Study on the Selection Model of Staying Adjustment Bus Lines along Rail Transit

To fully achieve effective rail transit, prevent the waste of conventional bus capacity along a rail transit line, and relieve the urban traffic congestion problem, it is necessary to screen for the adjustment of conventional bus lines prior to the operation of rail transit to provide a basis for further optimization of bus lines. Based on the analysis of spatial relationships between a rail transit line and conventional collinear bus lines and considering the time advantage characteristics of rail transit in rush hours, a model of the generalized travel time costs and travel time savings proportion in the collinear section of rail transit and bus was proposed. To evaluate the utility of rail transit relative to conventional bus collinear lines, the conventional bus lines to be adjusted were determined. Taking Xiamen as an example, the bus lines of Hubin East Road Station as the endpoint of metro line 1 were employed to calculate the model using GPS data of the buses, and the bus lines to be adjusted in the Hubin East Road were determined. The results show that the model is effective in the elastic selection of conventional bus lines that need to be adjusted and provides decision-making support for urban comprehensive public transport planning.


Introduction
In the process of continuous urbanization, the urban scale and population keep expanding, and the demand for long-distance and large-volume transportation keeps growing. However, limited by urban road resources, traffic congestion is formed. erefore, the development mode of "public transport priority" emerged at a historic moment [1]. Rail transit, with its advantages of large volume, fast speed, and punctuality, occupies a dominant position in the public transport system and is widely considered as the main way to solve urban traffic problems. Because rail transit needs to carry the main flow of urban passenger flow, line alignment is usually repeated with the layout of dense urban main and secondary trunk lines of conventional bus lines. To achieve a large volume a er the operating of rail transit and prevent the waste of conventional bus capacity, the optimization and adjustment of conventional bus lines along rail transit need to be evaluated prior to the operation of a rail transit system.
A er the operating of rail transit, passengers of conventional buses along the line are attracted, which requires some conventional bus lines to be adjusted and reorganized before the rail transit is operated. Public transportation system a er the introduction of rail transit has been widely studied, mainly focusing on the network integration of the metro bus system, the evacuation planning of rail interruption, and the social benefits of the metro bus system [2][3][4][5][6][7]. However, the optimization and adjustment of rail transit and bus network mostly consider their coordinated operation. Some scholars determined the lines that need to be adjusted by studying the regions where passenger flows competed between rail transit and bus [8,9]. is paper starts with the collinearity characteristics of rail transit and conventional bus, evaluates the utility of rail transit and conventional bus of the collinear channel, and adjusts the conventional bus lines before the rail transit is operated, so as to avoid the waste of conventional bus capacity.
Whether from the traffic demand or direct policy initiatives, urban public transport system with rail transit as the main and conventional bus as the auxiliary has become an inevitable trend [10]. To ensure a large capacity of rail transit and avoid the waste of conventional bus capacity, it is necessary to optimize and adjust the conventional bus lines along the rail transit line in advance before the rail transit is put into operation. Since the problem of traffic congestion in rush hours need to be improved first a er the rail transit is introduced, this paper first considers the time advantage brought by the rail transit in rush hours and the time utility of the rail transit and conventional bus in collinear channel. Based on this evaluation, the conventional bus lines to be adjusted are determined, which provides a basis for further formulating adjustment measures.

