Stabilisation strategy for unstable transport systems under general evolutionary dynamics

Stability of equilibria in transport systems has been discussed for decades. Even in deterministic cases where stochasticity is ignored, stability is actually not a general property as a counterexample has been found in (within-day) dynamic traffic assignment problems. Instability can be a source of uncertainty of travel time. Although pricing may stabilise an unstable transport systems, it is not always acceptable to the public. This study aims to develop a pricing strategy that stabilises a transport system with a minimum toll. We show that this toll may, depending on the accuracy with which the no-toll equilibrium can be estimated, be very small. The proposed toll scheme ensures that the travel cost function including the toll is strictly monotone increasing. We then show that the proposed toll scheme stabilises a wide range of evolutionary dynamics and the amount of toll actually imposed on travellers can be very small. We also propose a heuristic procedure to minimise the amount of toll. It can be also recognised as a solution method to find an unstable equilibrium solution of a transport system. This suggests that we may be able to find an equilibrium solution of any transport problems including those of dynamic traffic assignment (DTA); in these cases, how to construct a solution algorithm that always converges to an equilibrium solution in general problems is still an open question.