Importance evaluation of edges in transportation network under dynamic and randomly disruptive event
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摘要: 采用动态贝叶斯重要度的新方法评估了交通网络连边的重要性；应用随机过程理论刻画外部扰动事件的发生过程，并构建了交通网络可靠性模型；利用概率技术，导出了每条连边的动态贝叶斯重要度的计算公式，并确定了其最大值和取得最大值的相应连边；基于该计算公式，设计了数值算法以评估每条连边在不同时刻的动态贝叶斯重要度的值；引进了一个交通网络的实际案例，其连边受到的动态随机扰动冲击过程是一个给定尺度参数和形状参数的饱和非时齐泊松计数过程，演示了动态贝叶斯重要度的计算方法，并对连边的重要性排序关于尺度参数和形状参数的变化进行了敏感性分析。研究结果表明：无论外部随机扰动事件如何变化，网络的单边割是最重要的连边，进一步证实了理论分析的正确性；本文提出的动态贝叶斯重要度能及时精确地识别所有连边的重要性程度，其同时考虑外部随机扰动事件的扰动和网络结构，弥补了传统静态连边重要度仅考虑连边“位置”的缺陷；尺度参数或者形状参数越大，则2条连边的重要性排序的变化越快。Abstract: A dynamic Bayesian importance measure method was proposed for edge importance evaluation of transpartation network. The random process theory was applied to characterize the generation process of external disruptive events, and a transportation network reliability model was established. Probabilistic techniques were utilized to obtain a formula of dynamic Bayesian importance measure of each network edge, and a maximum value for the importance measure and corresponding maximum edges were determined. Based on the formula, an numerical algorithm was developed to evaluate the Bayesian importance measure of each edge at different times. An actual case of a transportation network was introduced, and the dynamic random disruptive shock process incurred by the edges was a saturated non-time homogeneous Poisson counting process with given scale parameters and shape parameters. The calculation method of dynamic Bayesian importance measure was demonstrated, and the sensitivity analysis of the scale parameter and shape parameter of the importance ranking of the connected edges was made. Research results show that, regardless of the changes in random disruptive events from the external environment, the one-edge cut in the network remains the most important edge, which verifies the correctness of the theoretical analysis. Considering external random disruptive events and the network structure, the Bayesian importance measure can timely and accurately identify the importance of all edges, which fills the gap left by the traditional static measure for edge importance that only considers the position of an edge. As the values of the scale parameters and shape parameters become larger, the importance ranking of the two edges changes faster.
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图 3 M1(t)与M7(t)关于参数α的敏感性分析(β=10)
Figure 3. Sensitivity analysis of M1(t) and M7(t) with parameter α (β=10)
图 4 M1(t)与M7(t)关于参数β的敏感性分析(α=0.5)
Figure 4. Sensitivity analysis of M1(t) and M7(t) with parameter β (α=0.5)
表 1 基于动态贝叶斯重要度的连边排序(前7名)
Table 1. Ranking of edges based on dynamic Bayesian importance (top 7)
排序 连边i Mi(0.1) 连边i Mi(10) 连边i Mi(30) 连边i Mi(40) 连边i Mi(100) 1 15 1.000 0 15 1.000 0 15 1.000 0 15 1.000 0 15 1.000 0 2 19 1.000 0 19 1.000 0 19 1.000 0 19 1.000 0 19 1.000 0 3 14 0.942 5 14 0.839 0 14 0.874 4 14 0.887 2 14 0.928 6 4 10 0.942 4 10 0.819 2 10 0.851 8 10 0.864 7 10 0.907 3 5 11 0.941 3 13 0.715 4 13 0.743 3 13 0.761 3 13 0.826 7 6 16 0.941 2 16 0.616 7 17 0.452 7 17 0.408 0 17 0.278 3 7 17 0.938 4 17 0.614 3 16 0.449 7 16 0.402 6 16 0.262 3 
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