Improving Synchronization in an Air and High-Speed Rail Integration Service via Adjusting a Rail Timetable: A Real-World Case Study in China

Air and high-speed rail (AH) integration services are gaining ground with the development of the high-speed railway and airline industries. A well-designed feeder train timetable with good synchronization is of great signicance in an AH integration service, because it can improve the connectivity at transfer nodes and oer more opportunities for intermodal passengers to travel. In this study, we propose a multi-objective model of a feeder railway timetable problem in an AH integration service to improve synchronization. e aims of the optimization model are to maximize the number of synchronizations and the coverage of synchronized ights, as well as to minimize the transfer penalties of passengers. We focus on a scenario of a partial subnetwork in which one direction of a two-direction railroad line with one transfer station is considered. e model is applied to Shijiazhuang Zhengding International Airport, China. e results illustrate the eectiveness of the approach developed in the paper.


Introduction
With the rapid development of the airline and high-speed rail (HSR) industries, the two transport modes have moved beyond competition and into cooperation in some particular cases [1]. Many airports around the world are connected to railway systems, which facilitates the integration of transport modes. In this case, the rail trip usually serves as a leg of the journey as a substitute for short-haul feeder ights. Givoni and Banister [2] summarized the bene ts of intermodal services for airlines, airports and railways, such as alleviating capacity constraints at major airports, expanding the catchment area, addressing environmental issues, etc.
Due to their advantages, air and high-speed rail (AH) integration services are provided all over the world. Historically, this type of service originated in Europe. In 1994, the Charles de Gaulle Airport TGV station was designed as a tool for expanding the airport capacity in France. Many cities, such as Brussels and London, can be reached within 3 hours by train from the TGV station in the airport [3]. In Germany, the AH integration service dubbed "AIRail" was created in 2001 with the German train operator Deutsche Bahn, network carrier Lu hansa and airport operator Fraport as cooperation partners. is project successfully integrated ticketing and baggage and allowed the use of any train from any station in Germany to reach the airport and vice versa [4]. Until 1993, an earlier service had been dedicated exclusively to airplane ticket holders: from 1982 on, the Lu hansa Airport Express trains connected the intercontinental ight services of the Frankfurt airport with the city centres of Bonn, Cologne and Dusseldorf, as well as Stuttgart later on [4], at speeds of up to 200 km/h. Presently, AH integration services are extending to Asian countries, especially China, where intermodal travel is well supported by the existing infrastructure. China has a vast territory and AH integration services can enhance the service accessibility of various locations. e rapid development of the HSR and airline industries over the past few years represents a valuable opportunity for AH integration services. By 2018, China had the world's largest HSR network, amounting to 29,000 km of HSR coverage, with speeds between 200 km and 350 km per hour. Meanwhile, air transport has also developed rapidly. e number of civilian airports amounts to 235, and there are 37 airports with a yearly throughput of more than 10 million passengers. Moreover, there are currently 10 integrated hubs in which airports are linked to HSR stations. Some AH integration service products are offered in China. For example, China Eastern Airlines works with the Shanghai Railway Bureau to attract passengers from nearby cities to the Shanghai Hongqiao and Pudong airports by offering integrated air-HSR tickets [5].
Transfer is important in an AH integration service. Passengers who use AH integration services have to transfer between trains and flights to complete their travel, and they are more concerned with service connectivity and transfer coordination [6]. e connection times between two modes should be neither too short, such that there is not sufficient time for passengers to transfer from HSR trains to aircra s, nor too long, making the total travel time unacceptable and discouraging transit use. Li and Sheng [7] found that an AH intermodal service becomes less attractive with increasing connection times. When the connection time exceeds a certain threshold, an AH integration service will lose its competitiveness. e transfer quality improvement is especially important when the train frequencies on the lines under consideration are low. For transfers from trains to flights, a high frequency of trains means that passengers have enough opportunities to select the trains with appropriate transfer times. In Germany, the average frequency of daily trains exceeds 90 (here, the number of train services is summed across all directions, but for each passenger, the number of train services that are offered on her route, is the even more relevant criterion) at the airports which are equipped with long-distance railway stations, including Frankfurt, Düsseldorf, Cologne-Bonn, and Leipzig/Halle [4]. Among these stations, Frankfurt has the maximum frequency of 358. Dense synchronized timetables provide plenty of connections with appropriate transfer times. However, when train frequencies at some airport train stations are low, passengers may spend additional waiting time, or lack enough time during the process of transferring. is may discourage people from using AH integration services.
Designing a synchronized timetable for AH integration services is an effective way to improve the quality of transfers, and it requires cooperation between the rail and air operator. However, currently, there is no intermodal institution to offer a coordinated timetable for rail and air transport in China. Flight timetabling involves coordination between the Civil Aviation Administration of China (CAAC), airline companies, airports and other stakeholders (the CAAC is responsible for air transport safety and administers seven regional civil aviation administrations. Some airlines (Tier-1) which were split from the CAAC's airline operations are the largest state-owned airlines, and some airlines (Tier-2) are subsidized by local government. In addition, there are some fully privately owned airlines (Tier-3). Airports in China are owned and operated by the airport authorities of local governments [8]). Railway timetabling is scheduled uniformly by the China Railway Corporation (CRC) (the CRC is the national railway operator and is in charge of construction, operation, and management). From the perspective of management, it is easier to adjust a railway timetable because railway timetabling involves only one operator. erefore, in this paper, synchronization is improved by adjusting a feeder HSR timetable in an AH integration service.
We propose a multi-objective optimization model of a feeder HSR timetable problem in an AH integration service to maximize the number of synchronizations and the coverage of synchronized flights, as well as to minimize the transfer penalties of passengers, aiming at improving synchronization.

