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UBC Theses and Dissertations

Inter-city passenger transport connectivity : measurement and applications Zhu, Zhenran 2017

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  INTER-CITY PASSENGER TRANSPORT CONNECTIVITY: MEASUREMENT AND APPLICATIONS  by Zhenran Zhu B.S. Shanghai Jiao Tong University, 2015  A THESIS SUBMITTED IN PARTIAL FUFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in The Faculty of Graduate and Postdoctoral Studies (Business Administration in Transportation and Logistics)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) May 2017  © Zhenran Zhu, 2017ii  Abstract This study proposed a model to calculate connectivity of multiple transport modes involving quantity and multiple dimensions of quality. Ranking results have been produced for the air-rail connectivity of 2016 and the air connectivity of 2005-2016, with a focus on Chinese cities. The connectivity model incorporates multiple quality-adjustment (discount) factors, including capacity and velocity penalties to correct/adjust for the quality of a connection. The three major economic zones in China, namely, Beijing-Tianjin-Hebei, Yangtze-River Delta, and Pearl-River Delta, are found to have leading connectivity. We also identify the underlying drivers of the variation in airport connectivity over the period of 2005-2016. It is observed that Chinese airports experienced great increase in air connectivity over the study period. Beijing Capital, Shanghai Pudong, and Guangzhou Baiyun are far ahead of other airports in terms of overall connectivity, which is especially so in terms of international connectivity. However, the growth of some tourism cities and small cities has been stagnant and they suffered losses of connectivity at times. Airport competition measured by HHI, average fare, investment in local city’s fixed assets and airport facilities, macroeconomic conditions, and population are found to be closely associated with an airport’s connectivity. We also find the presence of low-cost carriers (LCCs) are conducive for air connectivity while HSR has the effect of decreasing airport connectivity.  iii  Lay Abstract This study is focused on grading cities with the performance of city-to-city transportation, which I call connectivity. A new model is proposed, with three major contributions.  First, services of multiple transport methods are evaluated and summarized into one comprehensive grade. When considering air and rail transport, both performance of air/rail service and the cooperation between air and rail are evaluated and merged into one score. Second, the model considers multiple dimensions of standards, such as availability of seats, transfer service, travel speed, etc. Third, the model is flexible and sensitive, because it evaluates with up-to-date trip-level schedule data. When one new flight is added or when a train is operated with higher speed, the score will be higher. It can be used to monitor the real-time performance and trace history performance. Also, analysis has been conducted to find the economic factors that may have an effect on connectivity.  iv  Preface This dissertation is ultimately an original, unpublished, independent work by the author, Zhenran Zhu.  A version of Chapter 4 and part of Chapter 1 and 5 is under review with Journal of Transportation Research Part A. I was responsible for model construction, computing, and data analysis. Anming Zhang, Yahua Zhang, and Kun Wang were involved in concept formation, regression analysis, and manuscript composition.   v  Table of Contents Abstract .......................................................................................................................................... ii Lay Abstract ................................................................................................................................. iii Preface ........................................................................................................................................... iv Table of Contents .......................................................................................................................... v List of Tables ............................................................................................................................... vii List of Figures ............................................................................................................................. viii Acknowledgements ....................................................................................................................... x Dedication ..................................................................................................................................... xi 1   Introduction .............................................................................................................................. 1 2 Methodology and Data ......................................................................................................... 6 2.1 Connectivity Utility Model .............................................................................................. 6 2.2 Data .................................................................................................................................. 9 2.3 Applied Connectivity Utility Model .............................................................................. 11 3 Numeric Results and Analysis ........................................................................................... 25 3.1 Terminal Connectivity.................................................................................................... 25 3.2 City and Region Connectivity ........................................................................................ 37 3.3 Vulnerability Analysis.................................................................................................... 45 3.4 Robustness Analysis ....................................................................................................... 48 vi  4 Analysis for Drivers of Connectivity ................................................................................. 53 4.1 The Methodology and Data for Detecting the Drivers of Air Connectivity ....................... 53 4.2 Results Analysis .................................................................................................................. 59 4.2.1 Connectivity Results Analysis ..................................................................................... 59 4.2.2 Regression Results Analysis ........................................................................................ 66 5 Conclusion ........................................................................................................................... 72 Bibliography ................................................................................................................................ 77 Appendices ................................................................................................................................... 85 Appendix 1: List of cities .......................................................................................................... 85 Appendix 2: List of terminals ................................................................................................... 86 Appendix 3: Terminal connectivity .......................................................................................... 90 Appendix 4: Connectivity of international airports (with China), top 50. ................................ 94 Appendix 5: Connectivity of foreign countries (with China), top 80. ...................................... 95 Appendix 6: City connectivity with different radiation discount functions ............................. 