考虑乘客满意度的公交发车间隔优化
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摘要
随着“绿色出行”的大力倡导,更多人出行选择公交和地铁,使得公交车的等待乘客增加。作为服务性较强的公交公司来说,考虑乘客的满意度来确定合理的发车间隔是十分必要的。公交车在站点间行驶的时间常常是随机变化的,使得乘客等待时间波动较大,影响乘客满意度。本文首先考虑乘客在等待一定时间后会自行离开并产生不满,将公交车行驶时间的随机波动与乘客满意度相结合建模,对公交车发车间隔进行了优化。利用最优性条件,本文得到了基于乘客满意度的最优公交发车间隔的结构性质。之后将模型进行深化,利用损失风险与期望效用理论来刻画乘客的满意度,这样更加实际的表示出乘客的等待心理。
为此,本文结合56路公交线路来进行讨论分析,详细研究了考虑乘客满意度的最优公交发车间隔。
首先,利用时间节点来描述乘客等待最长时间,即乘客等待时间超过时间节点会选择离开。由于乘客和公交车到达站点均是随机变量,因此用这种方式描述的乘客满意度也为随机变量。用这种表达方式来建立乘客满意度、发车间隔与公交公司总净收益的关系模型,同时文中考虑了损失成本。
其次,对上述模型进行理论分析,证明模型的二阶导数小于零,即在考虑乘客满意度的条件下,得到的最优发车间隔使得公交公司的总净收益最大。并结合实际数据计算出相应的最优值,同时也提供出仿真结果。利用MATLAB进行一维搜索和仿真计算,对于考虑乘客满意度的第一个模型,在单站点计算的模型近似值和仿真的真实结果均为24分钟；对多站点进行仿真计算的最优发车间隔为8分钟。由于单站点情况和多站点情况下得到的最优发车间隔相差较多,为此本文分析了站点数对最优发车间隔的影响。同时,本文还研究了模型中其他重要的变量对发车间隔和总净收益的影响。得出到达率越大最优发车间隔越小,总净收益越大；公交车在两站点间行驶时间的方差越大,得到的最优发车间隔越小,总净收益也越小。
随后,对满意度的描述进行深化,利用期望效用理论理论来描述乘客的满意度,使乘客满意度的描述更加具体化,更符合实际。
最后,从损失风险、期望效用理论来考虑乘客满意度,分别建立了：公交车在两站点间行驶时间为定值时的考虑乘客满意度的公交发车间隔模型,和公交车在两站点间行驶时间为随机变量时的乘客等待效用模型。同时对模型进行了理论分析,通过证明得出第一个目标函数的二阶导数是小于零的,即存在最优发车间隔使得在考虑乘客满意度的条件下,公交公司的总净收益最大。同时对第二个模型求了一阶差分,得出随着发车间隔的增加,乘客的效用降低。文中也对结合期望效用理论来描述乘客满意度的公交车优化模型进行了实际分析,得到在单站点情况下的最优发车间隔为26分钟。
With "green travel" advocating, more and more people travel by bus and subway, which makes waiting passengers increasing. As bus companies are service industry, considering passenger satisfaction to determine a reasonable headway is so very necessary. Bus travel time between sites is often random variation, making passenger waiting time fluctuations, affecting passenger satisfaction. Firstly, the paper considers the passengers waiting to leave on their own after a certain time and generate dissatisfaction; the bus travel time stochastic volatility combined with the modeling of passenger satisfaction for bus departure interval is optimized. Using optimal conditions, this paper obtains the structure properties of optimal bus passenger satisfaction based on interval. After the model is deepening, to characterize the passengers satisfaction using expected utility theory, so that more practical express passenger waiting psychology.
Therefore, this paper combines one of the bus lines-56road in the Chengdu to discussion and analysis, a detailed study of the bus scheduling optimization of passenger satisfaction is considered.
First, using the time node to describe the passenger waiting-time, passenger waiting time exceeds the time node, they will choose to leave. The passengers and bus arrival at the site randomly, hence the description of passengers'satisfaction is random. Relationship model uses this expression, which combines passenger satisfaction, departure interval with the bus company benefits. At the same time, the paper also considers the cost of losses.
Next, on the theoretical analysis of the model, it is proved that the model has the optimal interval. Combined with the actual data to calculate the corresponding optimal value, the paper also provides the simulation results. One-dimensional search and simulated by MATLAB, for the first model considering the passenger satisfaction, real results in a single site model approximation and Simulation is24minutes; The sites simulation optimization of headway is8minutes. Due to the single site and the site condition of optimal departure interval is relatively different, this paper analyzes the impact of the number of stations on the optimal headway. At the same time, this paper also studies the influence of other important variables in the model on the departure interval and total net income. The arrival rate of more optimal departure interval is smaller, the more total net income; Bus travel time in the variance between two sites is more large, the smaller obtained optimal departure interval and total net income are.
