Analysis of passenger boarding time difference between adults and seniors based on smart card data
基于智能卡数据的成人与老年人乘客乘车时间差分析

Key words: elderly passengers; smart card data; boarding time differences; analysis of variance; regression analysis; marginal effect
关键词：老年旅客;智能卡数据;登机时间差;方差分析;回归分析;边际效应

DOI: 10.3969 /j. issn.
DOI： 10.3969 /j. issn.

ublic transit has been regarded as an essential solution to the increasing challenges of urban traffic congestion, especially in some developing countries like China. Governments and public transit agencies have taken several measures to make the public bus services more attractive to citizens.
UBLIC交通一直被认为是应对日益严重的城市交通拥堵挑战的重要解决方案，特别是在中国等一些发展中国家。政府和公共交通机构已采取多项措施，使公共巴士服务对市民更具吸引力。

Among them, one measure for attracting more passengers to take buses is to ensure bus service reliability, and another critical measure is to promote accessibility for some special passenger groups like seniors. The dwelling
其中，吸引更多乘客乘坐公交的措施之一是确保公交服务的可靠性，另一个关键措施是促进老年人等一些特殊乘客群体的无障碍。住宅

Received 2018-07-20, Revised 2018-12-10.
收稿日期 2018-07-20， 修回日期 2018-12-10.

Biographies: Lei Da (1993-), male, Ph. D. candidate; Chen Xuewu (corresponding author), female, doctor, professor, chenxuewu@ seu. edu. cn.
个人简介：大雷（1993-），男，博士生;陈学武（通讯作者），女，博士，教授，chenxuewu@。教育。快递 之 家。

Foundation item: The National Natural Science Foundation of China ( No. 51338003, 71801041).
基金项目：国家自然科学基金（71801041年第51338003号）。

Citation: Lei Da, Chen Xuewu, Cheng Long, et al. Analysis of passenger boarding time difference between adults and seniors based on smart card data[J]. Journal of Southeast University (English Edition), 2019,35 (1): 97 H02. DOI: . issn. 1003 - 7985. 2019.01. 014. time accounts for a substantial proportion of bus travel time, and thus it has a significant effect on service reliability. Besides, it is clear that the dwelling time is mainly spent in allowing passengers to get on and off the bus. Movements in the whole process of taking a bus, especially the boarding movement, reflect the accessibility to bus service for each type of passengers. Hence, a critical issue is to study the passenger boarding movement.
引自：Lei Da， Chen Xuewu， Cheng Long， et al.基于智能卡数据的成人与老年人乘客乘车时间差分析[J].东南大学学报（英文版）， 2019,35 （1）： 97 H02.DOI： .国际标准刊号。1003 - 7985.2019.01. 014.时间在公交车旅行时间中占很大比例，因此对服务可靠性有重大影响。此外，很明显，停留时间主要花在让乘客上下车上。乘坐巴士的整个过程中的移动，尤其是登车移动，反映了每种乘客对巴士服务的可及性。因此，一个关键问题是研究乘客登机运动。