Literature Review
With the large-scale development of rail transit, most scholars have focused on the integration of metro and bus system from the perspective of public transport network. e complementary capacity of bus services to the metro network can be improved by optimizing the connectivity between the two systems, which mainly concentrates on the construction of metro bus integrated network and their coordinated operation level. Jin et al. [2] focused on introducing localized integration with bus services. A two-stage stochastic programming model was developed to assess the intrinsic metro network resilience as well as to optimize the localized integration with bus services. Song et al. [4] determined the lines of ridership reduction under the influence of the metro and evaluated different bus service patterns using a pivot point demand model to "feed" various metro stations. Sun et al. [5] took the integrated network of rail transit and bus lines as the subject of study and build a multi-objective programming model for bus network optimization and adjustment to adjust the route direction and operation parameters. Qin and Zhou [8,9] determined the collinear length of bus lines that need to be adjusted (above 6 km) by evaluating the length of passenger flow competition interval generated by bus and rail transit. In addition, as a mode of transportation with large volume, evacuation planning for rail transit is an important consideration. Zhang et al. [6] determined the initiation time of substitute bus services for metro disruption management, especially under uncertain recovery time by trading-off their initiation cost and passenger delay cost, thereby minimizing the total system cost. Lv et al. [3] developed an evacuation planning model based on the interval chance-constrained integer programming (EICI) method in response to bus-subway corridor incidents. With the rapid development of metro bus system, scholars have begun to pay attention to its social benefits. Zolnik et al. [7] explored who benefits from metro bus system according to the rider and the commuter data sources, respectively, as well as how they benefit, taking Lahore's new metro bus system as an example. e optimization and adjustment of conventional bus lines mostly consider the integration of line network, and seldom study it from the perspective of passenger's travel utility. Due to the different attributes of travel time and cost of rail transit and conventional bus, the travel utility of rail transit and bus in the collinear channel is different, and passengers' choices of travel modes are different. In previous studies, the generalized travel cost has contained important travel characteristic information and is usually used as an evaluation index of travel utility in studies of travel mode choice [11][12][13][14]. For example, Feng and Yang [12] took the generalized travel cost as the travel utility, improved the traditional logit model, and predicted the sharing rate of travel modes. In this paper, the concept of the generalized travel time cost is introduced by referring to the study of generalized travel cost, and the travel utility of bus and rail transit of the collinear section is evaluated, followed by determining whether most passengers will choose rail transit during peak hours to identify the conventional bus lines that need to be adjusted before the rail transit is operated. In general, the generalized travel cost includes the costs of travel time, travel cost, and travel comfort [12,14,15]. Additionally, some scholars have also considered the travel time uncertainty [13,16]. e indicators of travel time are usually based on traffic survey data [12][13][14] or a conversion between the travel distance and average speed of transportation modes [17]. e index of travel cost has usually been measured by the fare level of the mode of transportation [12,13]. However, the measurement indicators of travel comfort have mostly used the degree of crowding [13], travel time [14], travel distance [15], etc. In the actual process, travel comfort is difficult to quantify, and there is no unified quantitative algorithm at present. To facilitate the calculation, the generalized travel costs in existing studies were converted into costs [12][13][14][15]. For value conversion between time and cost, the production method, income method, and disaggregate model are the most prevalent methods used for calculating the travel time value [12,13,[17][18][19]. Referring to the generalized travel cost, this paper mainly evaluates the travel utility of bus and rail transit in the collinear channel. To highlight the time utility of rail transit during peak periods, the generalized travel cost is converted into time for calculations. Meanwhile, since the travel time of conventional buses is extremely unstable due to the impact of road congestion in rush hours, this paper uses vehicle GPS data to conduct a statistical analysis of the travel time of conventional buses, including time uncertainty factors, to obtain a more stable and accurate time utility. For the value conversion between time and cost, this paper adopts the income method and production method, respectively. Moreover, the travel comfort is related to personal physical exertion and the perceived degree of congestion, which is difficult to evaluate for the majority of passengers. While travel congestion during rush hours leads to little difference in the comfort between conventional buses and rail transit, comfort is not considered in this paper. In summary, this paper introduces the concept of the generalized travel time, evaluates the travel time and travel cost of conventional bus and rail transit in the collinear channel, builds a model of the generalized travel time cost and travel time savings proportion, and determines the conventional bus lines along the rail transit that need to be adjusted. e adjustment of conventional bus lines along the rail transit takes place a er the rail transit is put into operation, so the adjustment of conventional bus lines lags behind [2,4,8,9,10]. In practice, most cities have applied an experience value of the uniform index of greater than a collinear length of above 6 km in China [10], and the utility of rail transit relative to conventional bus along the line was not considered for targeted adjustment. In this paper, the time advantage of rail transit is taken into consideration first. On the basis of analyzing the spatial relationship between rail transit and bus lines, a generalized travel time cost and travel time savings proportion model is established for the rush hours of the collinear section of bus and rail transit. e model considers the road traffic conditions during rush hours, the transfer time of conventional bus and rail transit, the distance between two stations, the rail transit station design and other factors, which flexibly screens the conventional bus lines to be adjusted. e model provides a basis for further optimization of conventional bus lines in the collinear section of the rail transit. is research provides decisional support for urban integrated public transport planning.

