Stochastic Traffic Equilibrium Based on Travel Time Robust Reliability

An assumption that pervades the current reliable traffic equilibrium problem is that probability distributions of the origin-destination (O-D) demand or/and link capacities are known explicitly. However, these distributions are difficult to be accurately obtained. This paper relaxes this assumption. It only needs to know the first m moments of travel demand (where m is a positive integer associated with the formulation of link cost function), and then applies two worse-case Value-at-Risk (WVaR) and Conditional value-at-risk (CVaR) risk measures to define robust percentile travel time (RPTT) and robust mean-excess travel time (RMETT) and prove that this two kinds travel time is equal under general distribution. By incorporating the defined travel time and travelers' perception error, the robust percentile stochastic user equilibrium (RPSUE) or robust mean-excess stochastic traffic equilibrium model (RMESTE) is proposed, which is formulated as an equivalent route-based variational inequality. Conditions are established guaranteeing existence of this equilibrium. A heuristic solution problem is introduced to solve the variational inequalities problem. A numerical example is used to illustrate the applications of the proposed model and the solution algorithm.

摘要在基于走行时间可靠性的交通均衡问题中，普遍存在假设是引起走行时间变异的O-D (Origin-Destination)需求或路段通行能力的概率分布是精确已知的。然而，现实中这些概率分布很难精确获得。本文放松这个假设而仅要求知道O-D需求的前m阶矩(这里m是和路段费用函数的形式相关的正整数)，通过运用最坏风险价值和最坏条件风险价值指标定义鲁棒分位走行时间和鲁棒超过期望走行时间，并证明在一般分布下两种出行时间是等价的。基于此定义，通过整合出行者的感知误差，提出了鲁棒分位随机用户均衡(鲁棒超过期望随机交通均衡)模型，模型被表示为一个变分不等式，并证明了解的存在性，然后运用一种启发式算法求解该模型。数值算例显现了模型在应用上的特性及算法上的有效性。