96 Appendix 7: Airport connectivity from 2005 to 2016 .............................................................. 98    vii  List of Tables Table 1      Extra time at terminals for air-rail and rail-air transfers ............................................. 16 Table 2      MCT for all possible transfers .................................................................................... 17 Table 3      Radiation discount experiments .................................................................................. 38 Table 4      Robustness tests .......................................................................................................... 49 Table 5      Descriptive statistics of the variables .......................................................................... 59 Table 6      Top ranked airports in 2005 and 2016 ........................................................................ 61 Table 7      The estimations of overall air connectivity................................................................. 67 Table 8      The estimations of domestic air connectivity ............................................................. 70 Table 9      The estimations of international connectivity ............................................................. 71    viii  List of Figures Figure 1      Two types of connections: direct and indirect ............................................................. 7 Figure 2      Six categories of connections .................................................................................... 12 Figure 3      Example for repeated calculation .............................................................................. 20 Figure 4      An example of radiation discount-distance ............................................................... 23 Figure 5      Geographical distribution of terminals ...................................................................... 26 Figure 6      Top 20 terminals of overall connectivity................................................................... 27 Figure 7      Overall connectivity of airports ................................................................................. 28 Figure 8      Airport connectivity components: direct, indirect and mixed ................................... 29 Figure 9      Airport connectivity components: domestic, international, and mixed ..................... 30 Figure 10    Top 20 railway stations of overall connectivity ........................................................ 31 Figure 11    Components of railway station connectivity ............................................................. 32 Figure 12     Connectivity of international terminals .................................................................... 33 Figure 13    Connectivity of international countries ..................................................................... 34 Figure 14    Centrality of terminals ............................................................................................... 35 Figure 15    Global routes (larger than 100).................................................................................. 36 Figure 16    Domestic Routes (larger than 200) ............................................................................ 37 Figure 17    Radiation Discount VS distance for all cases ............................................................ 39 Figure 18    City Connectivity for All Cases ................................................................................ 40 Figure 19    City rankings with different cases ............................................................................. 41 Figure 20    City connectivity with Case 2.................................................................................... 42 Figure 21    Connectivity of city routes ........................................................................................ 43 Figure 22    Routes between listed cities....................................................................................... 44 ix  Figure 23    Share of rail connectivity against route distance ....................................................... 45 Figure 24    City impact ................................................................................................................ 47 Figure 25    City Resistance .......................................................................................................... 48 Figure 26    Robust test on domestic airports-normalized connectivity ....................................... 50 Figure 27    Robust test on domestic airports-ranking .................................................................. 51 Figure 28    Robustness test on international airports (direct flights to China) ............................ 52 Figure 29    Connectivity of top connected airports 2005-2016 ................................................... 62 Figure 30    Connectivity of least connected airports 2005-2016 ................................................. 62 Figure 31    Connectivity of some tourism routes ......................................................................... 63 Figure 32    The distribution of airports across regions ................................................................ 64 Figure 33    Connectivity to the network outside the region ......................................................... 64 Figure 34    Connectivity inside the region ................................................................................... 65 Figure 35    International connectivity of major cities .................................................................. 66     x  Acknowledgements I offer my enduring gratitude to my advisor Professor Anming Zhang, who has offered unparalleled guidance, support, and encouragement throughout the whole journey of my Master program. He has been a great role model for me as a senior researcher, an inspiring teacher, and a sincere friend. I offer my gratitude to Professor Robin Lindsey for his interesting class and inspiring conversations, and for serving as my thesis committee member. I sincere appreciation extends to Professor Tae Oum and Professor Sanghoon Lee for their support and encouragement on my research and also for serving as my thesis committee member. I would like to thank Kun Wang for widening my vision of research and always providing valuable suggestions when I have questions. I would also like to thank Professor Yahua Zhang, and my friends and fellow students in the PHD office, for inspiring and encouraging me throughout my work. Special thanks are owed to my parents, who have supported me throughout my years of education in all ways, and encouraged me to follow my heart and work with my best effort.     xi  Dedication          .   1  1   Introduction The transport network plays a critical role in the development of economies at both the inter-city and intra-city levels. Multiple transport modes, such as air, road, rail, water, and pipeline transport, work together on moving passengers and cargo from city to city. On the one hand, it is the rapidly growing transport network that has enabled the idea of globalization to come into reality in the past four decades. On the other hand, transport network is also a dash board showing the evolution of bilateral and multilateral relationship between countries and even cities. A large volume of literature has reported the causality relationship between transportation infrastructure and local economy (e.g., Li and Qi, 2016, and studies cited therein). Beside economy, transport network is also a major concern for security reasons (Iida and Bell, 2003; Taylor and D’Este, 2007). When natural disasters like earthquakes and floods happen, or when wars break out, well-connected transport network provides resilient service during extreme time and brings hope for trapped people and interrupted business. Therefore, it is important for government, business owners, as well as civilians to monitor the comprehensive status of transport network, and make strategic plans accordingly. A lot of research has been conducted on the topic of transport network, especially in the field of air transport. Terminals like airports are usually compared and benchmarked in terms of the volume of passenger and traffic as well as operation efficiency (e.g., Oum et al., 2003). Although these indicators are valuable, they do not directly give clear information about the level of accessibility and competitive position of the terminal in the whole transport network (Burghouwt and Veldhuis, 2006; Burghouwt and Redondi, 2013).  