Number of Synchronizations.
e first objective is to maximize the number of synchronizations in the AH integration service by adjusting the current rail timetable. In this study, we redefine synchronization as follows: if the interval between the arrival of a train and the departure of a flight (or the arrival of a flight and the departure of a train) at a transfer node is within a separation time window, we say a synchronization is reached in the AH integration service.
is definition is extended from those of Ceder et al. [9] and Eranki [10], who focused on bus networks. Maximizing synchronization to optimize the transfers is important for operators and passengers [11]. In an AH integration service, a synchronized timetable can improve the connectivity at transfer nodes and offer more opportunities for passengers to travel. Meanwhile, it might bring several concomitant benefits such as creating induced intermodal passengers.

Coverage of Synchronized Flights.
We should also consider the coverage of synchronized flights while improving the synchronization number between trains and flights. Assuming that the major leg of an AH-itinerary is the flight, then this perspective aims to make the largest number of flights accessible by train. Notice that the highest number of synchronizations and the highest number (maximum coverage) of synchronized flights are not necessarily equivalent. A small case is used to illustrate this problem as shown in Figure 1. We assume that the appropriate transfer time range from the HSR station to the airport is 1-2 hours. Figure 1(a) shows the flight plan and the initial train schedule before adjusting the rail timetable. Only two synchronization events are valid and the number of synchronized flights is two. e timetabling model, aiming only to maximize the number of synchronizations, has many solutions, and Figure 1(b) illustrates one of them. When the second train arrives 15 minutes early, the number of synchronizations increases to three and the coverage of synchronized flights remains unchanged. Another solution, shown in Figure 1(c), optimizes the synchronization and the coverage. e former number is 3, but the coverage number increases to 3, which means that any of the flights has corresponding feeder trains. As the seat capacity of a train is much larger than that of an aircra , this is further motivation to preferably cover a flight that was not covered before, instead of covering a flight that was already covered by one train with a second train. e improvement of coverage will improve the accessibility and attract flight passengers to arrive at the airport by HSR. Hence, the optimization of the coverage of synchronized flights is regarded as a further objective.

