Congestion pricing has become an effective instrument for traffic demand management on road networks. This paper proposes an optimal control approach for congestion pricing for within day timescale that incorporates demand uncertainty and elasticity. Real time availability of the traffic conditions' information to the travelers and traffic managers allows periodic update of road pricing. We formulate the problem as an infinite-horizon countable-state Markov decision process (MDP) and analyze the problem to see if it satisfies conditions for conducting a satisfactory solution analysis. Such an analysis of MDPs is often dependent on the type of state space as well as on the boundedness of travel cost functions. We do not constrain the travel cost functions to be bounded and present an analysis centered around weighted sup-norm contractions that also holds for unbounded cost functions. We find that the formulated MDP satisfies a set of assumptions to ensure Bellman's optimality condition. Through this result, the existence of an optimal stationary policy for the MDP is shown. An approximation scheme is developed to resolve the implementation and computational issues of solving the control problem. Numerical results suggest that the approximation scheme efficiently solves the problem and produces accurate solutions.

中文翻译：

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随机交通网络日常拥堵定价的最优控制方法

拥堵收费已成为道路网络交通需求管理的有效工具。本文提出了一种包含需求不确定性和弹性的日内拥堵收费最优控制方法。交通状况信息对旅行者和交通管理者的实时可用性允许定期更新道路定价。我们将问题表述为无限水平可数状态马尔可夫决策过程 (MDP)，并分析问题以查看其是否满足进行令人满意的解决方案分析的条件。对 MDP 的这种分析通常取决于状态空间的类型以及旅行成本函数的有界性。我们不限制旅行成本函数是有界的，并且提出了一个以加权超范数收缩为中心的分析，该分析也适用于无界成本函数。我们发现制定的 MDP 满足一组假设，以确保贝尔曼的最优条件。通过这个结果，显示了 MDP 的最优平稳策略的存在。开发了一种近似方案来解决解决控制问题的实现和计算问题。数值结果表明近似方案有效地解决了问题并产生了准确的解决方案。开发了一种近似方案来解决解决控制问题的实现和计算问题。数值结果表明近似方案有效地解决了问题并产生了准确的解决方案。开发了一种近似方案来解决解决控制问题的实现和计算问题。数值结果表明近似方案有效地解决了问题并产生了准确的解决方案。