Later, the paper makes the passenger satisfaction deepening. We describe the passengers using expected utility theory in satisfaction; making the passenger satisfaction description is more specific and practical.
In the end, we establish bus scheduling model with passenger satisfaction, from the risk of loss and expected utility theory to consider passenger satisfaction.We set up:bus travel time for considering bus departure interval model of passenger satisfaction of the fixed value in between two sites, and bus travel time to wait for the utility model is a random variable when the passengers at two sites. At the same time, we give a theoretical analysis of the model, which shows that the two order derivative of the first objective function is less than zero, i.e. the existence of the optimal interval that in considering the passenger satisfaction conditions, the bus company's total net income is the most. At the same time, we calculate the first-order difference for the second model, that with the increase of headway, the reduce passenger utility. The paper also combines the expected utility theory to describe the bus optimization model of passenger satisfaction, obtained in a single site in case of optimal departure interval is26minutes.
为此,本文结合56路公交线路来进行讨论分析,详细研究了考虑乘客满意度的最优公交发车间隔。
首先,利用时间节点来描述乘客等待最长时间,即乘客等待时间超过时间节点会选择离开。由于乘客和公交车到达站点均是随机变量,因此用这种方式描述的乘客满意度也为随机变量。用这种表达方式来建立乘客满意度、发车间隔与公交公司总净收益的关系模型,同时文中考虑了损失成本。
其次,对上述模型进行理论分析,证明模型的二阶导数小于零,即在考虑乘客满意度的条件下,得到的最优发车间隔使得公交公司的总净收益最大。并结合实际数据计算出相应的最优值,同时也提供出仿真结果。利用MATLAB进行一维搜索和仿真计算,对于考虑乘客满意度的第一个模型,在单站点计算的模型近似值和仿真的真实结果均为24分钟；对多站点进行仿真计算的最优发车间隔为8分钟。由于单站点情况和多站点情况下得到的最优发车间隔相差较多,为此本文分析了站点数对最优发车间隔的影响。同时,本文还研究了模型中其他重要的变量对发车间隔和总净收益的影响。得出到达率越大最优发车间隔越小,总净收益越大；公交车在两站点间行驶时间的方差越大,得到的最优发车间隔越小,总净收益也越小。
随后,对满意度的描述进行深化,利用期望效用理论理论来描述乘客的满意度,使乘客满意度的描述更加具体化,更符合实际。
最后,从损失风险、期望效用理论来考虑乘客满意度,分别建立了：公交车在两站点间行驶时间为定值时的考虑乘客满意度的公交发车间隔模型,和公交车在两站点间行驶时间为随机变量时的乘客等待效用模型。同时对模型进行了理论分析,通过证明得出第一个目标函数的二阶导数是小于零的,即存在最优发车间隔使得在考虑乘客满意度的条件下,公交公司的总净收益最大。同时对第二个模型求了一阶差分,得出随着发车间隔的增加,乘客的效用降低。文中也对结合期望效用理论来描述乘客满意度的公交车优化模型进行了实际分析,得到在单站点情况下的最优发车间隔为26分钟。
With "green travel" advocating, more and more people travel by bus and subway, which makes waiting passengers increasing. As bus companies are service industry, considering passenger satisfaction to determine a reasonable headway is so very necessary. Bus travel time between sites is often random variation, making passenger waiting time fluctuations, affecting passenger satisfaction. Firstly, the paper considers the passengers waiting to leave on their own after a certain time and generate dissatisfaction; the bus travel time stochastic volatility combined with the modeling of passenger satisfaction for bus departure interval is optimized. Using optimal conditions, this paper obtains the structure properties of optimal bus passenger satisfaction based on interval. After the model is deepening, to characterize the passengers satisfaction using expected utility theory, so that more practical express passenger waiting psychology.
Therefore, this paper combines one of the bus lines-56road in the Chengdu to discussion and analysis, a detailed study of the bus scheduling optimization of passenger satisfaction is considered.
First, using the time node to describe the passenger waiting-time, passenger waiting time exceeds the time node, they will choose to leave. The passengers and bus arrival at the site randomly, hence the description of passengers'satisfaction is random. Relationship model uses this expression, which combines passenger satisfaction, departure interval with the bus company benefits. At the same time, the paper also considers the cost of losses.
Next, on the theoretical analysis of the model, it is proved that the model has the optimal interval. Combined with the actual data to calculate the corresponding optimal value, the paper also provides the simulation results. One-dimensional search and simulated by MATLAB, for the first model considering the passenger satisfaction, real results in a single site model approximation and Simulation is24minutes; The sites simulation optimization of headway is8minutes. Due to the single site and the site condition of optimal departure interval is relatively different, this paper analyzes the impact of the number of stations on the optimal headway. At the same time, this paper also studies the influence of other important variables in the model on the departure interval and total net income. The arrival rate of more optimal departure interval is smaller, the more total net income; Bus travel time in the variance between two sites is more large, the smaller obtained optimal departure interval and total net income are.