Previous studies mainly focused on investigating and analyzing the determinants of bus dwelling time using field survey data on a macro level, whereas the microscopic characteristics of bus passengers in the boarding or alighting process receive little attention . Furth found that higher variability of dwelling time might increase the risk of bus service unreliability. Based on the manually collected data, Tirachini identified the effects of different factors, including the type of bus floor, the age of passengers as well as the type of fare collection system. Furthermore, by using the archived bus dispatch system data, Bertini and El-Geneidy found that the dwelling time per passenger was not necessarily related to the total number of passengers. Shalaby et al. proposed a bus travel time prediction model and discovered that the boarding passengers had a more significant influence than the alighting ones on dwelling time. Li et al. developed a simulation model to estimate the bus dwell time, and similarly, González et al. established a bus dwelling time estimation model which considered the influence of occasional incidents. Then the emergence of smart card technology provided a new and more efficient way for researchers to model the bus dwelling time and analyze the relationship between dwelling time and the boarding/ alighting process. Using the smart card data, Widanapathiranage et al. presented a model of busway station dwelling time, while Sun et al. used the smart card data for the first time to study the bus boarding and alighting dynamics by measuring the interval between two successive boarding/alighting passengers. Before their study, the average dwelling time per passenger was treated as a constant. However, they did not explore the distinct boarding/alighting characteristics of passengers at different ages. Moreover, Zhao et al. introduced the index of rank to identify how passenger boarding/alighting time changed in a dynamic process.
以往的研究主要集中在宏观层面利用实地调查数据对公交车停留时间的决定因素进行调查和分析，而公交车乘客在上下车过程中的微观特征很少受到关注 。Furth 发现，停留时间的可变性越大，可能会增加公交服务不可靠性的风险。根据人工收集的数据，Tirachini 确定了不同因素的影响，包括公交车地板的类型、乘客的年龄以及收费系统的类型。此外，通过使用存档的公交调度系统数据，Bertini和El-Geneidy 发现，每位乘客的停留时间不一定与乘客总数相关。Shalaby等人 提出了公交车出行时间预测模型，发现上车乘客比下车乘客对停留时间的影响更大。Li等人 开发了一个模拟模型来估计公交车停留时间，同样，González等人 建立了一个公交车停留时间估计模型，该模型考虑了偶发事件的影响。然后，智能卡技术的出现为研究人员提供了一种新的、更有效的方法，可以对公交车停留时间进行建模，并分析停留时间与上下车过程之间的关系。Widanapathiranage等人利用智能卡数据 提出了一个公交车站停留时间模型，而Sun等人则首次 使用智能卡数据，通过测量两个连续上下车乘客之间的间隔来研究公交车上下车的动态。 在他们的研究之前，每位乘客的平均停留时间被视为一个常数。然而，他们没有探讨不同年龄乘客的明显上下车特征。此外，Zhao等人 还引入了等级指数来识别乘客上下车时间在动态过程中的变化。

Although some researchers applied the smart card data
尽管一些研究人员应用了智能卡数据
to the study of passenger boarding/alighting behavior, few of them took ages into account in their articles. However, this attribute of passengers plays a vital role in determining passenger movement time since different types of passengers may spend different amounts of time when boarding or alighting a bus.
在研究乘客上下车行为时，很少有人在文章中考虑年龄。然而，乘客的这一属性在决定乘客移动时间方面起着至关重要的作用，因为不同类型的乘客在上下车时可能会花费不同的时间。

In China, most of the smart card systems only have passenger boarding records. Given this limilation, our study focuses on the microscopic analysis of the passenger boarding process. There are two objectives in this study: the first one is to identify the difference of the boarding time between adults and seniors, and the second one is to investigate the effect of various factors on passenger boarding time.
在中国，大多数智能卡系统只有乘客登机记录。鉴于这种轻量化，我们的研究重点是对乘客登机过程的微观分析。本研究有两个目标：第一个是确定成人和老年人登机时间的差异，第二个是调查各种因素对乘客登机时间的影响。

Changzhou is a prefecture-level city in southern Jiangsu province of China, bordering the provincial area of Nanjing to the west and Zhejiang province to the south. As a part of China's highly developed Yangtze Delta region, Changzhou now covers an area of 4385 square kilometers, with a total population of 4.7 million in its five urban districts and one satellite city. There is no metro service in Changzhou now. However, over 260 bus lines have formed an effective bus system, and bus trips account for of daily trips for all citizens in Changzhou .
常州是中国江苏省南部的一个地级市，西与南京省接壤，南与浙江省接壤。常州是中国高度发达的长江三角洲地区的一部分，目前面积4385平方公里，5个城区和1个卫星城总人口470万。常州现在没有地铁服务。然而，260多条公交线路已经形成了一个有效的公交系统，公交出行 占常州 市民的日常出行量。