An appropriate measure is needed to assist policy makers and airport management to benchmark and monitor the network performance 2  against that of other airports (Burghouwt and Redondi, 2013). This is the same for the other transport modes. Different transport modes can be simultaneously competitors and cooperators with each other. A measure that provides information of not only one transport mode but the whole transport network with multiple transport modes will be especially useful. In computing, connectivity is defined as capacity for the interconnection of platform, systems and applications. In complex networks, connectivity is a measurement for the extent of nodes being connected with other nodes. In transportation, the concept of connectivity was first introduced to evaluate the importance of an airport in terms of its connection to other airports. In the field of transport economics, much literature defines connectivity based on infrastructure availability and capacity, inspired by the theory of complex networks. Terminals like airports and train stations are defined as nodes, and the routes connecting those terminals are defined as edges (Hossain and Alam, 2017). Connectivity has different definitions and metrics in different articles (Calatayud et al., 2016). A good summary of the commonly used connectivity models can be found in Burghouwt and Redondi (2013). They include the shortest path length accessibility model (Shaw, 1993; Shaw and Ivy, 1994; Malighetti et al., 2008), the quickest path length accessibility model (Paleari et al., 2010), the weighted number of connections model (Burghouwt and de Wit, 2005), and the NetScan connectivity unit (NCU) model (Veldhuis, 1997; Burghouwt and Veldhuis, 2006; Veldhuis and Kroes, 2002; De Wit et al., 2009). An air freight connectivity model (NetCargo) based on the NetScan model was developed in Boonekamp and Burghouwt (2017). However, they either consider only one aspect of the connection quality (Burghouwt and Veldhuis, 2006), mostly time, or they take limited number of connections into account (Shaw, 1993; Shaw and Ivy, 1994; Malighetti et al., 2008; Paleari et al., 2010; Mandel et al., 2017).  3  This research contributes to the literature that investigates connectivity by proposing a connectivity model (Connectivity Utility Model, CUM) involving multiple quality factors for passenger transportation taking into consideration every connection (every flight, train, etc.), following the Dynamic Weighted Model (Zhu et al., 2017) and NetScan model (Veldhuis, 1997; Burghouwt and Veldhuis, 2006; Veldhuis and Kroes, 2002; De Wit et al., 2009). By involving multiple quality factors, CUM produces connectivity result that is more comprehensive and more consistent with service quality, and therefore provides more valuable information for its audience. By including multiple modes, CUM provides a universal and transferrable connectivity result, and better reveals the quality and quantity of overall inter-city transport service. Also, as CUM is based on trip-level data, which means that it will catch all changes of transport service supply, including adding one flight or increasing the speed of one train, it can be used to predict future connectivity, track the real-time connectivity and history connectivity. There are a number of studies discussing the relationship between different modes, especially between high-speed rail (HSR) and air transport. With wide application in Japan, Europe, China, and more to come, HSR has long been regarded as a competitor against air transport. Wang et al. (2016) discussed the effect of HSR network on the development of low cost carrier in China. There are also articles arguing that there is large potential for air and HSR transport to cooperate and integrate, especially in regions where the hub-and-spoke network strategy is well adapted by airlines (Givoni and Banister, 2006; Givoni, 2016). Air-rail alliances have been launched in some European airports, with railway service used as additional spokes for airlines. Travel agencies in China also started to sell air-rail ticket bundle with low price, guiding passengers to land at smaller airports with more available slots and then take HSR to get to first-tier cities. Xia and Zhang (2016a) have discussed the result of competition and cooperation between HSR and air 4  transport, and concluded that cooperation would be a non-zero-sum game when the airport is short of capacity and the cost of linking train station with airport is not too high. The benefit of air-rail intermodal integration has been widely discussed (Xia and Zhang, 2016b; Cokasova, 2013; Román and Martin, 2014; Vespermann and Wald, 2011). However, studies measuring connectivity considering multiple transport modes and transfers across modes remain sporadic. In this paper, as air transport, rail transport, and cross-mode transfer are all counted, a different angle is provided to see how well the air and rail mode works together with the current infrastructure and time slots. Connectivity could be an attribute not only for a terminal but also for a city. When we look at the connectivity of a city instead of a single terminal, all terminals contribute to the city’s connectivity aggregately. For passenger transportation, the level of connectivity for a city is actually the utility passengers feel when using services at all terminals to get to their destination. As passengers need to get to the terminal from home or from work before the service, the location1 of the terminal also has impact on the passenger’s utility, and therefore on the city’s connectivity. This research also takes into consideration the effect of terminal locations on the connectivity that a terminal contributes to the city. In the past few decades, transport network in China has gone through major changes. And the change will continue in the foreseeable future. The geographic distribution of China’s transport network is very uneven, concentrating in large cities like Shanghai, Beijing and Guangzhou, and in east part of China. In 2016, there were 28 airports that handled more than 10 million                                                  1 Not only location but also transport service between residential area to the terminal would affect the passenger’s utility. For example, although Pudong International Airport is 35 km away from city center, the maglev train takes only 7 minutes to go 30 km. 5  passengers and the passenger throughput of these 28 airports accounted for 79.1% of the nation’s total passenger traffic. Beijing Capital International Airport handled about 90 million passengers while Shanghai’s two airports processed more than 100 million. Large cities become more and more crowded and small cities are losing energy for the lack of young civilians. To help balancing the network and accelerate development in other parts of China, plans of transport infrastructure construction come out continuously. According to the updated “Medium-to-Long-Term Railway Network Plan” covering the period 2016-2025 with an outlook to 2030, China’s HSR network will by 2025 reach a total of 38,000 km, including eight north-south and eight east-west trunk lines (Fu et al., 2015). By 2030, China’s HSR network will reach a total of 45,000 km, and most cities with population of 0.5 million or more will be connected by HSR2. Before the Two Sessions3, a concept of building metropolitan area with HSR was reported in early 2017. In March 2017, the Civil Aviation Administration of China (CAAC) declared that 74 new airports would be built in the next few years, which will bring the number of civil airports to 260 by 2020, to 370 by 2025.  