On Some Transportation Management Problems for Ensuring Stable Network Equilibria

本文提出了一个基于“稳定均衡”概念的交通网络设计/管理框架，即非饱和区域内的交通需求和供给是平衡的。为了考虑确保稳定均衡的政策，我们首先定义了以下三个交通设计/管理问题：1)交通性能曲线向上移动（=“拥堵收费问题”），2)交通性能曲线向右移动（=“容量增加问题”），3)交通需求曲线向下移动（=“可行位置问题”）。然后，给出了这些问题的数学公式和分析。对于第一个问题，我们首先将网络流态描述为固定需求下的随机均衡分配，并将其推广到弹性需求情况下。我们的分析表明，该问题可以转化为一个等价的最优化问题，并证明了解的非唯一性。在此基础上，提出了一种求解大规模网络中拥塞收费模式的有效算法。第二个问题可以通过带分段链路代价函数的网络变换来解决。该技术将容量增加问题简化为一个标准的均衡分配问题，使我们能够开发大规模网络的求解算法。并证明了该模式的唯一性。对于第三个问题，我们首先考虑平衡条件下临界OD需求水平的求解问题。然后将该模型推广到交通区位均衡下可行的居住/企业区位格局问题。我们发现这些问题在链路-容量条件下可以转化为需求固定的Wardrop均衡分配。我们讨论了解的非唯一性，并给出了一种选择唯一解的有效方法。少

This study proposes a framework for designing / managing transportation networks based on the concept of "stable equilibria" which means that the transportation demand and supply equilibrate within non-saturated region. To consider a policy that ensures the stable equilibria, we first define the following three transportation design / management problems : 1) Upward-shift of transportation performance curves (= "Congestion toll problem"), 2) Right-shift of transportation performance curves (= "Capacity-increase problem"), 3) Downward-shift of transportation demand curves (= "Feasible location problems"). Then, mathematical formulations and analyzes for these respective problems are presented. For the first problem, we first analyze the model under the assumption that network flow pattern is described as the stochastic equilibrium assignment with fixed demand, and it is generalized for the elastic demand case. Our analyzes disclose that the problem can be cast into an equivalent optimiz … More ation problem, and the non-uniqueness of the solution is shown. By using the optimization representation, we develop an efficient algorithm for obtaining the congestion toll pattern in large scale networks. The second problem is found to be solved by a certain network transformation with piece-wise link cost function. The technique reduces the capacity-increase problem to a standard equilibrium assignment, and it enable us to develop solution algorithms for large scale networks. The uniqueness of the capacity-increase pattern is also proved. As for the third problem, we first consider the problem of obtaining the critical OD demand level under the equilibrium condition. The model is then extended to the problem of obtaining a feasible residential / firm location pattern under the transportation-location equilibrium. We find that these problems can be converted into Wardrop equilibrium assignment with fixed demand under the link-capacity conditions. We discuss the non-uniqueness property of the solution, and an efficient method for selecting the unique solution is developed. Less