The smart card automatic fare collection (AFC) system was introduced in Changzhou in October 2001, which aims to decrease cash transactions. Passengers only need to tap their smart cards at the front door when boarding and all the buses have only one card reader at the front door. Besides, bus lines in Changzhou charge the same price, which is not distance-based. Either cash or smart cards can make the payment, but smart card users can enjoy a fare discount from to . Moreover, seniors over 70 years old can enjoy the bus services for free. It was reported that more than of public transportation passengers in Changzhou used the smart card for payment in 2015. This proportion reached in some of the bus lines. When a passenger is tapping on from a bus, the detailed transaction information is recorded, including time, bus ID, bus lines ID, smart card ID, the type of smart card and other operational data.
2001年10月，常州市引进了智能卡自动收费系统，旨在减少现金交易。乘客上车时只需在前门点击智能卡，所有巴士在前门只有一个读卡器。此外，常州的公交线路收费相同，不按距离计算。现金或智能卡都可以付款，但智能卡用户可以享受从 到 的票价折扣。此外，70岁以上的老年人可以免费享受巴士服务。据报道，2015年常州市有超过 的公共交通乘客使用智能卡进行支付。这一比例在一些公交线路中达到 。当乘客从公交车上点击时，会记录详细的交易信息，包括时间、公交ID、公交线路ID、智能卡ID、智能卡类型和其他操作数据。

It should be noted that the transit system in Changzhou has an independent AFC system and the automatic vehicle location (AVL) system, which means that we cannot directly obtain the location of each boarding transaction. Hence, identifying the boarding location of each record is a significant issue for further studies in this research. Different from some other smart card systems in the world with complete information about boarding and alighting, the system in Changzhou, like most cities in China, can only provide boarding records. Besides, there is no automatic passenger counter (APC) system in Changzhou, which means that we cannot obtain the number of onboard passengers for each moving bus. Note that passengers are restricted to boarding at the front door and alighting at the rear door.
需要注意的是，常州的公交系统有独立的AFC系统和自动车辆定位（AVL）系统，这意味着我们无法直接获取每笔登车交易的位置。因此，确定每条记录的登机位置是本研究进一步研究的重要问题。与世界上其他一些拥有完整上下车信息的智能卡系统不同，常州的系统与中国大多数城市一样，只能提供登车记录。此外，常州没有自动乘客计数器（APC）系统，这意味着我们无法获得每辆移动巴士的乘客人数。请注意，乘客只能在前门上车，在后门下车。

This study contains one-week anonymous smart card data from March, 16th to 22nd, 2015 in Changzhou. We collected more than smart card transaction records from six bus lines with a high proportion of elderly passengers and a high rate (around 90%) of those making payments by smart card. The reasons why we choose smart card data from six bus lines are as follows: Firstly, all these bus lines have a relatively high proportion of elderly passengers (over ). Secondly, a cash payment made by passengers can create a large time interval, in that case, we cannot apply the recorded time from consecutive smart card data to calculate the boarding gaps and use it to approximate passenger boarding time. Therefore, it is necessary to select data from a dataset which has few cash transactions.
本研究包含 2015 年 3 月 16 日至 22 日在常州进行的为期一周的匿名智能卡数据。我们从六条公交线路收集了超过 智能卡的交易记录，这些线路的老年乘客比例很高，使用智能卡付款的比例很高（约90%）。我们从六条公交线路中选择智能卡数据的原因如下：首先，所有这些公交线路的老年乘客（超过） 比例都相对较高。其次，乘客的现金支付可能会产生很大的时间间隔，在这种情况下，我们无法应用连续智能卡数据中记录的时间来计算登机间隔并用它来估算乘客的登机时间。因此，有必要从现金交易很少的数据集中选择数据。

It is acknowledged that there are more than five types of cards used in the transit system. However, students, the disabled and other types of passengers make up only an extremly small proportion of the total number of passengers, which are ignored in the analysis. This research only focuses on analysis and modeling of adult and elderly passengers.
众所周知，交通系统中使用的卡不止五种。然而，学生、残疾人和其他类型的乘客只占乘客总数的极小比例，在分析中被忽略了。本研究仅侧重于对成人和老年乘客的分析和建模。

Tab. 1 shows the characteristics description of the operating buses. The contents include more than 20 fields of information, but only six fields are used in this study as listed in the table, including bus line ID, vehicle name, entrance type, length and number of doors. In Changzhou, most of the bus lines only have one type of vehicle.
表 1 显示了运行总线的特性描述。内容包括 20 多个信息字段，但本研究中仅使用了 6 个字段，如表中所列，包括公交线路 ID、车辆名称、入口类型、长度和门数。在常州，大多数公交线路只有一种车辆。

