Weibull dependence stochastic traffic assignment model considering risk prone drivers
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摘要: 建立了考虑风险爱好驾驶人的相依Weibull随机交通分配(Weibull-DSA) 模型, 分析了感知等价路径负效用的Weibull边缘生存函数, 假设驾驶人总是选择感知等价路径负效用最小的路径到达目的地, 采用Copula方法构建了感知等价路径负效用的联合生存函数, 预测了路径选择概率; 设计了模型的迭代求解算法, 对模型进行了理论分析和数值验证; 研究了广州市交通调查获得的风险系数, 基于风险爱好和风险中立驾驶人, 比较了采用Weibull-DSA模型与经典的Logit-SUE和Weibit-SUE模型计算的路径选择概率、路段交通量、饱和度与系统总出行时间。计算结果表明: 随着风险系数的降低, 3种分配模型的交通系统总出行时间变大; 在风险中立情况下, 应用Weibull-DSA模型、Logit-SUE模型和Weibit-SUE模型计算得到每OD对的所有连接路径选择概率的最大差值, 分别为0.17、0.33、0.34, 在风险爱好情况下, 由3种模型得到的最大差值分别为0.20、0.36、0.41, 因此, 采用Weibull-DSA模型计算得到的不同路径选择概率的最大差值明显小于经典模型计算得到的最大差值; 相对于风险中立情况, 风险系数使得每OD对的所有连接路径选择概率的最大差值变大; 无论是风险爱好还是风险中立驾驶人, 采用Logit-SUE和Weibit-SUE模型计算得到的路段饱和度均小于0.9, 采用Weibull-DSA模型计算得到路段饱和度大于0.9;与经典模型计算结果不同, 采用Weibull-DSA模型得到的不同路径选择概率的最大差值相差较小, 一些路径获得更多交通量, 使得路径中通行能力最小的路段的饱和度大于0.9, 这一特征给出了城市路网中部分瓶颈路段拥堵现象一个新的解释。Abstract: A Weibull dependence stochastic traffic assignment (Weibull-DSA) model considering risk prone drivers was established. The Weibull marginal survival function of perceived equivalent route disutility was analyzed.It was assumed that travelers always chose the routes with the minimized expected perceived equivalent route disutility to reach their destinations.Thejoint survival function of perceived equivalent route disutility was constructed by using Copula method, and the route choice probability was predicted.An iterative solution algorithm was designed for the model, and the theoretical analysis and numerical verification of the model were carried out.Risk coefficient obtained from the traffic survey in Guangzhou was analyzed.The route choice probabilities, road section traffic volumes, saturation degrees and total travel times were calculated by using Weibull-DSA model, classic Logit stochastic user equilibrium (LogitSUE) model and Weibit stochastic user equilibrium (Weibit-SUE) model under the assumption of risk prone and risk neutral drivers, respectively.Calculation result shows that as the risk coefficient becomes smaller, the total travel times of traffic system for all three kinds of traffic assignment models become larger.Under the risk neutral condition, the maximum differences among the route choice probabilities of all alternative routes connecting each OD pair are 0.17, 0.33, 0.34, respectively calculated by using Weibull-DSA model, Logit-SUE and Weibit-SUE model.Similarly, under the risk prone condition, the maximum differences calculated by the three models are 0.20, 0.36 and 0.41, respectively.Therefore, the maximum difference of different route choice probabilities calculated by Weibull-DSA model is obviously less than the maximum differences obtained by two classical models.Compared with the risk neutral situation, the risk coefficient increases the maximum difference of the route choice probabilities of all alternative routes connecting each OD pair.For either risk prone or risk neutral drivers, the saturation degrees of each road section calculated by Logit-SUE and Weibit-SUE models are all less than 0.9, whereas the saturation degrees obtained by Weibull-DSA model are more than 0.9.Unlike the calculation results of classical models, the maximum difference of route choice probabilities obtained by Weibull-DSA model is smaller, some routes get more traffic volumes, which makes the saturation degrees of road sections with the smallest capacity in the route are greater than 0.9.This feature gives a new explanation for the congestion phenomenon at some bottlenecks in the urban road network.
