A stable dynamic pricing scheme is essential to guarantee the desired performance of high-occupancy-toll (HOT) lanes, where single-occupancy vehicles (SOVs) can pay a price to use the HOT lanes. But existing methods apply to either only one type of lane-choice models with unknown parameters or different types of lane-choice models but with known parameters. In this study we present a new dynamic pricing scheme that is stable and applies to different types of lane-choice models with unknown parameters.

There are two operational objectives for operating HOT lanes: (i) to maintain the free-flow condition to guarantee the travel time reliability; and (ii) to maximize the HOT lanes’ throughput to minimize the system’s total delay. The traffic dynamics on both HOT and general purpose (GP) lanes are described by point queue models, where the queueing times are determined by the demands and capacities. We consider three types of lane-choice models: the multinomial logit model when SOVs share the same value of time, the vehicle-based user equilibrium model when SOVs’ values of time are heterogeneous and follow a distribution, and a general lane-choice model. We demonstrate that the second objective is approximately equivalent to the social welfare optimization principle for the logit model. Observing that the dynamic price and the excess queueing time on the GP lanes are linearly correlated in all the lane-choice models, we propose a feedback control method to determine the dynamic prices based on two integral controllers. We further present a method to estimate the parameters of a lane-choice model once its type is known. Analytically we prove that the equilibrium state of the closed-loop system with constant demand patterns is ideal, since the two objectives are achieved in it, and that it is asymptotically stable. With numerical examples we verify the effectiveness of the solution method.

稳定的动态定价方案对于确保高占用率（HOT）车道的理想性能至关重要，在这种情况下，单人占用车辆（SOV）可以为使用HOT车道付费。但是，现有方法仅适用于参数未知的一种类型的车道选择模型，或者适用于参数已知的不同类型的车道选择模型。在这项研究中，我们提出了一种稳定的新动态定价方案，该方案适用于参数未知的不同类型的车道选择模型。

运行HOT车道有两个运行目标：（i）保持自由流动状态，以确保行驶时间的可靠性；（ii）最大化HOT通道的吞吐量，以最小化系统的总延迟。HOT通道和通用（GP）通道上的流量动态均由点队列模型描述，其中排队时间由需求和容量决定。我们考虑三种类型的车道选择模型：当SOV共享相同的时间值时的多项式logit模型；当SOV的时间值是异构且遵循分布时的基于车辆的用户平衡模型；以及一般的车道选择模型。我们证明了第二个目标大约等于logit模型的社会福利优化原则。考虑到在所有车道选择模型中GP车道上的动态价格和超额排队时间是线性相关的，我们提出了一种基于两个积分控制器的动态确定价格的反馈控制方法。一旦知道了车道选择模型的类型，我们将进一步提出一种估计其参数的方法。通过分析，我们证明了具有恒定需求模式的闭环系统的平衡状态是理想的，因为在其中达到了两个目标，并且它是渐近稳定的。通过数值例子，我们验证了求解方法的有效性。一旦知道了车道选择模型的类型，我们将进一步提出一种估计其参数的方法。通过分析，我们证明了具有恒定需求模式的闭环系统的平衡状态是理想的，因为在其中达到了两个目标，并且它是渐近稳定的。通过数值例子，我们验证了求解方法的有效性。一旦知道了车道选择模型的类型，我们将进一步提出一种估计其参数的方法。通过分析，我们证明了具有恒定需求模式的闭环系统的平衡状态是理想的，因为在其中达到了两个目标，并且它是渐近稳定的。通过数值例子，我们验证了求解方法的有效性。