This study defines the price of anarchy for general reliability-based transport network design problems, which is an indicator of inefficiency that reveals how much the design objective value exceeds its theoretical minimum value due to the risk averse and selfish routing behavior of travelers. This study examines a new problem, which is a reliability-based continuous network design problem under cost recovery. In this problem, the variations of system travel time and path travel times, the risk attitudes of the system manager and travelers, congestion toll charges, capacity expansions, and cost recovery constraint are explicitly considered. The design problem is formulated as a min-max problem with the reliability-based user equilibrium constraint. It is proved that the price of anarchy for this problem is bounded above, and the upper bound is independent of travel time functions, demands, and network topology. The upper bound is related to the travel time variations, the value of reliability, and the value of time.

中文翻译：

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成本回收下基于可靠性的连续网络设计问题的效率低下

这项研究确定了基于一般可靠性的运输网络设计问题的无政府状态的价格，这是效率低下的指标，它揭示了由于旅行者的规避风险和自私的路线行为，设计目标值超出了理论上的最小值。这项研究探讨了一个新问题，这是在成本回收下基于可靠性的连续网络设计问题。在此问题中，明确考虑了系统行驶时间和路径行驶时间的变化，系统管理员和旅行者的风险态度，拥堵费，容量扩展和成本回收约束。设计问题被公式化为具有基于可靠性的用户平衡约束的最小-最大问题。事实证明，这个问题的无政府状态价格是有上限的，上限不受旅行时间功能，需求和网络拓扑的影响。上限与旅行时间变化，可靠性的值和时间的值有关。