Tab. 1 Bus characteristics description
表1 总线特性说明

Tab. 2 presents the description of the smart card data structure. In our research, only four recorded fields are used to analyze passenger boarding behavior: Card type, tapping time, bus ID and bus line ID.
表 2 显示了智能卡数据结构的说明。在我们的研究中，只有四个记录字段用于分析乘客的登机行为：卡类型、点击时间、公交 ID 和公交线路 ID。

Tab. 2 Smart card data structure description
表2 智能卡数据结构说明

Due to the requirement of identifying passenger boarding location, GPS data are also obtained from the AVL system. Tab. 3 shows the detailed contents of GPS data.
由于需要识别乘客登机位置，GPS数据也从AVL系统获得。表3显示了GPS数据的详细内容。

Tab. 3 GPS data structure information
表3 GPS数据结构信息

Data preprocessing is required before passenger boarding behavior analysis and modeling. The first step in data preprocessing is to determine the bus stop where the smart card users board. By linking the bus ID and bus line ID, we can narrow down the possibilities of the boarding location. Then, if we find that the tapping time in the smart card data is between the arrival time and departure time of one bus, we find the accurate boarding stop for this smart card record. The next step is to compute the boarding gap between two successive boarding records of two passengers. The computed boarding gap is the approximated boarding time for the latter passenger. In this way, we should notice that the boarding gap of the first passenger at each stop cannot be calculated, so the number of recorded activities is one fewer than the actual number of the boarding passengers. Since the smallest unit of the bus boarding gap is a second, the minimum gap is . Also, we will only use the terminology "boarding gap" to stand for the time that one passenger spends in boarding a bus in the rest of this research in order to avoid confusion. Fig. 1 shows a complete process of computing passenger gaps.
在对乘客登机行为进行分析和建模之前，需要对数据进行预处理。数据预处理的第一步是确定智能卡用户上车的公交车站。通过链接公交 ID 和公交线路 ID，我们可以缩小乘车位置的可能性。然后，如果我们发现智能卡数据中的点击时间介于一辆公共汽车的到达时间和出发时间之间，我们就会找到此智能卡记录的准确登车站。下一步是计算两名乘客的两个连续登机记录之间的登机间隔。计算出的登机间隔是后一名乘客的近似登机时间。这样，我们应该注意到，每个站点的第一位乘客的登机间隔无法计算，因此记录的活动数量比实际登机乘客的数量少一个。由于公交车上车间隔的最小单位是秒，因此最小间隔是 。此外，为了避免混淆，我们将仅使用术语“登机间隔”来代表一名乘客在登车时花费的时间。图1显示了计算乘客差距的完整过程。

Some extreme large gaps are defined as outliers in this study. These outliers are mainly caused by the following factors: 1) Passengers making payments by cash (Approximately of payments in the records are made by cash) ; 2) The passenger taking his card out after boarding; 3) Bus drivers waiting for the late-coming passengers. The clustering-based method is implemented to detect and clear the outliers.
在本研究中，一些极端较大的差距被定义为异常值。这些异常值主要由以下因素引起：1）乘客用现金付款（记录中的付款大致 是用现金支付）;2）旅客登机后取出办理卡;3）巴士司机等待迟到的乘客。实现基于聚类的方法，用于检测和清除异常值。

Visual program language and structured query language (SQL) are applied to accomplish the processes above.
应用可视化 程序语言和结构化查询语言 （SQL） 来完成上述过程。