Transfer Penalties of Passengers.
Moreover, given a valid synchronization event, intermodal passengers perceive transfer times differently. We still take transfers from trains to flights as an example. In a transfer node, some passengers prefer short transfer times for quick trips, while some passengers would like to spend some additional waiting time to guarantee that they can get to their flights, even with the long queues at baggage drop-o and security check. For this reason, we will introduce transfer penalization functions representing the di erent preferences of passengers. is leads to a minimization of penalties which is the third objective. e remainder of this paper is organized as follows. First, in Section 2, we present a literature review. In Section 3, an extended HSR timetable model of improving synchronization in AH integration services is developed. In Section 4, the Shijiazhuang Zhengding International Airport serves as a model illustration, and comparison analyses are conducted. Finally, Section 5 provides concluding remarks and potential avenues for future research.

Literature Review
In recent years, AH integration services have received worldwide attention. Many studies have adopted a qualitative or descriptive approach to discuss experiences [4,12], as well as the advantages and disadvantages [2,13]. In response to the quantitative literature, Socorro and Viecens [14] developed a theoretical model to analyze the circumstances under which integration between HSR trains and ights may be bene cial.
ey found that such integration can alleviate the capacity of a hub airport, but its environmental and social e ects are ambiguous. Okumura and Tsukai [15] discussed air-rail Journal of Advanced Transportation 4 integration services. erefore, this paper first proposed a feeder HSR timetable problem in an AH integration service by adjusting the original rail timetable to improve the transfer synchronization based on the given flight schedules. A multi-objective optimization model is formulated, aiming to maximize the number of synchronizations and the coverage of synchronized flights, as well as to minimize the transfer penalties of passengers. Finally, the model is applied to the case of Shijiazhuang Zhengding International Airport in China.

Model Construction
In contrast to traditional railway timetables (for example, [28][29][30][31]), this paper focuses on adjusting the original HSR timetable, aiming to improve the transfer synchronization in AH integration services. We consider this timetabling problem along one direction of a two-direction railroad line on which a transfer station is located. e railroad line can be a part of a large network, whereas we keep the rest of the network out of the scope of this study. e adjustments of the rail timetable include the departure times, arrival times, running times, dwell times and headways within a small deviation from the original timetable, while the set of trains that are to be scheduled remains unchanged.

