Hyperpath Searching Algorithm Method Based on Signal Delay at Intersections
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摘要:
城市道路中交叉口信号周期性变化会导致车辆出行的不确定延误，为降低车辆在交叉口处产生的信号延误，以路段旅行时间和交叉口期望延误最小为优化目标，提出一种改进的超路径规划方法. 首先，根据车辆到达交叉口的概率分布函数，推导出车辆在信号交叉口的期望等待时间和转向比例计算公式；其次，引入标号设定算法构建高性能超路径规划方法；最后，将改进的超路径规划方法应用于南京新街口区域的路网，通过最优超路径集合分析证实其适用性. 研究表明：与最短路出行策略相比，车辆遵循基于超路径规划方法的出行策略，在行进过程时从最优超路径集合中选择变换的行驶路线可降低67.1%的交叉口信号延误和22.3%的总旅行时间；此外，超路径出行策略可优化路网中的出行结构，缓解交通拥堵，实现流量均衡.
Abstract:The periodic change of intersection signals in urban road systems leads to the uncertain delay of vehicle travel. In order to reduce the delays of vehicles at signal-controlled intersections, an improved hyperpath searching algorithm was proposed with the minimization of travel time on the road segments and the expected delay at the intersections as the optimization goal. First, according to the probability distribution function of vehicles arriving at the intersection, the expected waiting time and the turning movement proportion were derived. Then, the high-performance hyperpath searching algorithm was developed with the introduction of the label setting algorithm. Finally, the improved hyperpath searching algorithm was applied to the road network at Xinjiekou area, Nanjing, and the optimal hyperpath set was used to evaluate the applicability of the algorithm. The results show that compared with the shortest path strategy, hyperpath searching algorithm reduces the intersection delay and the total travel time by 67.1% and 22.3%, respectively as drivers shift to a driving route in the optimal hyperpath set. Furthermore, the hyperpath-based strategy can optimize the trip distribution in the road network, alleviating traffic congestion and contributing to flow equilibrium.
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图 14 起点38到终点37的最短路径和最优超路径
Figure 14. Shortest path and optimal hyperpath from origin 38 to destination 37
图 16 进口道(7,9)处转向选择对总旅行时间的影响
Figure 16. Total travel time versus the set of turns on entrance (7,9)
图 17 进口道(19,20)转向选择对总旅行时间的影响
Figure 17. Total travel time versus the set of turns on entrance (19,20)
表 1 信号配时变化对超路径集合元素的影响
Table 1. Influence of signal timing on hyperpath set
序号 交叉口 周期/s 相位1 /s 相位2 /s 相位3 /s 路径 1
时间 /s路径 2
时间 /s组合
期望 /s最优超
路径1 A 110 40 50 20 131.4 149.3 121.6 A—B—C, A—D—C C 80 60 20 0 2 A 150 80 20 50 202.6 127.1 130.1 A—D—C C 120 30 90 0 3 A 47 12 15 20 124.4 138.8 125.1 A—B—C C 110 95 15 0 
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表 2 参数定义
Table 2. Notations
符号 含义 $ G(N,A) $ 有向网络图，其中N、A表示网络中的节点集合；路段集合 ${\varGamma ^ - }(i)$ 流入节点$i$的路段集合 ${\varGamma ^ + }(i)$ 流出节点$i$的路段集合 j 节点 i 的下游节点标号 k 节点 j 的下游节点标号 s 终点 r 起点 ${m_k}$ 转向节点k的转向行为 H 超路径的路段集合 ${M_{i,j}}$ 进口道$(i,j)$处，属于超路径的转向行为集合 $u_{i,j}$ 进口道$(i,j)$到终点的期望旅行时间 $ p\{ (j,k)|i\} $ 由节点 i 转向路段$ j—k $时，节点$ j$被选择的概率 $ p\{ k|j\} $ 由节点 j 转向节点 k 时，节点 k 被选择的概率 $ {P_{ {i,j} }} $ 在节点i处，路段$ i—j $被选择的概率 $c_{i,j}$ 路段$ i—j $的旅行时间 $ \xi_{i,j,m_k} $ 从节点 i 经过节点 j 转向节点 k 的期望延误时间 $ w_{i,j} $ 进口道为$ \left(i,j\right) $时，在节点 j 处的组合延误期望值 注：$\displaystyle \sum\nolimits_{(i,j) \in {\varGamma ^ + }(i)} {P_{{i,j} }} = 1 $
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表 3 路径选择概率
Table 3. Path choice probability
路径 路径走行路段 路径被选择
概率路径 1 38—7—9—10—14—17—18—
19—20—44—22—26—32—370.45 路径 2 38—7—9—13—16—17—18—
19—20—44—22—26—32—370.55
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表 4 两种路径出行策略对比
Table 4. Comparison between two routing strategies
出行策略 路径 总旅行时间/s 总旅行时间降低率/% 总延误时间/s 总延误时间降低率/% 最短路 路径 1 1 010.0 317.0 超路径 路径 1 或路径 2 784.8 22.3 104.2 67.1
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表 5 进口道(7,9)的相关参数
Table 5. Related parameters of entrance (7,9)
下游路段 转向行为 距终点的总旅行时间/s 路段旅行时间/s 延误时间/s 选择概率/% 组合延误时间/s 组合总旅行时间/s 9—10 左转 555.3 79.0 22.1 45 8.5 655.2 9—13 直行 582.3 52.0 19.2 55
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表 6 进口道(19,20)的相关参数
Table 6. Related parameters of entrance (19,20)
下游路段 转向行为 距终点的总旅行时间/s 路段旅行时间/s 延误时间/s 选择概率/% 组合延误时间/s 组合总旅行时间/s 20—21 直转 283.6 13.0 31.1 13.8 0 307.6 20—44 右转 255.3 40.0 0 86.2
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