Bush-based sensitivity analysis for approximating subnetwork diversion
Bush-based sensitivity analysis for approximating subnetwork diversion
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DOI：
10.1016/j.trb.2011.09.004
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发表时间：
2012
影响因子：
6.8
通讯作者：
S. Boyles
中科院分区：
文献类型：
--
作者：
S. Boyles
子网络分析常用于交通分配问题中，以减小所分析网络的规模，从而相应地减少计算时间。这在网络设计、次优定价或其他双层问题中尤为重要，在这些双层问题中，许多均衡运行必须作为主优化程序的子问题来求解。一个固定的行程表的基础上的平衡路径流的解决方案是经常使用的，但这忽略了重要的吸引力和分流的影响，司机（全球）改变路线，以响应（本地）子网的变化。本文提出了一种方法来取代一个区域网络与一个较小的，包含所有的子网，和地区。在假设平衡路径集不变的情况下，创建人工弧来表示每个原点和子网边界节点之间的“所有路径”。本文的主要贡献是估计这些人工弧的成本函数的过程，使用端节点之间的平衡旅行时间的导数来创建泰勒级数。一个基于导数的表示允许快速计算这些导数。提出了两种计算这些导数的方法，一种是基于网络变换和类似的技术，用于分析电阻电路，另一种是基于迭代求解一组嵌套的线性方程组。这些方法被应用到两个网络，一个小的和人工的，和其他的区域网络代表得克萨斯州奥斯汀大都市区。这些演示表明，与使用固定表相比，在准确性上有了很大的提高，并证明了所提出的方法的效率。
Subnetwork analysis is often used in traffic assignment problems to reduce the size of the network being analyzed, with a corresponding decrease in computation time. This is particularly important in network design, second-best pricing, or other bilevel problems in which many equilibrium runs must be solved as a subproblem to a master optimization program. A fixed trip table based on an equilibrium path flow solution is often used, but this ignores important attraction and diversion effects as drivers (globally) change routes in response to (local) subnetwork changes. This paper presents an approach for replacing a regional network with a smaller one, containing all of the subnetwork, and zones. Artificial arcs are created to represent “all paths” between each origin and subnetwork boundary node, under the assumption that the set of equilibrium routes does not change. The primary contribution of the paper is a procedure for estimating a cost function on these artificial arcs, using derivatives of the equilibrium travel times between the end nodes to create a Taylor series. A bush-based representation allows rapid calculation of these derivatives. Two methods for calculating these derivatives are presented, one based on network transformations and resembling techniques used in the analysis of resistive circuits, and another based on iterated solution of a nested set of linear equations. These methods are applied to two networks, one small and artificial, and the other a regional network representing the Austin, Texas metropolitan area. These demonstrations show substantial improvement in accuracy as compared to using a fixed table, and demonstrate the efficiency of the proposed approach.