Model Assumptions.
To facilitate model formulation, the following assumptions are made throughout the paper: We assume that a joint ticket may be offered with any airline and any railway operator in a transfer hub. In other words, any one flight may connect to any one train. (ii) ere are two types of connections: train-flight connections and flight-train connections. is paper focuses on train-flight connections. Since the punctuality of airlines is worse than that of railways [32], the probability of a passenger missing the corresponding HSR train in the case of a flight delay is larger. is makes it even more difficult to come up with reliable travel plans for the passengers, and thus in this first study we concentrate on train-flight connections. (iii) e flight timetable is given and remains unchanged. (iv) e HSR line plan is given, too. While the line plan including the set of trains, stop patterns and traveling routes remains unchanged, the optimization model may make use of the types of adjustments that we sketched, at the beginning of this section.
(v) e number of passengers who may use transfers is neglected in our model. It is difficult for transit planners to obtain transfer data with sufficient accuracy [24]. However, in our model, if the data on passenger demand are available for all transfers, they could be used as a multiplicative factor in the objective function. (vi) We assume that the minimum transfer time is known and fixed for all transfer passengers. For train-flight connections, the transfer time from a intermodal network formation from the viewpoint of passengers, with Haneda Airport as a research object. e results showed that the operational capacity shortage of Haneda Airport may be solved by providing additional HSR service. Chiambaretto et al. [16] estimated passenger preferences for intermodal travel regarding some basic attributes, such as ticket integration, ground-handling integration, price, transfer, and travel time. e results showed that in-vehicle, connecting, and access times are more valued than baggage integration. In addition, the study found that baggage integration is only valued for leisure travel. Li and Sheng [7] investigated the mode choice behaviour of the AH integration service for the Beijing-Guangzhou corridor using the logit model. e market shares of four city pairs were estimated, and sensitivity analyses were performed. However, few studies have focused on timetable coordination in AH integration services.
Although studies on timetable coordination in AH integration services are limited, there is a wealth of literature on timetable coordination for urban public transportation systems. Considerable research has attempted to minimize the transfer time, passenger travel time and waiting time at railway stations, as reviewed in Wong et al. [17], Liebchen [18], Zhou et al. [19], Guo et al. [6], Shafahi and Khani [20], and Kang et al. [21]. For example, Wong et al. [17] presented an MIP optimization model for planning a synchronized nonperiodic timetable that minimizes the total transfer waiting time for all passengers. Zhou et al. [19] presented a coordination optimization model for the first train departure times. e objective of the model is to minimize the total passenger waiting time at the origins and the transfer waiting time for the first connecting trains. Guo et al. [6] constructed a first train timetabling optimization model with explicit consideration of the importance of lines and transfer stations. Kang et al. [21] proposed an extended problem of last train timetabling by introducing bus bridging services and a defuzzification approach for the last train dwell times. e models and approaches were applied to the Vienna subway.
e synchronization issue has o en been studied in the literature. Domschke [22] minimized the waiting times of passengers at transfer stations. e author proposed a formulation that was similar to the quadratic assignment problem.
is study was extended in [23] and [24] to improve the quality of transfers. Ceder et al. [9] described the problem of maximal synchronization in creating a bus timetable at transfer nodes. Eranki [10] and Guo et al. [25] extended the definition of synchronization presented in Ceder et al. [9]. In Guo et al. [25], synchronization is defined as the separation time between two trains (belonging to different lines or different periods), which can be satisfactory within a specific time window at a station instead of both trains arriving at the same time. Wu et al. [26] presented a timetable synchronization optimization model that aimed to reduce the worst weighted transfer waiting time as well as the probability and propagation of delay. Cao et al. [27] proposed a model for the synchronized and coordinated railway scheduling optimization problem. ey maximized the number of synchronized meetings considering the importance of transfer stations and rail lines.
Although a number of studies have been developed for train timetabling, to the best of our knowledge, no research has focused on synchronized rail timetables for AH Outgoing ight index, : Station index, : Set of trains, where = ∪ , : Set of trains that serve the transfer station, : Set of trains that do not serve the transfer station, : Set of outgoing ights at the transfer node, : Set Pure running time for train on the segment ( , + 1), where ∈ \ des , , : Acceleration time for train at station , where ∈ , ∈ \ des , a continuous non-negative penalty variable , re ecting the speci c preferences of business and leisure passengers from the train to the ight for the transfer time. is is demonstrated by constraints (25)-(27), described later. e third objective 3 (with much lower priority than the above two objectives) is to minimize these transfer penalties: (6) and (7) ensure that the travel time , +1 − , of a train on a segment [ , + 1] considers the pure running time , , acceleration time , , deceleration time , and time supplement , . e running time of a train on a segment will be longer when the train stops at a station. e requirements for the dwell time should be satis ed to ensure operating e ciency and safety, as shown in constraints (8) and (9), respectively. e actual dwell time , − , of train at station should be greater than or equal to the minimum planned dwell time , _ to provide passengers with su cient times to board and alight. It should also be less than or equal to the maximum planned dwell time , in the case of a long travel time. When a train passes a station, the dwell time equals 0.

