Abstract

Most traditional metrics compare origin-destination (OD) matrices based on the deviations of individual OD flows and often neglect OD matrix structural information within their formulations. Limited metrics exist in literature for the structural comparison of OD matrices. One such metric is mean structural similarity index (MSSIM) that computes statistics on groups of OD pairs defined by local sliding windows. However, MSSIM can result in different values based on the choice of the size of the window. In literature, no clear consensus has been reported on the level of acceptability of the window size and the resulting MSSIM values. Addressing this need, we propose the concept of geographical window, and develop geographical window based structural similarity index (GSSI) that exploits OD matrix structure by computing statistics on the group of OD pairs that are geographically correlated. Compared to traditional sliding window based MSSIM, the advantages of GSSI technique identified from real case study application are (a) it preserves geographical integrity; (b) it compares results with physical significance; (c) it captures local travel patterns; (d) it compares large-scale sparse OD matrices; and (e) it is computationally efficient. A thorough sensitivity analyses suggest that GSSI is a robust statistical metric and has potential for practical applications such as, benchmarking different OD estimation methods; improving the quality of solution by maintaining structural consistency in the OD estimation process; and identifying gaps in the transit service by comparing local (within a geographical window) travel patterns of car and public transit.

摘要

大多数传统指标根据单个 OD 流的偏差比较起点-终点 (OD) 矩阵，并且经常忽略其公式中的 OD 矩阵结构信息。文献中关于 OD 矩阵结构比较的指标有限。一个这样的度量是平均结构相似性指数 (MSSIM)，它计算由局部滑动窗口定义的 OD 对组的统计数据。但是，根据窗口大小的选择，MSSIM 可能会产生不同的值。在文献中，关于窗口大小的可接受程度和由此产生的 MSSIM 值没有明确的共识。针对这种需求，我们提出了地理窗口的概念，并开发基于地理窗口的结构相似性指数 (GSSI)，该指数通过计算地理相关的 OD 对组的统计数据来利用 OD 矩阵结构。与传统的基于滑动窗口的 MSSIM 相比，从实际案例研究应用中识别出的 GSSI 技术的优点是（a）它保持了地理完整性；(b) 将结果与物理意义进行比较；(c) 它捕捉当地的旅行模式；(d) 它比较了大规模的稀疏 OD 矩阵；(e) 计算效率高。彻底的敏感性分析表明，GSSI 是一个强大的统计指标，具有实际应用的潜力，例如对不同的 OD 估计方法进行基准测试；通过在 OD 估计过程中保持结构一致性来提高解决方案的质量；