Beside proposing the Connectivity Utility Model (CUM), this paper also provides numeric results with a focus on 40 major domestic cities of China and involving both air and rail transport. The next section gives a description about CUM and presents data sources. The numeric results are reported and analyzed in Section 3. A regression analysis based on 10 years of air connectivity to investigate the drivers behind airport connectivity is reported in Section 4. Section 5 contains some concluding remarks and policy implications.                                                    2 Retrieved March 20, 2017, from http://www.chinanews.com/gn/2016/07-20/7946139.shtml 3 National People's Congress and Chinese People's Political Consultative Conference 6  2 Methodology and Data 2.1 Connectivity Utility Model The connectivity model used in this research is proposed based on the NetScan model first developed by Veldhuis (1997), and the Dynamic Weighted Model by Zhu et al. (2017). Traditional approaches measuring connectivity include using the number of destinations or the number of direct flights offered from a terminal. The NetScan model considers flight-level data, with both direct and indirect connections and the travel time involved. And the Dynamic Weighted Model considers connectivity contributed by direct connections of air and rail. The basic idea of the NetScan model is to assign a quality index (ranging between 0 and 1) which measures the quality of relative travel time to every flight connection (De Wit et al., 2009). A quality index of 1 is given to a non-stop flight while connections with multiple stops will be discounted with an index smaller than 1 as multi-stop flight takes a longer time than non-stop flight. Additional time penalty for each stop the flight makes applies due to the inconvenience caused by the transfer, such as the risk of missing connections, loss of baggage, physical movement, etc.  However, time is not the only factor to affect connectivity. An airport is well-connected when a passenger can get to his/her destination with high utility, which means that a seat can be easily booked, with multiple choices for schedule, with low cost, etc. Here I propose the Connectivity Utility Model (CUM) and define connectivity of a connection k (flight, train, etc., both direct and indirect) from terminal𝑖 to terminal𝑗 as the aggregated utility for passengers taking the connection. The function can be expressed as: 7   connectivity𝑖𝑗𝑘 = 𝑓(𝑥1, 𝑥2, 𝑥3, 𝑥4, … ) (1)  Where 𝑥1, 𝑥2, 𝑥3, 𝑥4 refer to the preferences of passengers. Preferences could include the availability of seats, the freedom of choice in schedule, cost, etc. Preferences are generic across different transport modes, therefore, formula (1) can produce generic connectivity results for different modes when the utility function is the same. The utility function is open to all purposes of research or applications. For example, cost may be the most important factor to calculate connectivity for business passengers, while the freedom of schedule would be of more value for leisure passengers.  There are 2 kinds of connections, direct and indirect, as showed in Figure 1. Both direct and indirect connections produce connectivity for the start and end terminals, i and j. While the indirect connection also generates a different kind of connectivity at the middle terminal, terminal𝑥, because terminal𝑥 works as the hub terminal and enabled connection k1 and connection k2 to cooperate. We define this kind of connectivity at hub as centrality. Centrality of terminal𝑥 is the aggregated connectivity of indirect connections that transferred at terminal𝑥, which can be expressed as:  centrality𝑥 = ∑ connectivity𝑖𝑗𝑘∀𝑖,𝑗,𝑘 𝑡𝑟𝑎𝑛𝑠𝑖𝑡 𝑎𝑡 𝑥 (2)    Figure 1 Two types of connections: direct and indirect 8  The directional connectivity for all connections from terminal𝑖 to terminal𝑗 is the connectivity of route ij, which is the aggregated connectivity for all connections on the route. Connectivity of route ij can be expressed as:  connectivity𝑖𝑗 =∑connectivity𝑖𝑗𝑘𝑘 (3)  The connectivity of terminal𝑖, including all connections from and to the terminal, is the aggregation of connectivity for all routes starting or ending at terminal𝑖, which can be expressed as:  connectivity𝑖 =∑connectivity𝑖𝑗𝑗+ ∑connectivity𝑗𝑖𝑗 (4)  The connectivity of 𝑐𝑖𝑡𝑦𝑎 is the aggregated connectivity of all terminals that contributes to the city’s transport service. There are different ways to aggregate terminal connectivity. One common method can be adding connectivity of all terminals within the administrative area of 𝑐𝑖𝑡𝑦𝑎. However, terminals also contribute to connectivity of adjacent cities in reality. For example, Shanghai Hongqiao International Airport also contributes to Suzhou’s air connectivity because Suzhou is only 70 minutes away by highway and 20 minutes away by HSR from Hongqiao Airport. Even though there’s no airport within the administrative area of Suzhou, it’s easy for civilians in Suzhou to get to Hongqiao Airport and enjoy air service there, even easier than for some residents in Shanghai who live far away from Hongqiao Airport. Therefore, connectivity contribution from terminal𝑖 to 𝑐𝑖𝑡𝑦𝑎 is assumed to be a function of terminal𝑖’s connectivity and the relative location of terminal𝑖 against 𝑐𝑖𝑡𝑦𝑎. Connectivity of 𝑐𝑖𝑡𝑦𝑎 can be expressed as: 9   connectivity𝑎 =∑𝑓(terminal𝑖,  𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑖𝑎)𝑖 (5)  Same as formula (1), the function in formula (5) is also open for all purposes. As connectivity of routes and terminals in the CUM is calculated by aggregating connectivity of all basic connections in operation (a flight, a train, etc.), it carries full information of the transport network and represents the true real-time status of it. Connectivity𝑖𝑗, which is the connectivity for route ij and also the weight for edgeij in the network, represents the service level from terminal𝑖 to terminal𝑗. Connectivity𝑖, which is the connectivity of terminal𝑖, is the service level as well as importance of terminal𝑖 in the network. Centrality𝑥, the amount of connectivity transiting at terminal𝑥, shows the service level of the terminal as a hub. And finally, connectivity𝑎  is the level of transport service at city𝑎.   2.2 Data Although the CUM can calculate connectivity for all transport modes, we only consider rail and air transport in the show case of this article because of data availability. Data of all flight schedules between Oct 4 to 26, 2016 is from IATA AirportIS database. Flight data includes flight number4, number of seats, origin airport, destination airport, take-off time, landing time, and number of stop-overs. Time zone is then matched to every airport and block time is calculated in minutes. Data of train services is accessed from 12306.cn5, for the same time period. Train data includes train number, vehicle code, start station, end station6, from-station,                                                  4 For code-sharing flights, only the operating flights are retained. 5 The official website for China Railway, the only state-owned rail service supplier in China. 6 Start station is the station where the train starts the service and end station is the last stop for the train. 