Concept of Collinear Lines.
In the same passenger flow corridor, when the direction of a conventional bus line is similar to that of a rail transit line and within the service area on both sides of the rail transit line, both lines are collinear. Collinear lines can be classified as follows: fully collinear line, intermediate collinear line, and endpoint collinear line [21]. Due to the different services provided by rail transit and conventional bus transit, no fully collinear line exists. As a result, the intermediate collinear line and the endpoint collinear line are the main subjects in this paper (as shown in Figure 1). e study area of the collinear line depends on the service radius of the rail transit affected by the service radius of the rail transit station, which can be considered as the direct service area of the rail transit. According to the "Guidelines for Planning and Design of Urban Rail Areas" [22] issued by the Ministry of Housing and Urban-Rural Development, the influence area of a rail transit station refers to an area that is approximately 500-800 m from the rail transit station, in which the station entrance can be accessed within approximately 15 min of walking and is closely related to the rail transit function. According to the urban practice experience in China, the direct-attractive range of the station is an area that is perpendicular to a rail transit line within 750 m on each side. At the end of the line, the range is a radius of 750 m from the station [23]. erefore, this paper employs 750 m as the research range of the collinear line (as shown in Figure 2).

Spatial Relationship between Collinear Bus Lines and
Rail Transit Line. For the endpoint collinear line, due to the existence of a breakpoint point between the conventional bus line and the rail transit line, the original conventional bus passengers will transfer once in the collinear section when moving to rail transit, and the research object can be abstractly described as the "point-line" spatial mode. However, two breakpoints exist between the conventional bus line and the rail transit line in the collinear section of the intermediate collinear line. e original conventional bus passengers will transfer twice in the collinear section when moving to rail transit, and the research object can be abstractly described as the "point-line-point" spatial mode (as shown in Figure 3).

Factors Affecting the Adjustment of Bus Lines along Rail
Transit. A er operation of the rail transit commences, travel time is saved due to the advantage of fast speed. To screen the conventional bus lines to be adjusted to be collinear with the rail transit, the influencing factors of the travel utility of passengers between rail transit and conventional buses in the collinear section should be analyzed.

Generalized Travel Time Costs (1) Generalized Travel Time Costs of Conventional Buses
(i) Travel Time. During peak hours, due to the congestion of urban roads, the speed of each bus and the stop time at each stop differ. e average travel time of the vehicles in the collinear section also differs. erefore, this paper uses the real-time GPS trajectory data sent by the floating vehicle equipped with GPS equipment to dynamically acquire information such as the time, vehicle terminal ID, latitude and longitude coordinates, instantaneous speed, direction, and calculates the average travel time of the collinear vehicles in peak hours to obtain the conventional bus travel time .
(ii) Time Conversion Value of the Travel Cost. By the investigation and study of conventional bus fares in China, most cities such as Foshan, Wuxi and Jinan have adopted a transfer discount system. is paper adopts a discount system of transfers, and the model is constructed according to the actual travel processes of residents in terms of the public transport fare expenditure. e travel cost of conventional buses in collinear section can be expressed as follows: In the equation, is the fare level for a conventional bus (yuan/ride); is the discount rate of transferring for the conventional bus; and is the number of bus rides on one trip. e original conventional bus travel cost only calculates the travel costs of the passengers on collinear lines. No transfer occurs, that is, only one bus ride, 푎 = 1.
different modes of transportation within the same passenger flow corridor during peak hours, so as to satisfy the travel needs of passengers.

Generalized Travel Time Costs.
Public transportation during peak hours primarily consists of the mass commuter group. Usually, the production method and the income method are used to calculate the travel time value. With the popularity of global positioning systems, using big data to obtain traffic status has been widely applied. In this paper, when comparing the travel utility of rail transit and conventional buses in a collinear section, the advantage of time savings of rail transit is first considered, which is converted into the time cost and used as the evaluation index of comprehensive utility. e aggregate model of the travel time and the time conversion value of the travel cost of the collinear section are established using the GPS data of buses.