Fig. 1 Process of computing boarding gaps
图1 登机间隙的计算过程

The critical issue of this study is to figure out if there is a statistically significant difference in the boarding gap between adult passengers and elderly passengers. Thus, we calculate the statistics of boarding gap for adult passengers and elderly passengers. The percentages of the boarding gap for both types of passengers are computed by dividing the total number of boarding records for one type of passenger by the number of different boarding gaps. The line charts in Fig. 2 show the percentages of boarding gaps for both adult and elderly passengers. The scale of the vertical axis reflects the value of the frequency distribution. The scale of the horizontal axis indicates time durations of different boarding gaps. As can be seen in Fig. 2, elderly passengers are likely to spend more time when boarding a bus.
本研究的关键问题是弄清楚成年乘客和老年乘客之间的登机差距是否存在统计学上的显着差异。因此，我们计算了成年乘客和老年乘客的登机差距统计数据。两种类型乘客的登机间隔百分比是通过将一种乘客的登机记录总数除以不同登机间隔的数量来计算的。图 2 中的折线图显示了成人和老年乘客的登机间隔百分比。纵轴的刻度反映了频率分布的值。横轴的刻度表示不同登机间隔的时间持续时间。从图2可以看出，老年乘客在上车时可能会花费更多的时间。

Descriptive statistics ( see Tab.4) demonstrate that the average boarding gap of elderly passengers is higher than that of adult passengers. Then, we conduct a one-way analysis of variance (ANOVA) to further check the difference in their average boarding gaps by examining the variances of samples.
描述性统计（见表4）表明，老年乘客的平均登机差距高于成年乘客。然后，我们进行单因素方差分析（ANOVA），通过检查样本的方差来进一步检查其平均登机差距的差异。

Analysis of variance is a hypothesis-testing technique used to analyze the differences among means. In this study, ANOVA allows us to determine whether there are systematic treatment effects that cause the mean in one group to differ from the mean in another. Note that using ANOVA to compare the means from two independent samples is equivalent to using a test to make this comparison. However, ANOVA seems to be more suitable for this research due to its conservativeness . The results of ANOVA are presented in Tab. 5.
方差分析是一种假设检验技术，用于分析均值之间的差异。在这项研究中，方差分析使我们能够确定是否存在系统治疗效应，导致一组的平均值与另一组的平均值不同。请注意，使用方差分析比较两个独立样本的均值等同于使用 检验进行此比较。然而，方差分析由于其保守性 ，似乎更适合这项研究。方差分析的结果见表5。

From these results, we can demonstrate that the difference in boarding gap between these two types of passengers reaches a significant level. Thus, we should take into account this difference in the following study.
从这些结果中，我们可以证明这两类乘客之间的登机差距差异达到了显着的水平。因此，我们应该在下面的研究中考虑到这种差异。

(a)

(d)

(b)

(e)

(c)

(f)

Fig. 2 Distribution of boarding gap. (a) Bus line 6 with one-step entrance; (b) Bus line 12 with one-step entrance; (c) Bus line 14 with onestep entrance; (d) Bus line 16 with one-step entrance; (e) Bus line 39 with two-step entrance; (f) Bus line 56 with two-step entrance
图2 登机间隙分布图。（a） 6号线巴士，一进式出入口;（b） 12号线公交车，一进门;（c） 14号线公交车，一进门;（d） 16号巴士线，一进门;（e） 39号巴士线，设有两级入口;（f） 56号巴士线，设有两级入口