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图 2 连接OD对1-5的6条路径的路径选择概率
Figure 2. Route choice probabilities of six alternative routes connecting OD pair 1-5
图 3 连接OD对5-1的6条路径的路径选择概率
Figure 3. Route choice probabilities of six alternative routes connecting OD pair 5-1
图 4 连接OD对3-7的6条路径的路径选择概率
Figure 4. Route choice probabilities of six alternative routes connecting OD pair 3-7
图 5 连接OD对7-3的6条路径的路径选择概率
Figure 5. Route choice probabilities of six alternative routes connecting OD pair 7-3
图 6 风险中立情况下Logit-SUE模型得到的路段饱和度
Figure 6. Saturation degrees of road sections resulting from Logit-SUE model under risk neutral condition
图 7 风险中立情况下Weibit-SUE模型得到的路段饱和度
Figure 7. Saturation degrees of road sections resulting from Weibit-SUE model under risk neutral condition
图 8 风险中立情况下Weibull-SUE模型得到的路段饱和度
Figure 8. Saturation degrees of road sections resulting from Weibull-SUE model under risk neutral condition
图 9 风险爱好情况下Logit-SUE模型得到的路段饱和度
Figure 9. Saturation degrees of road sections resulting from Logit-SUE model under risk prone condition
图 10 风险爱好情况下Weibit-SUE模型得到的路段饱和度
Figure 10. Saturation degrees of road sections resulting from Weibit-SUE model under risk prone condition
图 11 风险爱好情况下Weibull-SUE模型得到的路段饱和度
Figure 11. Saturation degrees of road sections resulting from Weibull-SUE model under risk prone condition
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[1] CHEN A, JI Zhao-wang, RECKER W. Travel time reliability with risk-sensitive travelers[J]. Transportation Research Record, 2002 (1783): 27-33. [2] FISK C. Some developments in equilibrium traffic assignment[J]. Transportation Research Part B: Methodological, 1980, 14 (3): 243-255. doi: 10.1016/0191-2615(80)90004-1 [3] DAGANZO C F, SHEFFI Y. On stochastic models of traffic assignment[J]. Transportation Science, 1977, 11 (3): 253-274. doi: 10.1287/trsc.11.3.253 [4] EVANS S P. Derivation and analysis of some models for combining trip distribution and assignment[J]. Transportation Research Part B: Methodological, 1976, 10 (1): 37-57. [5] LEBLANC L J, MORLOK E K, PIERSKALLA W P, et al. An efficient approach to solving the road network equilibrium traffic assignment problem[J]. Transportation Research Part B: Methodological, 1975, 9 (5): 309-318. [6] SHEFFI Y, POWELL W. A comparison of stochastic and deterministic traffic assignment over congested networks[J]. Transportation Research Part B: Methodological, 1981, 15 (1): 53-64. doi: 10.1016/0191-2615(81)90046-1 [7] GARTNER N H. Optimal traffic assignment with elastic demands: a review part I. Analysis framework[J]. Transportation Science, 1980, 14 (2): 174-191. doi: 10.1287/trsc.14.2.174 [8] HOROWITZ J L, SPARMANN J M, DAGANZO C F. An investigation of the accuracy of the clark approximation for the multinomial probit model[J]. Transportation Science, 1982, 16 (3): 382-401. doi: 10.1287/trsc.16.3.382 [9] DAGANZO C F. Unconstrained extremal formulation of some transportation equilibrium problems[J]. Transportation Science, 1982, 16 (3): 332-360. doi: 10.1287/trsc.16.3.332 [10] DAFERMOS S. Traffic equilibrium and variational inequalities[J]. Transportation Science, 1980, 14 (1): 42-54. doi: 10.1287/trsc.14.1.42 [11] DAFERMOS S. Relaxation algorithms for the general asymmetric traffic equilibrium problem[J]. Transportation Science, 1982, 16 (2): 231-240. doi: 10.1287/trsc.16.2.231 [12] DAFERMOS S. An extended traffic assignment model with application to two-way traffic[J]. Transportation Science, 1971, 5 (4): 366-389. doi: 10.1287/trsc.5.4.366 [13] ALLSOP