Travel Time Saving
Proportion. Among the changes in travel time before and a er the travel mode transfer, the proportion of travel time savings within 10% can be considered as no travel time savings [20]. e proportion of travel time savings refers to the proportion of the time saved a er transferring to rail transit relative to the original bus travel time. erefore, in this paper, the proportion of time saved by choosing rail transit in the collinear section is defined as less than 10% of the total travel time of the conventional bus line, which indicates that the rail transit has no time advantage in the collinear section, that is, the time services provided by the two modes in the transport corridor are equal.

Model Construction
e "point-line" space mode diagram is shown in Figure 4. When passengers choose rail transit in the collinear section, they need to have a transfer, that is, a transfer from the conventional bus to rail transit. By (1) conventional bus to rail transit; is the walking time to the station during transferring; is the walking time in the rail transit station; and w is the waiting time in the rail transit station. e average travel time of the rail transit in the collinear section can be converted according to the total running time of the rail transit line and the proportion of collinear line mileage. e waiting time in the station can be defined according to the maximum tolerance time of passengers, which is usually the average travel time of the two stations with the minimum distance on the rail transit line. e passenger's walking time is determined by the standardized design of the rail transit station. According to the Metro Design Code [24], the space for walking primarily includes the entrance and exit, the station hall (passage, stairs or escalator), and the platform (as shown in Figure 5). e walking time to the station and the walking time in the station during the transfer process are defined according to the total distance traveled and the average walking speed of a passenger in the station, as shown in Equations (5) and (6).
In the equations, 0 is the walking distance to the station; v 0 is the walking speed of an ordinary adult; 1 is the walking time of the station exit/entrance; 2 is the walking time on the passage, stairs or escalator; and 3 is the walking time on the platform.
According to the calculation results of the passenger's value of the time unit (yuan/min), the time conversion value (min) of the travel cost a er conversion can be expressed as follows: In this equation, is the travel cost of conventional bus transit, and is the value of the hour unit. e generalized travel time cost of the conventional bus in the collinear section is equal to the sum of the travel time and the time conversion value of the travel cost, which can be expressed as follows: (3) (4) 푇 0 = 푇 + 푇 = 푇 + 푡 + 푡 + 푡 w .  In the equation, ὔ is the transfer time from rail transit to the conventional bus; ὔ is the walking time to the bus stop when transferring; and ὔ w is the waiting time at the bus stop. In the transfer time from rail transit to bus, the walking time to the bus stop ὔ is measured using the method in Section 4.1.1. However, the waiting time at the bus stop ὔ w is half of the average departure interval of conventional bus lines, referring to existing research [25]. In terms of travel cost, when choosing rail transit, there will be a transfer in the conventional bus itself, which requires increasing the fare of the conventional bus. erefore, the generalized travel time costs of rail transit can be expressed as: In the formula, ὔ is the time of the second transfer, and the number of bus rides 푎 = 2.
e passenger's transfer walking time 1 , 2 , and 3 inside the station can be estimated according to the design of the station, as shown in Equations (7), (8), and (9). According to the graphic design of the station, the walking distance of the exit/entrance, the plane distance of the entrance stairs or the escalator, the walking distance of the hallway, the plane distance of the stairs or escalators in the hall, and the plane distance of the platform when waiting can be measured, and expressed as 1 , 耠 1 , 2 , 耠 2 , and 3 , respectively. In addition, in the design of a transfer station, there are usually multiple stairs or escalators (stairs for descending passengers, and stairs and escalators for ascending passengers). e farthest distance from the stairs where the passenger chooses to get on and off the platform is the ratio of the platform distance to the number of stairs, and the number of stairs is defined as .
In the equations, v 1 is the average walking speed of a passenger in a straight channel of the station when in a crowd; v 2 is the speed of the escalators in the rail transit station; v 3 represents the average walking speed when descending stairs; v 4 is the average speed when ascending stairs; and is the designed height of each floor in the station.
(ii) Time Converting Value of Travel Cost. Usually, rail transit employs a segment billing system and a mileage billing system. e mileage billing system sets a basic starting price and then increases the travel cost according to the increase in the travel distance.
is the travel cost of rail transit, which can be expressed as follows: In the equation, is the travel cost of rail transit in the collinear section; 0 is the starting price of rail transit; 0 is the farthest distance that the rail transit starting price can afford (km); is the travel distance of the passenger (km); and is the charge of the rail transit distance unit (yuan/km). e travel cost of the original conventional bus refers to the cost of choosing a bus to complete a trip. Travelers who choose rail transit in the collinear section will choose the conventional bus first and then transfer to the rail transit or choose the rail transit first and then transfer to the conventional bus to complete a trip. erefore, in the calculation of the travel cost of rail transit, the travel cost of conventional bus should be calculated. e method of converting the travel cost into a time value is the same as that described above, and the time conversion value of the travel cost of passengers who choose to transfer to rail transit is , which can be expressed as follows: e values of walking speed in each case are described as follows [28]. e average walking speed of passengers walking to the station v 0 is 4.68 km/h. e average walking speed of passengers in the channel where the flow of passengers is more concentrated in the rail transit station v 1 is 3.6 km/h. e average walking speed of passengers descending the stairs in the station v 2 is 2.74 km/h, and the average walking speed of passengers ascending the stairs v 3 is 1.02 km/h. e running speed of the escalator v 4 is 2.34 km/h. e station type of the Hubin East Road Station of Xiamen Metro Line 1 is double-layer island, and three transfer stairs are set up in the station hall and station platform. According to Equations (5)-(9), the walking distance to the station is 0 , the walking distance of the entrance/exit is 1 , the plane distance of the entrance stairs or the escalator is 耠 1 , the walking distance in the hall is 2 , the plane distance of the stairs of the station hall or the escalator is 耠 2 , and the plane distance of the platform when waiting is 3 . According to the design of the Hubin East Road Station, the indicators 0 , 1 , 耠 1 , 2 ,