Train Operation Constraints. Constraints
Constraints (10) and (11) ensure that every train has a departure time window at its start station ori and an arrival time window at its terminus station des . An overly large deviation from the original timetable will directly in uence the cost or performance of the railway system. On the one hand, timetable adjustments may change the turnaround times of trains at terminus stations. If the di erence between the adjusted timetable and the original timetable becomes too large, it will have a strong in uence on the vehicle schedule, resulting in extra trains with high additional costs. On the other hand, as this study focuses on only a part of the network, timetable adjustments of the target railroad line will a ect the timetables of the converging and diverging lines. us, time windows are imposed to restrict the timetable shi . Constraints (12)- (15) state that the departure and arrival time windows are relatively close to the input timetable. (6) , +1 − , ≥ , + , , , + , +1 , +1 ∀ ∈ , ∈ \ des , , +1 − , ≤ , + , , , + , +1 , +1 + , ∀ ∈ , ∈ \ des .

Mathematical Formulations.
We present a multi-objective mixed integer programming model of the timetabling problem for all trains that make use of the target railroad line. ere are two kinds of trains running on the line. e rst kind of train serves the transfer station. In other words, these trains stop at the transfer station. e second kind of trains does not serve the transfer station. e transfer synchronization between trains and ights can be improved by adjusting the timetable of the rst kind of trains. Meanwhile, due to the interaction between trains, the timetables of other trains might have to be adjusted, too, to guarantee safety constraints. e timetable is adjusted within a planning horizon, and we let be the upper bound of the time horizon.

Objective Functions.
(1) Maximizing the Number of Synchronizations. For trainight connections, a synchronization in an AH integration service is valid if the di erence between the arrival of a train and the departure of a ight is within a separation time window _ , at the transfer station. Let _ denote the minimum transfer time, and is the acceptable maximum transfer time of passengers. As we assume the ight timetable to be given, the departure time of any ight is xed. us, a synchronization between a train and a ight is valid if the arrival time of the train is within the connection time window of the ight at the transfer node. e departure time of the outgoing ight minus the maximum transfer time is the lower bound of the connection time window , and the departure time minus the minimum transfer time _ is the upper bound of the connection time window : e auxiliary binary, , , which indicates whether the train synchronizes with the ight at the transfer station, is introduced, see Equation (21). If the synchronization is valid, , = 1; otherwise, it is 0. erefore, the rst objective function -denoted by 1 -is put forward to maximize the number of synchronizations: (2) Maximizing the Coverage of Synchronized Flights. e number of synchronized ights should be increased while improving the synchronization number between trains and ights. Here, additional binary variable , which indicates whether the ight is synchronized with some trains, is introduced, see Equation (24). is equal to 1 if the ight is synchronized; otherwise, it is 0. e second objective 2 , aiming to maximize the coverage of the ights by the trains, is proposed: (3) Minimizing the Transfer Penalties of Passengers. e di erent preferences of passengers should also be considered. Even though a train synchronizes with a ight , passengers on the train perceive transfer times di erently. Here, we introduce (3) . Journal of Advanced Transportation

Passenger Preference Constraints.
As mentioned above, intermodal passengers have di erent preferences for transfer times. We divide passengers into two types based on the purpose of trips: business and leisure passengers. Business passengers prefer shorter transfer times while leisure passengers prefer longer transit times to reduce the risk of missing the plane [33]. For a valid synchronization , between a train and a ight , business passengers from the train to the ight are less sensitive to the short transfer time and could thus prefer arriving at the transfer station during , + /2 ; when the transfer time exceeds + /2, they become sensitive and the penalty should increase, e.g., from + /2 to . In contrast, leisure passengers prefer slightly longer transfer times and they would like to arrive at the transfer station during , + /2 . ey are more sensitive to short transfer times, and thus the penalty should increase there, e.g., from + /2 to . erefore, we introduce a continuous non-negative penalty variable , representing the preferences of the passengers from the train to the ight for the transfer time, as shown in constraints (25)- (27). Due to the objective function 3 (5), the optimization model will push , to the smallest possible value. e slope coe cient v 1 represents the sensitivity that models the penalty that the business passengers associate with a waiting time that exceeds + /2, and 1 is the proportion of business passengers among the total passengers. Analogously, v 2 is the corresponding coe cient for the leisure passengers associating with a waiting time of less than + /2, and 2 is the proportion of leisure passengers. e values of v 1 , v 2 , 1 , and 2 can be estimated by stated preference surveys. It should be noted that the timetable adjustments will be su ciently a ected by the proportion of v 1 × 1 / v 2 × 2 . erefore, the values of both v 1 and v 2 are set to be between 0 and 1 in this paper. When a train can synchronize with a ight ( , = 1), the penalty , is a