10  to-station, available seats between from-station and to-station7, time to depart at from-station, and time to arrive at to-station. Although the analysis will be focused on 40 major Chinese domestic cities, the connection dataset is a full set of all existing air and rail services, from and to terminals both among and out of the 40 cities including international flights8. So, the overall connectivity, centrality, domestic connectivity and international connectivity9 will all be produced. The list of 40 cities include all provincial capital cities, and sub-provincial cities. There are 41 airports and 95 train stations involved. The full list of the cities and terminals are attached in appendix 1 and 2, respectively. Indirect connections are generated with direct connection data, following the enumeration method realized with codes written in R language. The produced indirect connection dataset is then filtered with loose constraints in travel distance and transfer time, which can be expressed as:  𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖ℎ + 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒ℎ𝑗 ≤ 2×𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖𝑗 (6)    30 ≤ 𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘 ≤ 1440  𝑓𝑜𝑟 𝑎𝑖𝑟 − 𝑎𝑖𝑟 (7)   5 ≤ 𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘 ≤ 1440  𝑓𝑜𝑟 𝑟𝑎𝑖𝑙 − 𝑟𝑎𝑖𝑙 (8)   60 + d𝑡×1.5 ≤ 𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘 ≤ 1440  𝑓𝑜𝑟 𝑎𝑖𝑟 − 𝑟𝑎𝑖𝑙 𝑜𝑟 𝑟𝑎𝑖𝑙 − 𝑎𝑖𝑟 (9)                                                   7 From-station and to-station are 2 stations between the first station and the last station of a train service. From-station is the original station of a train ticket, which is where the passenger gets on the train, and to-station is the destination station of a train ticket, where the passenger gets off the train. Although train tickets are sold with flexible origin and destination, there’s a planned supply for different sections according to history data on 12306.cn. As all train data is acquired 10 days before departure, we assume the seat inventory for every section is the supply of seats for that section. 8 International flights including flights from and to all airports around the world except for airports in the region of South America, due to data availability. 9 Flights from mainland China to Hong Kong and Macau are considered as international flights, as passengers need to go through customs. When comparing domestic connectivity of airports, flights from Hong Kong and Macau to mainland China are considered as domestic flights for Hong Kong and Macau. 11   d𝑡 ≤ 100  𝑓𝑜𝑟 𝑎𝑖𝑟 − 𝑟𝑎𝑖𝑙 𝑜𝑟 𝑟𝑎𝑖𝑙 − 𝑎𝑖𝑟 (10)  Where 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖ℎ denotes the great circle distance10 between origin terminal i and transit terminal h; 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒ℎ𝑗 denotes the great circle distance between transit terminal h and destination terminal j; 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖𝑗 denotes the great circle distance between origin terminal i and destination terminal j; 𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘 denotes the transfer time at transit terminal for indirect connection k from terminal𝑖 to terminal𝑗; and d𝑡 denotes the great circle distance from the 2 transit terminals when the connection is air-rail or rail-air transfer. Formula (6) and (10) are the spatial constraints for transfer. When taking indirect connections, the total distance of the connection is constrained to be smaller than 2 times of the direct distance. And when taking air-rail and rail-air connections, the distance between the transit airport and the transport railway station is constrained to be smaller than 100 km. Formula (7) – (9) are the time constraints for transfer. 30 minutes and 5 minutes are assumed to be the minimum transfer time at airport and train station respectively. For air-rail and rail-air transfer, the minimum transfer time is assumed to be 60 minutes plus the time to move between 2 transit terminals. The speed to move between terminals is assumed to be 40 km/h. As mentioned above, (6) - (10) are loose constraints to help reduce the size of dataset and prepare for further processing.   2.3 Applied Connectivity Utility Model In the show case of this paper, we consider only air and rail transport connections with maximum one stop. There are six categories of connections involved, direct air connection, indirect air                                                  10 All great circle distances in this research are calculated with Python package “Geographiclib”, using GPS coordinates of OD. 12  connection with one stop, direct rail connection, indirect rail connection with one stop, air connection connected with rail connection, and rail connection connected with air connection. The six categories of connections are showed in Figure 2.       Figure 2 Six categories of connections Specific functions for formula (1) and (4) are chosen in the show case. The preferences considered in this research are availability of seats (capacity), trip duration (velocity), and quality of transfer (for indirect connections). Other preferences like cost can be easily attached when the data is available. As there are multiple preferences, and the preferences, capacity, velocity and transfer quality, are independent from each other, the utility function should be either additive or 13  multiplicative11. Furthermore, dissatisfaction of any of the three preferences would lead to 0 utility12. Therefore, multiplicative utility function is adopted. Here we assume equal weight for all preferences and scale utility score of all preferences to be between 0 and 1. All numeric results are produced following this assumption. When different weights or different formula is adopted, the numeric results will change accordingly. People using the model can emphasize on their focus and objective by adjusting the weights and the equation system.  The utility score of capacity, velocity and transfer quality are named as capacity discount, velocity discount and transfer discount respectively, for simplification. And here we have:  Connectivity𝑖𝑗𝑘 = 𝐷𝐶𝑎𝑝𝑖𝑗𝑘  ×  𝐷𝑉𝑒𝑙𝑖𝑗𝑘×  𝐷𝑇𝑟𝑎𝑛𝑠𝑖𝑗𝑘 (11)  Where 𝐷𝐶𝑎𝑝𝑖𝑗𝑘 denotes the capacity discount for connection k between terminals i and j.13  𝐷𝑉𝑒𝑙𝑖𝑗𝑘 represents the velocity discount, and 𝐷𝑇𝑟𝑎𝑛𝑠𝑖𝑗𝑘 is the transfer discount14.  Capacity is a key indicator measuring connection quality. Larger aircraft tend to carry more passengers, to provide more available seats, and thus increase connectivity, ceteris paribus. Two airports are better connected when airlines change the aircraft to larger ones when the frequency remains the same. Capacity discount is a function of available seats for a specific connection. We adopt a concave function (squared root) instead of a linear form for capacity discount. This is because we believe that the marginal benefit of adding more seats diminishes to a certain point,                                                  11 Theorem 1 in (Keeney, 1974). 12 Corollary in (Keeney, 1974). Also, intuitively, if the connection is super-fast and with not mid-stops, there would still be no connectivity when there’s no available seat. 13Every connection on a route between terminal i and terminal j is treated as a different connection, even for the connection with the same connection number (flight number/train number) on a different date, as the connection might use a different type of vehicle. Therefore, the frequency for every connection in this model is 1.   14 Transfer discount factor is always 1 for direct flights. 14  and the extra benefit of adding a 100-seat flight is larger than that of increasing the seat capacity from 100 to 200 for one flight, because of the benefit of schedule freedom the extra connection brings. The aircraft with the most available seats currently in use is Airbus 380, with 538 seats. The rail section with the most available seats in China has 2684 seats.  