Travel Time Savings proportion.
e longer the travel time, the more time can be saved by choosing rail transit. Since the "point-line-point" space mode has increased the transfer time compared with the "point-line" space mode, the travel time savings proportion can be expressed as follows:

Case Analysis
e Hubin East Road Station of Xiamen Metro Line 1 is selected as a case study. All conventional bus lines within a 750-m service range perpendicular to each side of this station's line are included in the case study. According to the direction and stop information of bus lines, 29 conventional bus lines in the collinear section are determined, as shown in Figure 7, and the conventional bus lines to be adjusted are screened using the above model.

Data Sources.
To determine the average travel time of conventional buses during peak hours, the study extracted the vehicle GPS information of the collinear lines with Hubin East Road Stop as the endpoint within two weeks working days from July 24, 2017, to August 6, 2017, including the vehicle number, line information, stop information, and arrival time.

Model Verification.
In this paper, the conventional bus line 44, which has 9 collinear stops with Xiamen Metro Line 1 is selected for the calculation.

Generalized Travel Time Costs of Conventional Bus
Transit.
e total length of conventional bus line 44 is 12.44 km, and the fare is 1 yuan for the whole journey, which is 8.32 km of the collinear section with rail transit. It belongs to the "point-line-point" spatial mode mentioned above, and the collinear section of the conventional bus transit is located between the Green Community Station and the Gaoqi Station. e generalized travel time cost of line 44 is divided into two parts: the average travel time and the time conversion value of the travel cost. According to the Xiamen Urban Transport Development Annual Report [26], the early peak-hour period is 7:30-8:30. Vehicle GPS information from July 24, 2017 to August 6, 2017 of line 44 is selected to calculate the average travel time of the collinear section. e average travel time is 35.80 min. According to the fare of line 44, is equal to Intermediate collinear line      calculated using the method mentioned above. e results are listed in Table 1. Table 1 lists the model results of the  generalized travel time cost difference for the collinear section  of conventional bus and rail transit and the travel time  e travel cost of the rail transit refers to the Shenzhen rail segment pricing system. e metro line has 2 collinear segments, and the cost is 3 yuan. To transfer to rail transit, conventional bus must be selected before and a er the transfer. e cost is 2 yuan. Since transfer discount information in Xiamen is temporarily unavailable, the transfer discount rate is not considered in the calculation process, and the time conversion value of the travel cost calculated by the income method is: e generalized travel time costs of the rail transit in the collinear section is:

