Stability of equilibria in transport systems has been discussed for decades. Even in deterministic cases, where stochasticity is ignored, stability is not a general property; a counterexample has been found in (within-day) dynamic traffic assignment problems. Instability can be a source of uncertainty of travel time and although pricing may stabilise an unstable transport system, pricing is not always acceptable to the public. This study aims to develop a pricing strategy that stabilises a transport system with minimum tolls. We show that with our stabilising pricing system tolls are bounded above and converge to zero when the error in estimation of a no-toll equilibrium converges to zero. We then show that the proposed toll scheme stabilises a wide range of evolutionary dynamics. We also propose a heuristic procedure to minimise the toll level. The procedure can also be viewed as a method of finding a possibly unstable equilibrium solution of a transport system. This suggests that, while we have not provided a rigorous proof, we may be able to find an equilibrium solution of any transport problem including problems which arise in dynamic traffic assignment (DTA); in these DTA cases, how to construct a solution algorithm that always converges to an equilibrium solution is still an open question. The methods proposed here will be extended so that they apply in more realistic behavioural settings in future work.

在运输系统中平衡的稳定性已经讨论了数十年。即使在确定性的情况下，随机性被忽略，稳定性也不是普遍的属性。在（一日内）动态流量分配问题中发现了一个反例。不稳定可能是旅行时间不确定性的来源，尽管定价可以稳定不稳定的运输系统，但定价并不总是为公众所接受。这项研究旨在制定一种定价策略，以最小的通行费稳定运输系统。我们证明，使用我们的稳定定价系统，当免费通行费均衡估算的误差收敛到零时，通行费会限制在上方并收敛到零。然后，我们表明拟议的通行费方案稳定了广泛的演化动力学。我们还提出了一种启发式程序，以将通行费水平降至最低。该过程也可以看作是找到运输系统可能不稳定的平衡解的方法。这表明，尽管我们没有提供严格的证据，但我们也许能够找到任何运输问题的均衡解决方案，包括动态交通分配（DTA）中出现的问题；在这些DTA情况下，如何构建始终收敛到平衡解的解算法仍然是一个悬而未决的问题。