We choose the capacity of Airbus 380 as a benchmark to calculate the capacity discount15, which can be expressed as:  𝐷𝐶𝑎𝑝𝑖𝑗𝑘 =√𝑆𝑒𝑎𝑡𝑖𝑗𝑘Seat0 (12)  Where 𝑆𝑒𝑎𝑡𝑖𝑗𝑘 represents the number of seats on connection k. For indirect connections, the seat number is bounded by the section with fewer seats. Seat0 is the number of seats of the benchmark vehicle, which in this study is 538. Velocity is another important indicator for connection quality. The slower the velocity is, the longer time, i.e. more value of time, the passenger needs to sacrifice. The velocity is the average distance the passenger moves in a time unit. To move from terminal𝑖 to terminal𝑗, the time the passenger needed is not only the time in vehicle. The passenger also needs to arrive at terminal in advance to check in, check bags, go through security check, etc. He/she also needs to stay at the destination terminal for baggage pick up and security check. In addition, if the passenger takes an indirect connection, the time he/she spends at the transit stop would be more uncomfortable than in-vehicle time, because the next connection may be missed, the baggage may be lost, there may be a long distance of physical movements in between, etc. Additional time penalty for each stop the connection makes applies. Both the extra time at terminals and the penalty for transfer                                                  15 Some connections with trains will have capacity discount larger than 1. This is ok because when we use a different benchmark capacity, capacity discount of all connections will rescale in the same way.  15  time should be represented in the velocity discount. Following the same structure of capacity discount, the velocity discount is calculated based on the following system of equations:  𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑𝑖𝑗𝑘 = 𝑇𝑎𝑟𝑟𝑖𝑣𝑒𝑖𝑗𝑘 − 𝑇𝑑𝑒𝑝𝑎𝑟𝑡𝑖𝑗𝑘 + p𝑇×𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘 + 𝑡𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙𝑖𝑗𝑘 (13)   Velocity𝑖𝑗𝑘 = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖𝑗𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑𝑖𝑗𝑘 (14)   D𝑉𝑒𝑙𝑖𝑗𝑘 = √Velocity𝑖𝑗𝑘Velocity0 (15)  Where 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑𝑖𝑗𝑘 is the adjusted time length (duration) of connection𝑘 from terminal𝑖 to terminal𝑗. The scheduled in-vehicle time between two terminals is the difference between the scheduled arrival time and scheduled departure time,16 represented by 𝑇𝑎𝑟𝑟𝑖𝑣𝑒𝑖𝑗𝑘 − 𝑇𝑑𝑒𝑝𝑎𝑟𝑡𝑖𝑗𝑘. Extra time at terminals is represented by 𝑡𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙𝑖𝑗𝑘. When the connection has intermediate stop, the additional time spent at the transit terminal (𝑡𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑗𝑘) is penalized by p𝑇, the extra penalty assumed for the additional time spent at intermediate point. The velocity (Velocity𝑖𝑗𝑘) is calculated by dividing the great circle distance between terminal𝑖 and terminal𝑗 with adjusted time duration. Velocity discount is calculated by comparing the velocity of a connection against the benchmark velocity, Velocity0. Again, we use a concave function instead of a linear functional form.17 Extra time at airports and extra time at train stations are different, as the procedures to go through are different. We assume the extra time needed at airport to be 100 minutes for domestic flights and 180 minutes for international flights, and the extra time needed at train station to be 45 minutes in this research. For air-rail and rail-air transfers, the assumed extra time at terminals                                                  16 Transit time is included if the connection has an intermediate stop.  17 It should be noted that in both our model and the NetScan model, short-haul routes would suffer more discount in terms of velocity, as the same benchmark of velocity is applied for all ranges of distance. In fact, the average velocity of short-haul connections should be slower than that of long-haul connections, especially when the extra time needed at terminals is taken into consideration. However, this is consistent with the fact that transport modes with shorter extra time needed, such as HSR and highway, are preferred for short-haul travels. 16  is listed in Table 1. Also, we assume the extra penalty for transit time to be 50%. The benchmark velocity, Velocity0, is assumed to be 800 km/h18. Table 1 Extra time at terminals for air-rail and rail-air transfers First Section Second Section Extra Time at  Origin Terminal Extra Time at Destination Terminal Domestic Flight Train 90 15 International Flight Train 120 15 Train Domestic Flight 30 30 Train International Flight 30 60  For indirect connections, connectivity is largely dependent on the quality of transfer. There are a lot of aspects to consider to reveal the level of transfer quality, such as transit time, procedures and distance to go through, services during transfer, etc. Also, for cross-mode transfer, like air-rail or rail-air transfer, the passenger needs to move from one terminal to another terminal. Sometimes the distance could be as far as 50 kilometers. Here we model transfer quality in two dimensions, time and service.  Time quality for transfer measures the quality of transfer time. For airports, minimum connection time (MCT) is the allowed minimum time between two connecting flights at the transit airport when a joint ticket is sold. Basically, when the transfer time is larger than MCT, the passenger should be able to catch the connecting flight, though with a risk to run at some time or depart without luggage. Although different airlines have different MCT at every airport, we assume the same MCT19 for all airports and all airlines because of data availability. Here we define MCT for rail-rail, air-rail, and rail-air transfer, following the same intuition. MCT standards are listed in Table 2.                                                   18 In the future with more advanced technology, the maximum velocity of a vehicle would be larger than 800 km/h, which would bring velocity discount larger than 1. This won’t affect the result because when we use a different benchmark velocity, velocity discount of all connections will rescale in the same way. 19 The MCT standard here is from China Eastern Airline’s MCT at Shanghai Pudong International Airport and Shanghai Hongqiao International Airport. 17  Table 2 MCT for all possible transfers First Section Second Section Whether at the same terminal20 MCT (minutes) Domestic Flight Domestic Flight Yes 60 Domestic Flight Domestic Flight No 100 Domestic Flight International Flight Yes 120 Domestic Flight International Flight No 160 International Flight Domestic Flight Yes 120 International Flight Domestic Flight No 160 International Flight International Flight Yes 90 International Flight International Flight No 130 Train Train Yes 30 Domestic Flight Train No 𝟔𝟎 + 𝟐×𝐝𝐭21 International Flight Train No 𝟏𝟎𝟎 + 𝟐×𝐝𝐭 Train Domestic Flight No 𝟖𝟎 + 𝟐×𝐝𝐭 Train International Flight No 𝟏𝟐𝟎 + 𝟐×𝐝𝐭  Time quality is a function of the difference between the actual transfer time and MCT. When the transfer time is too short, the transfer will be impossible to make, and therefore the time quality is 0. When the transfer time is too long, though the transfer will be fully possible, the transfer will be less comfortable as the passenger needs to stay at the transit terminal for too long. The time quality is set to be 0.2 when transfer time is the same as MCT, 1 when transfer time is 30 minutes longer than MCT, and 0.7 when transfer time is 3 hours longer than MCT or even longer. Here we construct the time quality function as:                                                  20 Transfers at the same airport but at different terminals are allowed, while transfers at different airports are not allowed in this research. 21 d𝑡 is the great circle distance between the destination terminal of the first section and the original terminal of the second section. 