Results Analysis.
By the income method, the general travel time costs difference between the bus line 44 conventional bus collinear line and the metro line is calculated to be 4.46 min. e generalized travel time costs difference is 4.44 min, as calculated by the production method. is paper also applies the production method and income method to calculate the general travel time costs of other collinear lines. e results show that the difference between the two methods is very small. erefore, this paper uses the income method to calculate the travel time conversion value. With regard to the comprehensive utility of the generalized travel time costs, the income method is used to convert it to the difference in generalized travel time costs, which is calculated to be 4.46 min. e uniform conversion to the cost calculation reveals that the generalized travel costs difference of the bus line 44 collinear section is 2.55 yuan. e general travel time costs of all conventional bus collinear lines were calculated and converted into cost; the model results were not affected. To reflect the time utility of rail transit, because the results of calculating the travel time with location data is more accurate, this paper uniformly converted to time for calculation.

Travel Time Savings Proportion.
e travel time savings proportion for bus line 44 a er transferring to rail transit in the collinear section is: erefore, bus line 44 is selected for adjustment. e generalized travel time cost difference between conventional bus transit and rail transit corresponds to 29 collinear bus lines, and the travel time savings proportion is

Discussion and Conclusions
is paper studies the adjustment of conventional bus lines along a rail transit line, and the time utility brought by rail transit is taken into consideration first. A model of the generalized travel time costs and travel time savings proportion is established to evaluate the utility of a collinear section between conventional bus and rail transit, and then the conventional bus lines to be adjusted are screened. e adjustment of conventional bus transit along a rail transit line is usually based on an empirical value (a collinear length that exceeds 6 km), which indicates that the conventional bus lines to be adjusted and the rail transit have certain commonalities in space. Based on the time utility of rail transit, especially during rush hours of commuting, the time utility of the collinear section is evaluated by means of aggregate analysis, and the conventional evaluate the time utility of the collinear channel. In the process of evaluating generalized travel costs, the studies of [12][13][14][15] have uniformly converted time into costs for research. To highlight the time utility of rail transit in the peak period and reduce the conversion loss, the cost is uniformly converted into time for calculation. For the estimated value of travel time, most studies have utilized the state preference (SP) data of passengers [12][13][14]18]. Here, the aggregate model is mainly used to evaluate the time utility of the collinear channel. To avoid the instability of the travel time of conventional bus in the peak period, the travel time of a conventional bus is calculated using the GPS data of the bus to obtain the accurate travel time in the peak period. Regarding the transfer time between conventional bus and rail transit using passenger survey statistics [20,29], this paper takes into account factors such as the distance between conventional bus and rail transit transfer stations and the design of rail transit station, and makes an objective evaluation of the time required for the transfer process. By evaluating the time utility of rail transit and conventional bus in the collinear channel, the bus lines that need to be adjusted along the rail transit are determined. According to the passenger flow distribution and the corresponding transfer intention, the adjustment principle of the conventional bus lines to be adjusted will be further determined in the future.
is paper analyses the factors that affect the adjustment of conventional bus lines along rail transit. By considering whether passengers in the collinear section will shi during peak hours, the model of the generalized travel time costs and the travel time savings proportion is established based on the GPS data of the conventional bus, and the conventional bus lines to be adjusted can be screened flexibly, so as to prejudge the adjustment of conventional bus lines before the rail transit is put into operation. e model provides a basis for further optimization of the conventional bus lines in the collinear section of the rail transit. Since the study analyzes only two weeks of GPS data via the continuous analysis of GPS data, a more accurate travel time during peak hours can be obtained to calculate the travel time savings proportion, and the conventional bus line to be adjusted can be screened. Combined with card data, the passenger flow distribution of the "transfer once" and "transfer twice" conventional bus lines and the corresponding transfer intention research can be calculated, and the adjustment principle of cancels, retentions, and mergers for the conventional bus collinear section and the noncollinear section can be formulated. At the end of this paper, the calculations demonstrate the rationale of establishing the model, which provides a scientific basis for the elastic adjustment of the conventional bus line of a rail transit collinear section. is research provides decisional support for urban integrated public transport planning.

Data Availability
The GPS data used to support the findings of this study were supplied by Xiamen GNSS Development & Application Co., Ltd. under license and so cannot be made freely available.