Traffic Equilibrium Model of Reliable Network Based on Bounded Rationality
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摘要:
为探索交通系统不确定性和出行者心理感知差异对出行路径选择行为的影响，将路网可靠性和有限理性融入出行者的路径选择决策中，提出双目标交通网络均衡模型. 为应对模型多解问题，建立出行可靠性和有限理性下的贝叶斯随机用户均衡模型，运用贝叶斯统计和双层规划框架估计权重系数，采用变分不等式刻画交通均衡模型；分别设计迭代算法（iterative algorithm，IA）和相继平均算法（method of successive average，MSA）求解贝叶斯权重系数估计和变分不等式交通网络均衡模型. 算例表明：随着观测变量和输入变量扰动变小，估计参数的均方根误差逐步减小；IA在运行15 s后均方根误差达到0.05，MSA在1 s内收敛精度达到10−6；变分不等式均衡模型可以同时反映出行者的风险态度和有限理性决策过程.
Abstract:To explore the influence of the uncertainties of traffic systems and travelers’ perception differences on route choice behavior, the bi-objective traffic network equilibrium model is proposed by introducing the network reliability and bounded rationality into travelers’ route choice decision process. To solve multiple solutions of bi-objective user equilibrium model, the Bayesian stochastic user equilibrium model considering travel time reliability and bounded rationality is built, where the Bayesian statistics and bi-level program framework are used to estimate the weight coefficients, and the variational inequality is adopted to build the traffic equilibrium model. The iterative algorithm (IA) and the method of successive average (MSA) are used for the Bayesian estimation model of weight coefficient and variational inequality traffic network equilibrium model, respectively. Case studies show that, the root mean square error (RMSE) of the estimated parameter is decreasing with the increasing of disturbances of observed data and input variable; RMSE reaches to 0.05 after running IA for 15 s, and the convergence accuracy of MSA reaches 10−6 within 1 s; the variational inequality equilibrium model explores traveler’s risk preference and bounded rational decision process.
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Key words:
- traffic engineering /
- traffic equilibrium /
- reliability /
- bounded rationality /
- Bayesian
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图 3 估计权重的RMSE随观测路段流量和输入需求扰动的影响
Figure 3. RMSE of estimated weights with different disturbances of observed flows and input ODs
图 6 平均出行时间、有限理性阈值、可靠出行时间和路径流量演化过程
Figure 6. Evolution processes of mean travel time, boundedly rational threshold, reliable travel time, and traffic flow
表 1 算例1的模型均衡解
Table 1. Equilibrium results of proposed model for case 1
OD 路径 时间均值/min 有限理
性阈值/min权重
系数可靠出
行时间/min感知多目标出行阻抗均值/min 流量/辆 1—2 1—12—8—2 35.94 7.69 2.00 0.52 44.67 368.24 1—5—6—7—8—2 38.36 0.70 47.45 23.02 1—5—6—7—11—2 40.35 0.72 49.48 3.02 1—5—6—10—11—2 43.77 0.25 51.96 0.25 1—5—9—10—11—2 44.41 0.20 52.50 0.15 1—12—6—7—8—2 40.04 0.66 49.05 4.65 1—12—6—7—11—2 42.04 0.67 51.07 0.61 1—12—6—10—11—2 45.46 0.07 53.29 0.07 1—3 1—5—6—7—11—3 39.58 8.20 1.50 0.72 48.86 327.15 1—5—6—10—11—3 43.01 0.26 51.60 21.28 1—5—9—10—11—3 43.65 0.21 52.17 12.07 1—12—6—7—11—3 41.27 0.68 50.49 64.53 1—12—6—10—11—3 44.69 0.10 53.04 5.04 1—5—9—13—3 39.85 0.46 48.74 369.93 4—2 4—5—6—7—8—2 39.66 8.21 2.50 0.67 49.55 302.33 4—5—6—7—11—2 41.66 0.69 51.60 39.21 4—5—6—10—11—2 45.08 0.18 53.74 4.66 4—9—10—11—2 41.41 0.05 49.75 250.74 4—5—9—10—11—2 45.72 0.09 54.16 3.05 4—3 4—5—6—7—11—3 40.89 7.82 3.00 0.70 50.81 1.40 4—5—6—10—11—3 44.31 0.19 52.70 0.21 4—5—9—10—11—3 44.95 0.11 53.10 0.14 4—9—13—3 36.84 0.42 45.92 184.53 4—5—9—13—3 41.15 0.42 50.23 2.43 4—9—10—11—3 40.64 0.08 48.70 11.30 
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