18   𝑞𝑖𝑗𝑘𝑇 ={      0, ∆𝑡𝑖𝑗𝑘 < −10(∆𝑡𝑖𝑗𝑘 + 10)×0.02, −10 ≤ ∆𝑡𝑖𝑗𝑘 < 0∆𝑡𝑖𝑗𝑘30×0.8 + 0.2, 0 ≤ ∆𝑡𝑖𝑗𝑘 < 301 −∆𝑡𝑖𝑗𝑘 − 30500, 30 ≤ ∆𝑡𝑖𝑗𝑘 ≤ 1800.7, ∆𝑡𝑖𝑗𝑘 > 180 (16)  Where 𝑞𝑖𝑗𝑘𝑇  represents the time quality for the transfer of indirect connection k from terminal𝑖 to terminal𝑗; ∆𝑡𝑖𝑗𝑘 represents the difference of time between the transfer time of connection k from terminal𝑖 to terminal𝑗 and MCT at the transit terminal of this connection. ∆𝑡𝑖𝑗𝑘 is negative when the transfer time is shorter than MCT. Service quality for transfer measures the quality of transfer service, such as easiness of moving, waiting room service, and flexibility when the second connection is missed because of delay, etc. Service quality is different for different transfer occasions. For air-air transfer, service quality is mainly decided by alliances. When both flights are served by the same alliance or same airline, the service quality is good. When one flight is served by low cost carrier, the service quality will be relatively worse. Service quality for air transfer is assumed to be 1 when both flights are served by the same airline that is not low cost carrier; 0.9 when served by the same alliance but different companies (alliance of low cost carriers is not counted); 0.3 when served by full-service airlines from different alliances22 or the same low cost carrier; and 0.1 for other situations. For rail-rail transfer, the service quality is assumed to be always 1 as it’s easy to move from one train to another and all train services are provided by the same company, China Railway. For air-rail transfer and rail-air transfer, as there’s no alliance between railway and airlines in China yet, the service quality is mainly dependent on the transport service between the airport and train station. Though the transport service between airport and train station varies with different cities, it’s highly correlated with the distance between terminals. When the distance is short, like the Hongqiao Railway Station and Hongqiao International Airport, the service quality is high because the passenger doesn’t need to take a taxi and suffer the risk of congestion, the inconvenience of moving with luggage, and the cost of moving. When the distance is long, the                                                  22 Some airlines from different alliances would cooperate in a small range of routes and provide great connecting services. However, this detail is ignored in this show case because of data availability. 19  service quality will be low. Even for Shanghai Pudong International Airport (PVG), which is connected by Maglev trains, the transport service would still be low for a large number of passengers who prefer to use taxi, or subway to get to the airport. We set service quality to 1 when the distance is shorter than 2 km, 0.5 when the distance is 5 km, 0.1 when the distance is 30 km, and 0 when the distance is longer than 100 km. Service quality for air-rail and rail-air transfer can be expressed as:  𝑞𝑖𝑗𝑘𝑆 ={      0, d𝑡 > 1000.1 − 0.1×d𝑡 − 3070, 30 ≤ d𝑡 < 1000.5 − 0.4×d𝑡 − 525, 5 ≤ d𝑡 < 301 − 0.5×d𝑡 − 23, 2 ≤ d𝑡 < 51, d𝑡 < 2 (17)  Where 𝑞𝑖𝑗𝑘𝑆  is the service quality of transfer for indirect connection k from terminal𝑖 to terminal𝑗; d𝑡 is the distance in kilometers between the transit airport and transit railway station for this connection. And then the transfer discount can be expressed as:  𝐷𝑇𝑟𝑎𝑛𝑠𝑖𝑗𝑘 = 𝑞𝑖𝑗𝑘𝑇 ×𝑞𝑖𝑗𝑘𝑆  (18)  With equation (11) - (18), connectivity of any connection can be produced. However, for indirect connections from terminal𝑖 to terminal𝑗 transferring at terminalℎ, some direct connections from terminal𝑖 to terminalℎ and from terminalℎ to terminal𝑗 will be calculated for more than once. For example, in the case showed in Figure 3, connection k2, k3, and k4 take off from terminalℎ 40, 60, and 90 min after the landing of connection k1, respectively. K1-k2, k1-k3, and k1-k4 are all indirect connections between terminal𝑖 and terminal𝑗. Therefore, when calculating indirect connectivity from terminal𝑖 to terminal𝑗 through terminalℎ, connection k1 is counted for 3 indirect connections. Under certain circumstances, the indirect connectivity from terminal𝑖 to terminal𝑗 through terminalℎ will be higher than the direct connectivity from terminal𝑖 to terminalℎ, which is not reasonable. 20    Figure 3 Example for repeated calculation When multiple indirect connections share 1 direct connection, the best-case for indirect connectivity is that all capacity of the shared connection is used for those connecting flights. Therefore, the capacity of these indirect connections is constrained by the capacity of the shared connection, while velocity and transfer quality are not. Example showed in Figure 3 is the most simplified situation. Both the first section and the second section might be shared. Here we add an upper limit for indirect connectivity, which is:  ∑ 𝐷𝐶𝑎𝑝𝑖(ℎ)𝑗𝑘∀𝑘 𝑤𝑖𝑡ℎ 𝑠𝑘′1≤ 𝐷𝐶𝑎𝑝𝑖ℎ(𝑗)𝑠𝑘′1 (19)   ∑ 𝐷𝐶𝑎𝑝𝑖(ℎ)𝑗𝑘∀𝑘 𝑤𝑖𝑡ℎ 𝑠𝑘′2≤ 𝐷𝐶𝑎𝑝𝑖ℎ(𝑗)𝑠𝑘′2 (20)  Where 𝑠𝑘′1  denotes a direct connection from terminal𝑖 to terminalℎ, which works as the first section of multiple different indirect connections; 𝑠𝑘′2  denotes a direct connection from terminalℎ to terminal𝑗, which works as the second section of multiple different indirect connections; 𝐷𝐶𝑎𝑝𝑖(ℎ)𝑗𝑘 denotes capacity discount of indirect connection k from terminal𝑖 to terminal𝑗 transferring at terminalℎ;  𝐷𝐶𝑎𝑝𝑖ℎ(𝑗)𝑠𝑘′1 denotes capacity discount of 𝑠𝑘′1 ; 𝐷𝐶𝑎𝑝(𝑖)ℎ𝑗𝑠𝑘′2 denotes capacity discount of 𝑠𝑘′2 . The left-hand side of equation (19) sums up the capacity discount of all 21  indirect connections taking the route ihj and uses 𝑠𝑘′1  as the first section from terminal𝑖 to terminalℎ. The right-hand side of equation (19) gives the capacity discount of 𝑠𝑘′1 . Equation (20) sums up the capacity discount of all indirect connections taking the route ihj and uses 𝑠𝑘′2  as the second section from terminalℎ to terminal𝑗. The right-hand side of equation (20) gives the capacity discount of 𝑠𝑘′2 . With equation (19) and (20), capacity discounts of all indirect connections sharing one mutual section are constrained by the capacity discount of the shared section. The intuition behind equation (19) and (20) is that capacity of indirect connections is constrained by capacity of both direct connections involved in the indirect connection. When equation (19) or (20) is not satisfied, the capacity of the shared section is assigned to the connection with the best velocity discount and transfer discount, as it is assumed that when capacity discount is the same, connection with better quality in other dimensions attracts the most passenger volume.23 To aggregate connectivity of terminals to cities, a series of functions are adopted in this research. These functions are constructed in order to simulate the attenuation of terminals’ contribution of connectivity for cities, when the distance between the terminal and the city becomes larger. As it’s similar to the spread of radiation, I call the discount “radiation discount” and the function “radiation function”. Here is an example:  𝐷𝑅𝑎𝑑𝑖𝑎 ={  𝑒−𝑑𝑖𝑎70 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎31.84) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 (21)                                                   23 With the upper limit for shared connections, every direct connection is still allowed to be counted for 1 time in each directional route. However, when the connection connects with connections with different destinations at the transfer station, the connection will still be calculated repeatedly, because it is difficult to assign capacity of the shared section to indirect connections of different routes. It allows direct connections with slots that cooperate better with other connections to contribute more connectivity. 