On Some Transportation Management Problems for Ensuring Stable Network Equilibria

本研究提出了一个基于“稳定均衡”概念的交通网络设计/管理框架，这意味着在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，我们首先定义以下三个交通设计/管理问题：1）交通性能曲线的上移（=“拥挤收费问题”），2）交通性能曲线的右移（=“容量增加问题”），3）交通需求曲线的下移（=“可行选址问题”）。然后，这些各自的问题的数学公式和分析。对于第一个问题，我们首先分析了模型的假设下，网络流模式被描述为随机均衡分配与固定的需求，并将其推广到弹性需求的情况下。我们的分析表明，这个问题可以转化为一个等价的优化问题， 关于我们 问题，并证明了解的非唯一性。通过使用优化表示，我们开发了一个有效的算法来获得大规模网络的拥塞收费模式。第二个问题被发现可以通过一定的网络变换与分段链接成本函数来解决。该技术减少了一个标准的平衡分配的容量增加的问题，它使我们能够开发大规模网络的解决方案的算法。同时证明了容量增长模式的唯一性。对于第三个问题，我们首先考虑在均衡条件下确定临界OD需求水平的问题。然后，该模型扩展到获得一个可行的住宅/企业的位置模式下的交通区位均衡的问题。我们发现，这些问题可以转化为Wardrop均衡分配与固定的需求下的链路容量的条件。我们讨论了解的非唯一性，并给出了一种有效的选择唯一解的方法。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