Safety Headway Constraints.
Limits on the headways for all trains ∈ should be satis ed to ensure operational safety. Constraints (16) and (17) ensure that the di erence between the departures of any two trains at station (visited by the both trains) satis es a lower bound . Analogously, constraints (18) and (19) ensure that the di erence between the arrivals of any two trains at station satis es a lower bound . is a large number that is no smaller than + max , . (20) states the logical relationship (ordering) in each section between any two trains. (21) is the synchronization number constraint between trains and ights at the transfer station. e constraint states that if the arrival time of a train is within the connection time window , generated by a ight , which means that the train can synchronize with the outgoing ight , then the value of variable , equals 1; otherwise, , equals 0.

Synchronization Number Constraints. Constraint
Constraint (21) can be linearized into constraints (22) and (23) using a large positive value ὔ . As can be observed in constraints (22) and (23), if , < or , > , then , = 0. If ≤ , ≤ , then in principle , could equal either 0 or 1, but the maximization objective function will force it to have a value of one. ὔ is a large number and its value is greater than or equal to .

Coverage Constraints.
e coverage variable represents whether the ight is synchronized with at least one feeder train. Because of the maximization objective function 2 , the variable must only be set to one, if some of the corresponding variables , have already been set to one. erefore, constraint (24) must be satis ed for any ight.    e maximum coverage of synchronized ights is xed, and we impose another constraint (29). e last single-objective model M3 is then reformulated as follows to minimize the transfer penalties of passengers. We can obtain the adjusted timetable.

Real-World Case
In this section, we apply the proposed model to Shijiazhuang Zhengding International Airport Station on the Beijing-Guangzhou corridor. In Section 4.1, the characteristics of the target airport and station are presented. Section 4.2 provides the data and parameter information. In Section 4.3, we investigate the adjusted results, and some analyses are presented.

Characteristics of the Target Airport and Station.
Shijiazhuang Zhengding International Airport is selected as the case study. Zhengding airport is adjacent to the Zhengding airport HSR station, and the station and the airport o er the infrastructure for AH integration services. e characteristics of Zhengding airport and the Zhengding airport station are listed below.
(i) e Zhengding airport HSR station is located on the Beijing-Guangzhou HSR corridor in mainland China, as shown in Figure 4 (only the section between (29) ∈ = .
V-shaped piecewise linear function of the arrival time , of the train , as shown in Figure 2. ὔὔ is a large positive number with a value no less than × max v 1 × 1 , v 2 × 2 . Figure 3 illustrates a train schedule that covers 5 stations and 3 trains. Station 3 is the transfer station. At the transfer point, there are two outgoing ights. e arrival time of train 1 is within the connection time windows of both outgoing ights. e arrivals of trains 2 and 3 are within the connection time windows of the second outgoing ight. However, train 3 does not serve station 3. erefore, there are 3 train-ight synchronizations. e coverage of synchronized ights is two.

Priori Method.
We choose to apply the a priori method [34] to our multi-objective model. In our formulation, the rst and second objectives have much higher priority than does the third objective. e rst two objectives aim to determine the synchronization events. Subsequently, the third-level optimization is to further narrow the solutions by minimizing the transfer penalties of di erent passengers. We aim to provide more smooth transfers, and thus, the rst objective has a higher priority than does maximizing the coverage of synchronized ights. e multi-objective model is converted into three single-objective problems that can be solved exactly by any optimization solver such as CPLEX.
First, we propose a single objective model for maximizing 1 , denoted by M1.   (vi) e demand for the AH integration service in Shijiazhuang has increased rapidly. In 2016, over 412,000 passengers nished their travel using the intermodal service of the Zhengding airport. In 2017, the passenger volume increased to 737,700, and the number exceeded 1132,000 in 2018.

