic tolling as described above is potentially very dangerous. Viewed as a system, it is an example of a second order control system that is inherently unstable and prone to oscillation. This is a structural property of such systems, and leaves them vulnerable to a situation where the tolls cycle up and down, constantly chasing the changes in traffic levels.
The paper will demonstrate the use of a dynamic systems-based model showing how and why this can happen. The model simulates drivers choosing between a toll road and an alternative route. Various algorithms for setting the tolls will be demonstrated, with changes to the information provided to the drivers at the point where they make a choice, and to the conditions of the alternative route. The problem persists, because it is inherent in such a system.
The paper will then consider how to design a dynamic tolling algorithm that is stable. This is possible, but the key is to make the algorithm predictive, using the tolls to prevent the congestion problem before it happens, not to fix it after it occurs. Technically this can be done with a first order system, one that will not oscillate.
The paper will end with consideration of some of the wider implications of this work, both for control systems of this type and for the models often used to design them.
Association for European Transport