Tab. 4 Statistics of passenger boarding gap
表4 旅客登机差距统计

Tab. 5 ANOVA for adult and elderly passengers
表5 成人和老年乘客的方差分析

Although the descriptive analysis in Section 2.1 has already revealed the variation of gaps to some extent, it is necessary to further explore changes in the dynamic boarding process before conducting the regression analysis. Fig. 3 presents the trends of the average boarding gap against the volume of boarding passengers at each bus stop. The average boarding gap has the highest variability with a large range of possible values for the average boarding gap when there is only one recorded boarding activity. The trend of this variation is clearly shown in the boxplot. As the number of passengers boarding a bus at a bus stop increases, the variability of the average boarding gap duration decreases and finally reaches a relatively stable value of . This pattern of variation is a reflection of the marginal effect of each extra boarding passenger on the dynamic process of boarding a bus. Considering the difference in boarding behaviors between adults and the elderly, we add the marginal effect for additional boarding of each type of passengers into our model. However, the marginal effects of adult and elderly passengers on can be reasonably complicated in this re- search since adults and the elderly have mutual influences on each other when boarding buses. In other words, we can claim four or even more types of marginal effects when we study this process, namely, the marginal effects of each additional boarding on the average boarding gap of adult passengers and elderly passengers, respectively.
尽管第2.1节中的描述性分析已经在一定程度上揭示了差距的变化，但在进行回归分析之前，有必要进一步探讨动态登机过程的变化。图 3 显示了每个巴士站的平均登车间隔 与上车乘客量的趋势。平均登机间隔 的变异性最大，当只有一次记录的登机活动时，平均登机间隔的可能值范围很大。这种变化的趋势清楚地显示在箱线图中。随着在公交车站上车的乘客人数的增加，平均上车间隔持续时间的变异性减小，最终 达到相对稳定的值 。这种变化模式反映了每个额外的登机乘客对上车动态过程的边际影响。考虑到成人和老年人登机行为的差异，我们将每种类型乘客额外登机的边际效应添加到我们的模型中。然而，成人和老年乘客对 乘客的边际影响在这次重新搜索中可能相当复杂，因为成人和老年人在上车时相互影响。换句话说，当我们研究这个过程时，我们可以声称有四种甚至更多类型的边际效应，即每增加一次登机对成年乘客和老年乘客平均登机差距的边际效应。

Fig. 3 Trend of average boarding gap against the volume of boarding passengers
图3 平均登机差距与登机旅客量的趋势

To simplify our analysis, we only consider two marginal effects: 1) The marginal effect of extra boarding ( no matter what type of passengers they are) on the average boarding gap of adult passengers ;2) The marginal effect of extra boarding on the average boarding gap of elderly passengers .
为了简化我们的分析，我们只考虑两个边际效应：1）额外登机（无论他们是什么类型的乘客）对成年乘客 平均登机差距的边际效应;2）额外登机对老年旅客 平均登机差距的边际效应。

Also, we include one dummy variable , which is active to be one if one bus has a two-step entrance; otherwise equals zero, representing a low floor entrance. One can expect that setting a two-step entrance in a bus increases passenger boarding gaps. Using a nonlinear regression model, we can measure the average cost of each
此外，我们还包括一个虚拟变量 ，如果一辆公共汽车有两步入口，则该变量为活动变量;否则 等于零，表示低楼层入口。可以预期，在公共汽车上设置两步入口会增加乘客的登机差距。使用非线性回归模型，我们可以衡量每个模型的平均成本
adult passenger boarding and elderly passenger boarding :
成人乘车 和老年乘车 ：

where denotes the total passenger boarding time at each bus stops; and are the time for the last passenger and the first passenger to board one bus, respectively; is the number of recorded boarding activities of adult passengers for each stop; represents the number of recorded activities of elderly passengers at each stop; is the total number of recorded boarding passengers and is the residual of the model; and represent the basic average boarding gaps for adult passengers and elderly passengers, respectively; and are the parameters indicating the contribution of bus entrance type to adult and elderly passengers. The regression results are shown in Tab. 6 .
其中 ，表示乘客在各巴士站的总上车时间; 分别 是最后一名乘客和第一名乘客登上一辆公共汽车的时间; 是每个站点记录的成年乘客登机活动次数; 代表每个站点记录的老年乘客活动次数; 是记录的登机乘客总数， 是模型的残余; 分别 代表成年乘客和老年乘客的基本平均登机间隔; 并且是 指示公交车入口类型对成人和老年乘客的贡献的参数。回归结果如表6所示。