Parameters Settings.
In this section, we concentrate on the rail section from Beijing to Zhengzhou in the Beijing-Guangzhou HSR corridor, including 14 stations. We consider the timetable for trains that depart from the starting stations between 6:30 and 20:00. During this planning horizon, there are 112 trains and 16 trains serving the Zhengding airport HSR station. e number of outgoing ights in Zhengding airport is 110. We make assumptions about other parameters due to a lack of validated data provided by any of the operators, as shown in Table 1.
e model was coded and solved using MATLAB R2015b and ILOG CPLEX 12.5 running on a PC with an Intel i5 3.0-GHz processor and 8 GB of RAM.

Model Applications.
e computational performances of three models are shown in Table 2. It requires 6923 seconds (115 minutes) to yield the optimal feeder rail timetable solution using CPLEX solver.

Optimal Rail Timetable Solution.
e number of synchronizations increases from 104 in the original rail timetable to 129 a er the adjustments, representing a rise of 24%. Figure 5 shows the number of synchronizations for each train that serves the transfer station before and a er the adjustments. It can be seen that more than half of the trains show improvements in the number of synchronizations. e coverage of synchronized ights increases from 83 to 86, which means that three more ights are served. erefore, the transfer synchronization can be improved by the proposed model. e adjusted timetable is presented in the Appendix.

E ects of Departure and Arrival Time Windows on
Synchronization. As constraints (10)- (15) show, the train departure times at the starting stations and arrival times at the terminus stations should not exceed the upper and lower bounds. Here, we test the e ects of the train time windows on Beijing South and Zhengzhou East is presented). An HSR trip between Beijing and the Zhengding airport HSR station takes only 70 minutes. (ii) Only 32 high-speed trains (including inbound and outbound trains) serve the Zhengding airport HSR station per day. e train frequency in each direction of the two-direction railroad line is 16. (iii) To alleviate the current tra c congestion issues at Beijing Capital airport, some domestic air ights are diverted to Shijiazhuang Zhengding airport according to "Opinions on Further Deepening the Reform of Civil Aviation Industry", facilitated by the CAAC. (iv) e distance from the Zhengding airport HSR station to the airport terminal is 3 kilometres. is journey takes passengers approximately 5 minutes by shuttle bus. e short transfer time provides considerable convenience to passengers regarding their luggage when arriving or departing from the station to the airport.
(v) Several low-budget airlines are based at the Zhengding airport, and these airlines typically o er lower ticket fares. erefore, the AH integration service in Shijiazhuang has price advantages, and it strengthens the competitiveness of the Zhengding airport compared to adjacent airports, such as the Tianjin Binhai Airport.   Table 3. We can nd that the proportion of v 1 -v 2 of 3 : 7 corresponds to the highest total penalties. When leisure passengers are less sensitive to the waiting time, the penalties are lower. erefore, reducing the sensitivity of leisure passengers during transfer has a good e ect on reducing the total penalties based on the current adjustments.

Accessibility.
Accessibility is an important concept that is broadly used in the eld of transportation planning. We introduce an indicator, called "accessible cities", counting the number of cities that can be reached from one origin using the timetable information. Notice that we only focus on the valid synchronizations, which means that the origin is served by train ∈ and the destination is served by the synchronized ight . A higher value of this indicator for a city implies that the AH integration service can provide more appropriate trips for passengers from the city and that the accessibility is greater. We measure the cities that are accessible from Beijing, Zhuozhou, Gaobeidian, Baoding, and Dingzhou before and a er adjusting the HSR timetable (see Table 4). e number of accessible cities increases for most origins a er the adjustments.
is indicator has the largest increase for Zhuozhou, adding 7 cities. In other words, passengers living in Zhuozhou can reach additional 7 cities through the optimized AH integration service. e indicator does not change for Dingzhou. e results show that the adjustments are e ective in improving the accessibility of AH integration services.

