Congestion pricing has long been considered an efficient tool for tackling road traffic congestion, but tolls are generally unpopular. Interest is growing in tradable permits as an alternative. Tolls and tradable permits are interchangeable if travel conditions are unchanging, but not if conditions vary and tolls and permit quantities are inflexible and cannot be adapted to current conditions. We compare the allocative efficiency of tolls and tradable permits on a bimodal network under uncertainty. Road links are congestion prone and public transit may be crowded. Road traffic entering a cordon area around the downtown is controlled using either a toll or a tradable permit. Two groups of travelers can drive or take transit. Group 1 travels downtown, and if it drives it must either pay the toll or use a permit. Group 2 travels to a suburb, and can avoid the cordon by taking a bypass. All demand and cost parameters of the model can vary, either systematically or irregularly. Each parameter combination constitutes a state. Travelers learn the state in advance, and adapt their mode and route choices accordingly. A planner minimizes expected total travel costs by either setting the level of the toll or choosing the quota of permits to distribute. Two cases are considered. In the first, the toll and quota are flexible and can be adjusted to daily travel conditions. In the second, the instruments are inflexible and must be set at the same level regardless of the state. If travelers have identical preferences, the optimal flexible toll is invariant to the numbers of travelers in each group and the capacity of the link entering the cordon. The toll is robust in the sense that inflexibility causes no welfare loss if these parameters vary. By contrast, the quota is not robust.

We derive a general rule for ranking the efficiency of a fixed toll and fixed quota. We then explore a numerical example. In most instances, the fixed toll outperforms the fixed quota by a significant margin although the quota can do better in some states. We also compare the welfare-distributional effects of tolls and permits, and find that suburban travelers fare better than downtown travelers from both forms of regulation.

长期以来，拥堵收费一直被认为是解决道路交通拥堵的有效工具，但通行费通常不受欢迎。作为替代品，人们对可交易许可证的兴趣正在增长。如果交通条件不变，通行费和可交易许可证可以互换，但如果条件发生变化，通行费和许可证数量不灵活且无法适应当前条件，则不能互换。我们比较了不确定条件下双峰网络的通行费和可交易许可证的分配效率。道路连接容易拥堵，公共交通可能很拥挤。进入市中心周围警戒线区域的道路交通使用收费或可交易许可证进行控制。两组旅客可以自驾或乘坐公交。第 1 组在市中心行驶，如果它开车，则必须支付通行费或使用许可证。第 2 组前往郊区，并且可以绕道避开警戒线。模型的所有需求和成本参数都可以系统地或不规则地变化。每个参数组合构成一个状态。旅行者提前了解状态，并相应地调整他们的模式和路线选择。规划者通过设置通行费水平或选择要分配的许可配额来最小化预期的总旅行成本。考虑两种情况。第一，通行费和配额灵活，可以根据日常出行情况进行调整。第二，仪器不灵活，无论处于何种状态，都必须设置在同一水平面上。如果旅行者有相同的偏好，则最佳灵活通行费不会随每组中的旅行者数量和进入警戒线的链路容量而变化。从某种意义上说，如果这些参数发生变化，不灵活不会造成福利损失，那么代价是稳健的。相比之下，配额并不稳健。

我们推导出固定通行费和固定配额效率排名的一般规则。然后我们探索一个数值示例。在大多数情况下，固定通行费的表现明显优于固定配额，尽管配额在某些州可能做得更好。我们还比较了通行费和通行证的福利分配效应，发现郊区旅客在这两种监管形式下的表现都优于市区旅客。