Later, the paper makes the passenger satisfaction deepening. We describe the passengers using expected utility theory in satisfaction; making the passenger satisfaction description is more specific and practical.
In the end, we establish bus scheduling model with passenger satisfaction, from the risk of loss and expected utility theory to consider passenger satisfaction.We set up:bus travel time for considering bus departure interval model of passenger satisfaction of the fixed value in between two sites, and bus travel time to wait for the utility model is a random variable when the passengers at two sites. At the same time, we give a theoretical analysis of the model, which shows that the two order derivative of the first objective function is less than zero, i.e. the existence of the optimal interval that in considering the passenger satisfaction conditions, the bus company's total net income is the most. At the same time, we calculate the first-order difference for the second model, that with the increase of headway, the reduce passenger utility. The paper also combines the expected utility theory to describe the bus optimization model of passenger satisfaction, obtained in a single site in case of optimal departure interval is26minutes.
引文
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[3]Banks JH. Effect of time-value distributions on transit headway optimizations [J]. Journal of Advanced Transportation,1991,25:161-186.
[4]Mark Wardman. A review of British evidence on time and service quality valuations [J].Transportation Re-search Part E,2001,37:107-128.
[5]Gabriel R. Bitran, Juan-Carlos Ferrer and Paulo Rocha e Oliveira. Managing Customer Experiences:Perspectives on the Temporal Aspects of Service Encounters [J].Informs, 2008,10(1):61-83.
[6]李海峰,孟庆愉.顾客等待心理与商业银行服务时间的优化配置[Z].金融论坛,1999,1：30-32.
[7]周伟.旅客时间价值.交通运输工程学报,2003,3(3)：110-116.
[8]郑欢,古福.大型超市顾客交费排队系统优化分析.管理学报,2005,2(2)：171-173.
[9]宗芳,隽志才,张慧永,贾洪飞.出行时间价值计算及应用研究[J].交通运输系统工程与信息,2009,3(6)：114-119.
[10]Daniel Kanheman and Amos Tversky. An analysis of decision under risk [J]. Econometrica,1979,47(2):263-291.
[11]David Bowman, Deborah Minehart and Matthew Rabin. Loss aversion in a consumption-savings model [J]. Journal of Economic Behavior & Organization,1999, 38:155-178.
[12]Nicholas Barberis and Ming Huang. Mental Accounting, Loss Aversion, and Individual Stock Returns [J]. The Journal of Finance,2001,56(4):1247-1292.
[13]Veronika Koberling and Peter P.Wakker. An index of loss aversion [J]. Economic Theory,2005,122:119-131.
[14]Mohammed Abdellaoui, Han Bleichrodt and Corina Paraschiv. Loss Aversion Under Prospect Theory:A Parameter-Free Measurement [J]. Management Science,2007, 53(10):1659-1674.
[15]王愚,达庆利,陈伟达.基于模糊先验概率的期望效用模型[J].管理科学学报,2002,5(3)：30-34.
[16]Norman H. Jennings and Justin H. Dickins. Computer simulation of peak hour operations in a bus terminal [J]. Management Science,1958,5(1):106-120.
[17]K. Jansson. Optimal public transport price and service frequency [J]. Journal of Transport Economics and Policy,1993,27(1):33-50.
[18]Robert R. Boorstyn, Almut Burchard and Jorg Liebeherr, Chaiwat Oottamakorn. Statistical Service Assurances for Traffic Scheduling Algorithms [J]. IEEE Journal on Selected areas in communications,2000,18(12):2651-2664.
[19]田琼,黄海军.一个考虑早到惩罚的高峰期地铁乘车均衡模型[J].交通运输系统工程与信息,2004,4(4)：108-113.
[20]陈芳.城市公交调度模型研究[J].中南公路工程,2005,30(2)：162-164.
[21]韩印.基于遗传算法的智能公交发车频率优化研究[J].计算机工程与应用,2008,44(33)：243-245.
[22]张荣杰,李铁柱.基于运输效益的城市公交发车频率[J].交通科技与经,2008,5：62-64.
[23]覃运梅,王玲玲.基于遗传算法的公交发车间隔模型[J].交通与安全,2009,2(3)：110-113.
[24]许旺土,何世伟,宋瑞,赵莉,何必胜.多时段公交发车间隔优化的随机期望值模型[J].北京理工大学学报,2009,29(8)：676-680.
[25]李志强.公交车发车间隔与排队长度的研究[J].北京化工大学学报(自然科学版),2010,37(3)：131-133.
[26]王超,徐猛.考虑道路交通拥堵的公交发车间隔优化模型[J].交通运输系统工程与信息,2011,11(4)：165-172.
[27]Alan J. Miller. Model for Road Traffic Flow [J]. Journal of the Royal Statistical Society. Series B (Methodological),1961,23(1):64-90.
[28]徐向阳,徐大伟,马洪坤.公交调度中放车调度模型研究[J].交通与计算机,2003, 21(4)：19-21.
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