Priority of Objectives.
We analyze the in uence of the priority of the objectives on synchronization (we only focus on the rst two objectives). When maximizing the coverage of synchronized ights has a higher priority than does maximizing the number of synchronizations, the results with di erent train time windows are shown in Figure 8. Obviously, the number of synchronizations and the coverage of synchronized ights increase with the enlargement of the time window. Comparing the results of this section with those of Section 4.3.2, when the width of the train time window is less than or equal to 20 minutes, the solutions

Train Timetable Shi .
e timetable shi is the di erence between the adjusted timetable and the original timetable. e shi of each train is measured by Equation (30): Figure 7 shows the timetable shi for all trains. As mentioned above, the width of the departure and arrival time windows is 30 minutes. In other words, every train can depart/arrive 15 minutes early or late compared to the original timetable. We nd that most trains make full use of the time windows, which means that many trains have a 15-minute timetable shi . e average time shi is 13.9 minutes. A 13.9-minute shi can be accepted by passengers because it is short compared to the average travel time of passengers served by the trains operating in the Beijing-Guangzhou corridor.

Passenger Preferences.
In the original timetable, the transfer penalties of business and leisure passengers for all valid synchronizations are 769.60, and the average penalty of each synchronization is 7.26. A er adjustments with a 30-minute train departure time window, the total penalties are 1009.40 and the average value is 7.82. is result indicates that a higher average penalty is the price for improving the number of synchronizations and the coverage of serviced ights based on the original timetable.
We assume that the number of business passengers and the number of leisure passengers are the same, and then change the sensitivity of business and leisure passengers to the transfer time. Given the maximum synchronization Data Availability e railway and air timetable data are from July 2018 from https://www.12306.cn/index/ (the railways ministry's o cial ticketing website) and http://www.ctrip.com/ (an online travel site).

Conflicts of Interest
e authors declare that there are no con icts of interest regarding the publication of this paper.

Acknowledgments
We would like to thank the editor and reviewers for their valuable and helpful comments and suggestions, which greatly improved this paper. We also appreciate the insightful suggestions from Xin Zhang and Zijin Mao at Beijing Jiaotong University. Meanwhile, we invite anyone who is interested in AH integration services to exchange her/his ideas with us. are the same, regardless of priority. However, the coverage of ights in this section is larger in the cases of windows of 26 or 30 minutes, while the number of synchronizations is less. Yet, it is interesting to notice that this yields just only one single additional ight that is served in addition. We conclude that in this particular data set, the rst objective function "maximizing the number of synchronizations" essentially already tends to maximize the coverage of synchronized ights. In particular, the rst objective function does not concentrate several trains too o en just around the very same outgoing ights.

Conclusions
AH integration services are becoming an important transportation mode with the development of HSR and air travel. During the travel process, passengers must transfer between the two modes to complete their journey. To provide intermodal passengers with more opportunities to travel, we focus on improvement of the synchronization in an AH integration service. A multi-objective model of a feeder railway timetable model is developed with the aim of maximizing the number of synchronizations and the coverage of synchronized ights, as well as minimizing the penalty of passengers. e model is solved using the CPLEX solver. We apply the model to Shijiazhuang Zhengding International Airport. e number of synchronizations increases by 24% compared to that in the original timetable, and the coverage of synchronized ights increases by 3. e average shi of each train is 13.9 minutes. e accessibility improves for most cities. e results show that the proposed model is e ective for improving synchronization at this airport. However, passengers' average penalty in each valid synchronization event is higher a er the adjustments. e delay characteristics of ights are not considered in this study. However, they in uence connections between trains