随机行程时间的电动公交调度模型  

Electric Bus Scheduling Model with Stochastic Travel Time

作　　者：巫威眺[1] 林越 李余 靳文舟[1] 李成[2] WU Wei-tiao;LIN Yue;LI Yu;JIN Wen-zhou;LI Cheng(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou 510641,Guangdong,China;China Urban Sustainable Transportation Research Center,China Academy of Transportation Sciences,Beijing 100029,China)

机构地区：[1]华南理工大学土木与交通学院,广东广州510641 [2]交通运输部科学研究院城市交通与轨道交通研究中心,北京100029

出　　处：《中国公路学报》2023年第6期235-253,共19页China Journal of Highway and Transport

基　　金：国家自然科学基金项目(72071079,52272310);交通运输部科学研究院城市公共交通智能化交通运输行业重点实验室开放课题(2022-APTS-06);广东省自然科学基金项目(2023A1515011696);广州市重点研发计划项目(202206030005,202103050002,202206010056)。

摘　　要：在低碳发展政策指引下,全国各地已开始普及电动公交。然而,由于电动公交车技术性能和运营环境的特点,如续驶里程、充电时长约束、随机路网环境等,为电动公交车辆和充电调度带来新的挑战。随机行程时间导致车次衔接中存在延误,由于连续车次任务的相依性,上游车次延误可能造成下游车次晚点,引发车次延误传播的“连锁反应”,致使车次和充电计划的风险承受能力变得非常脆弱,电动公交调度的效能无法得到充分释放。考虑电动公交调度问题中的车次延误传播效应,在分析随机行程时间对电动公交车次与充电计划影响的基础上,从单线调度到区域调度模式建立优化模型获得经济可靠的公交调度方案。首先,运用网络流模型描述电动公交调度过程,并引入马尔科夫过程刻画延误传播效应。在此基础上,计算期望等待时间、期望延误时间等服务质量指标并纳入到目标函数,建立混合整数线性规划模型。然后,运用多商品流模型,将单线调度模型拓展为通用的区域调度模型,设计“延误状态层”用以计算延误时间分布并提高计算效率。最后,以广州市的2条电动公交线路实际数据进行案例分析,调用商业求解器Gurobi获得精确解。结果表明:充电计划的最优时间窗间隔为40 min;在最优调度方案下,车辆能充分利用日间运营的闲暇时段进行充电,且这一特性不受时间窗间隔大小的影响;随着延误惩罚系数的增加,期望延误时间均值先减少后保持波动,当延误惩罚系数大于2元·min-2时,期望延误时间均值小于15 s,相较传统模型降低幅度超过50%,说明模型能有效降低行程延误;随着延误惩罚系数的增加,期望等待时间均值先增加后保持波动,说明模型可以智能调整车次之间的衔接顺序,增加等待时间作为缓冲时间,从而减少延误的发生。Guided by low-carbon development policies,many provinces and municipalities across the country have begun to popularize electric buses.However,the characteristics of the technical performance and operating environment of electric buses,such as their range,charging time constraints,and random road network environment,create new challenges for electric bus vehicle scheduling and charging plans.Stochastic travel times lead to delays in the connection of trips,and because of the interdependence of successive trips,delays in the upstream trips may cause delays in the downstream trips.This leads to the knock-on effect of delay propagation,making the risk tolerance of the trips and charging schedules very vulnerable and preventing the effectiveness of bus scheduling.In this study,we consider the effect of delay propagation in the electric bus scheduling problem,analyze the effect of stochastic travel times on bus trips and charging schedules,and develop optimization models from single-line to regional scheduling modes to obtain an economical and reliable bus scheduling solution.First,the network flow model was used to describe the electric bus scheduling process,and a Markov process was introduced to portray the delay propagation effect.On this basis,service quality indicators,such as expected waiting time and expected delay time,were calculated and added to the objective function,thereby developing a mixed-integer linear programming model.Then,a multi-commodity flow model was applied to extend the single-line scheduling model into a generic regional scheduling model,and a'delay state layer’was designed to calculate the delay time distribution and save computational expenses.Finally,a case study was conducted with actual data from two electric bus lines in Guangzhou,and the commercial solver Gurobi was used to obtain the exact solution.The results show that the optimal time window interval for the charging schedule is 40 min.Under the optimal scheme,the vehicles can make full use of the idle time in daytime operation

关 键 词：交通工程 公共交通 混合整数规划 车辆调度问题 随机行程时间 延误传播 

分 类 号：U491.11[交通运输工程—交通运输规划与管理]