R E. Delay at a fixed time traffic signals—I: theoretical analysis[J]. Transportation Science, 1972, 6 (3): 260-285. doi: 10.1287/trsc.6.3.260 [14] DIAL R B. A probabilistic multipath traffic assignment model which obviates path enumeration[J]. Transportation Research Part B: Methodological, 1971, 5 (2): 83-111. [15] FISK C, NGUYEN S. Solution algorithms for network equilibrium models with asymmetric user costs[J]. Transportation Science, 1982, 16 (3): 361-381. doi: 10.1287/trsc.16.3.361 [16] FLORIAN M. A traffic equilibrium model of travel by car and public transit modes[J]. Transportation Science, 1977, 11 (2): 166-179. doi: 10.1287/trsc.11.2.166 [17] FLORIAN M, NGUYEN S. A combined trip distribution modal split and trip assignment model[J]. Transportation Research Part B: Methodological, 1978, 12 (4): 241-246. [18] GARTNER N H. Optimal traffic assignment with elastic demands: a review part II. Algorithmic approaches[J]. Transportation Science, 1980, 14 (2): 192-208. doi: 10.1287/trsc.14.2.192 [19] MAHMASSANI H, SHEFFI Y. Using gap sequences to estimate gap acceptance functions[J]. Transportation Research Part B: Methodological, 1981, 15 (3): 143-148. doi: 10.1016/0191-2615(81)90001-1 [20] MIRCHANDANI P, SOROUSH H. Generalized traffic equilibrium with probabilistic travel times and perceptions[J]. Transportation Science, 1987, 21 (3): 133-152. doi: 10.1287/trsc.21.3.133 [21] TATINENI M, BOYCE D, MIRCHANDANI P. Experiments to compare deterministic and stochastic network traffic loading models[J]. Transportation Research Record, 1997 (1607): 16-23. [22] 俞礼军, 杨灿杰. 随机路网中风险爱好出行者的路径选择分析[J]. 华南理工大学学报: 自然科学版, 2015, 43 (12): 127-132, 140. doi: 10.3969/j.issn.1000-565X.2015.12.018YU Li-jun, YANG Can-jie. Analysis of route choice of riskprone drivers in a stochastic road network[J]. Journal of South China University of Technology: Natural Science Edition, 2015, 43 (12): 127-132, 140. (in Chinese). doi: 10.3969/j.issn.1000-565X.2015.12.018 [23] CASTILLO E, MENENDEZ J M, JIMENEZ P, et al. Closed form expressions for choice probabilities in the Weibull case[J]. Transportation Research Part B: Methodological, 2008, 42 (4): 373-380. doi: 10.1016/j.trb.2007.08.002 [24] KITTHAMKESORN S, CHEN A. Unconstrained Weibit stochastic user equilibrium model with extensions[J]. Transportation Research Part B: Methodological, 2014, 59 (1): 1-21. [25] KITTHAMKESOM S, CHEN A. A path-size weibit stochastic user equilibrium model[J]. Transportation Research Part B: Methodological, 2013, 57 (11): 378-397. [26] CHEN A, PRAVINVONGVUTH S, XU Xiang-dong, et al. Examining the scaling effect and overlapping problem in logitbased stochastic user equilibrium models[J]. Transportation Research Part A: Policy and Practice, 2012, 46 (8): 1343-1358. doi: 10.1016/j.tra.2012.04.003 [27] AHIPASAOGLU S D, ARIKAN U, NATARAJAN K. On the flexibility of using marginal distribution choice models in traffic equilibrium[J]. Transportation Research Part B: Methodological, 2016, 91: 130-158. doi: 10.1016/j.trb.2016.05.002 [28] ORDONEZ F, STIER-MOSE N E. Wardrop equilibria with risk-averse users[J]. Transportation science, 2010, 44 (1): 63-86. doi: 10.1287/trsc.1090.0292 [29] HOUGAARD P. A class of multivariate failure time distributions[J]. Biometrika, 1986, 73 (3): 671-678. [30] MAHER M J, ZHANG Xiao-yan, VLIET D V. A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows[J]. Transportation Research Part B: Methodological, 2001, 35 (10): 23-40. -
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