Tab. 6 Results of regression analysis
表6 回归分析结果

From the modeling results, we find that there is a difference of passenger between adults and seniors in the basic boarding gaps, namely and , suggesting that even without considering the specific characteristics of the bus, seniors are slower to board buses. The effects due to the existence of a two-step entrance at the front door are significant, increasing both the average boarding gaps for adults by and seniors by 0.120 , respectively. Note that there is a small distinction of between and , suggesting that the effect of the step entrance is higher for the elderly. We also find that the total number of recorded boardings has a negative marginal impact on the average boarding gap for both adults and seniors , indicating that the average boarding gap decreases with the increase of boarding passengers, which is consistent with the findings obtained by Sun et al . There is a clear difference betw een and , suggesting that the marginal effect is more significant for elderly passengers. To sum up, the process of tapping smart cards and waiting for reader responses accounts for a substantial part of the boarding time , and indeed seniors spend more time than adults in this process. Besides, the one-step entrance enables passengers to board more quickly than a two-step entrance by reducing the extra effort for passengers to walk up the steps, espe- cially for the elderly.
从建模结果中发现，成人和老年人在基本乘车差距上 存在乘客差异，即 和 ，这表明即使不考虑公交车的具体特征，老年人上车的速度也较慢。由于前门存在两级入口，其影响是显着的，成人 和老年人的平均登机差距分别增加了 0.120 。请注意，和 之间 有很小的 区别，表明阶梯入口对老年人的影响更高。我们还发现，记录的登机总数对成人和老年人的平均登机差距都有负的边际影响，表明平均登机差距随着登机乘客的增加而减小，这与Sun等人获得的研究结果一致 。和 之间存在明显的差异 ，表明边际效应对老年乘客更为显著。综上所述，点击智能卡和等待读者回复的过程占了登机时间的很大一部分，事实上，老年人在这个过程中花费的时间比成年人多。此外，一步式入口比两步式入口更快速上车，减少了乘客走上台阶的额外努力，尤其是老年人。

In this paper, regression analysis is conducted using data from the automatic fare collection system in Changzhou, with the objective of quantifying the boarding gap and difference between adult and elderly passengers and analyzing the influence of the specific determinants of total boarding time at each bus stop, such as age and steps inside buses. The results of ANOVA demonstrate that there is a statistically significant difference between adults and seniors in the time spent on boarding a bus. In regression analysis, the model is estimated to account for the total time for a queue of passengers to boarding. We find that there are some negative marginal effects on both adults and seniors , indicating that a high demand for taking a bus speeds up the boarding process of a queue of passengers waiting at a bus stop by decreasing the average passenger boarding time. Moreover, this effect is greater on seniors than adults. From an operational aspect, this marginal effect brings extra variability in the boarding process and then this is expected to have an impact on bus service reliability. Besides, the existence of a two-step entrance is found to make the boarding process slower, which is an expected outcome. This negative impact is more significant in seniors than adults. Although the total boarding time cannot adequately represent bus dwelling time, it can be seen as an essential component of the time spent on transferring passengers. Some policy recommendations might be proposed based on the results of our study. Seniors usually spend more time boarding a bus and bring more variability to the dynamic boarding process. Thus, it might be a cost-effective way for bus agencies to provide customized bus services for the elderly , using low floor buses with optimal capacity , to improve the efficiency of the whole transit system.
本文利用常州市自动收费系统的数据进行回归分析，旨在量化成人和老年乘客的乘车差距和差异，并分析每个公交车站总乘车时间的具体决定因素的影响，如车龄和车内步数。方差分析的结果表明，成人和老年人在上车时间上存在统计学上的显着差异。在回归分析中，该模型估计考虑了乘客排队登机的总时间。我们发现对成年人和老年人都有一些负面的边际效应，这表明对乘坐公共汽车的高需求通过减少乘客的平均上车时间来加快在公共汽车站等候的乘客的上车过程。此外，这种影响对老年人的影响大于成年人。从运营方面来看，这种边际效应会给上车过程带来额外的可变性，然后预计这将对公交服务的可靠性产生影响。此外，发现两步入口的存在使登机过程变慢，这是预期的结果。这种负面影响在老年人中比在成年人中更为显着。虽然总上车时间不能充分代表公交车停留时间，但它可以看作是换乘乘客所花费时间的重要组成部分。根据我们的研究结果，可能会提出一些政策建议。老年人通常会花更多的时间登上公共汽车，并为动态登车过程带来更多的可变性。 因此，对于公交机构来说，使用具有最佳容量的低地板公交车，为老年人提供定制的公交服务，以提高整个公交系统的效率，这可能是一种具有成本效益的方式。

Acknowledgments The authors appreciate Changzhou Public Transportation Group Corporation for providing the data used in this study.
致谢 作者感谢常州公共交通集团公司提供本研究中使用的数据。

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