22  Where 𝐷𝑅𝑎𝑑𝑖𝑎 denotes the radiation discount of terminal𝑖’s connectivity on city𝑎; 𝑑𝑖𝑎 denotes the great circle distance between centre of city𝑎 and terminal𝑖. It is assumed that the distance between city centre and the terminal represents the average travel distance for passengers living in the city to get to the terminal. Segmented function is adopted here. When the distance is very short, for example 500 metres, passengers will simply walk there. When the distance is medium, 2 to 10 km, passengers can take bus or subway or drive a short distance to get to the terminal. When the distance is longer, the passenger will have to drive. The level of inconvenience to get to the terminal is very sensitive to distance when the distance is short. The cosine function is applied because it provides a right shape. While when the distance is very long, like 100 km, the passenger always needs to drive or take an inter-city bus service, the inconvenience level is less sensitive to distance, therefore an exponential function with negative power is adopted. In the example of radiation function shown in equation (21), connectivity contribution diminishes to 50% when the distance is 50 km, 25% at 100 km, and 5% at 200 km. The relationship between radiation discount and distance in equation (21) is shown in Figure 4. 23   Figure 4 An example of radiation discount-distance Radiation discount simulates a general process of inter-modal transportation, which is taking public transport or driving to get to air and rail terminals. Apart from representing the effect of location on a terminal’s transport service level, radiation discount also allows terminals to generate connectivity for both passengers in the city and passengers in neighbourhood cities, which is true. Cities surrounded by large cities, like Suzhou and Shenzhen, are benefited by allowing connectivity radiation. In the meantime, connectivity varies with radiation discount function. Radiation discount function should be decided according to the purpose of connectivity measuring. Different radiation discount functions will be tested and discussed in the next section. In this research, we use sum of connection’s connectivity (which is a form of utility) as the connectivity of a route or a terminal. Mandel et al. (2017) made strong arguments that the service indicator of path ij should be log sum of the Logit path choice model24 instead of weighted                                                  24 ln∑ exp (𝑉𝑝)𝑝  00.10.20.30.40.50.60.70.80.911 21 41 61 81 101 121 141 161 181 201 221 241 261 281Radiation Discount24  sum of connection utility25, which gives each connection a weight (probability to be used) according to their connectivity compared with other connections in the same route and then takes the weighted sum of all connections in the route as its connectivity. Though Logit model is not used in this research, it’s interesting and useful to make sure that the same problem with models discussed in their paper do not happen with our model.  The major problem Mandel et al. argued against is that using weighted sum utility would lose information equal to the Shannon’s measure (Shannon, 1948), −∑ 𝑝𝑝ln (𝑝 𝑝𝑝)26,  compared with the log sum measure. The weighted sum of connectivity is more like taking the average connectivity of all connections. The amount of connections in a route is not appreciated. In some cases, the connectivity of a route calculated with weighted sum utility will decrease with extra connections added. For example, when a connection with poor quality, connectivity of 1, is added to a route with 1 good connection, connectivity of 5, the new connectivity of the route will be 4.928, which is smaller than the original connectivity. In our case, we use quality discount instead of p, which would always bring positive effect when there’re more connections available, as connectivity scores of connections in one route are independent from each other in CUM. As a matter of fact, all connections in one route are taken into consider in CUM model, while Mandel et al. (2017) only allowed 7 alternative paths for each domestic route, 10 for European OD routes, and 16 for intercontinental routes when applying the log sum measure.                                                     25 ∑ 𝑝𝑝𝑝 ∙ 𝑉𝑝, it is proved by Shannon (1948) that ln ∑ exp (𝑉𝑝)𝑝  = ∑ 𝑝𝑝𝑝 ∙ 𝑉𝑝 − ∑ 𝑝𝑝ln (𝑝 𝑝𝑝). 26𝑝𝑝 =exp (𝑉𝑝)∑ exp (𝑉𝑝)𝑝=𝑃𝑝=1, where 𝑉𝑝 is the utility (connectivity) derived by connection p, and 𝑝𝑝 denotes the possibility of choosing connection p. 25  3 Numeric Results and Analysis Numeric results and analysis with the applied CUM model are presented in 3 parts: terminal connectivity, city and region connectivity, and network connectivity. 3.1 Terminal Connectivity Terminal connectivity is made up of air connectivity, rail connectivity, and mixed (air-rail and rail-air) connectivity. Both airports and railway stations have mixed connectivity apart from air/rail connectivity. Therefore, it is an advantage to cooperate with terminals of the other type in neighbourhood. Figure 5 shows the geographic distribution of terminals with their connectivity represented by colour and pie size. Three major metropolitan city groups with high connectivity are observed in Beijing-Tianjin-Hebei, Yangtze River Delta, and Pearl River Delta economic zones. This result is similar to the finding of Zhang et al. (2004) and Hui et al. (2004) in terms of connectivity in China’s air cargo flows up to the early 2000s.  26   Figure 5 Geographical distribution of terminals The top 20 terminals of overall connectivity are listed in Figure 6, and a full list of terminal connectivity is reported in Appendix 3. Though all top 4 terminals are airports, winner of the battle between airports and railway stations is hard to decide. Six out of the top 10 terminals are airports, and 11 out of the top 20 are airports. Beijing Capital International Airport (PEK) is the best-connected terminal, followed closely by Shanghai Pudong International Airport (PVG), Hong Kong International Airport (HKG), Guangzhou Baiyun International Airport (CAN), and Nanjing South Railway Station (NKH). NKH is the only railway station among the top 5 terminals. According to China Central Television, NKH is also the second largest railway station in the world and the largest in Asia in terms of gross floor area, with passenger throughput 2.23 million over 10 days from September 28 to October 7 in 201627. Hangzhou East Railway Station                                                  27 Retrieved March 20, 2017, from http://www.nanjing.gov.cn/xxgk/bm/jtj/201610/t20161008_4203956.html 27  (HGHRail), Suzhou Railway Station (SZH), Chengdu Shuangliu International Airport (CTU), Shanghai Hongqiao Railway Station (AOH), and Kunming Changshui International Airport (KMG), take 6th to 10th place respectively.  Figure 6 Top 20 terminals of overall connectivity Though terminals in megacities (Beijing, Shanghai, Guangzhou, Hong Kong, etc.) are leading with big advantage, we see a large amount of “middle-class” terminals. There are 6 terminals with connectivity above 55,000, 13 above 40,000, 24 above 30,000, 57 above 20,000, 99 above 10,000, and 109 above 5,000. There are 8 terminals with connectivity below 1,000. HSR contributes largely to railway station’s connectivity. All train stations in the top 40 terminals have HSR service. 0100002000030000400005000060000700008000090000100000Top 20 TerminalsAirConnectivity RailConnectivity MixedConnectivity28   Figure 7 Overall connectivity of airports Connectivity of airports is showed in Figure 7. PEK, PVG, HKG and CAN lead with large advantage in terms of overall connectivity. Figure 8 presents the proportion of direct air, indirect air, and mixed connectivity of airports. Figure 9 shows the proportion of domestic air, international air, and mixed connectivity of airports. It is found that ratio of mixed connectivity against the overall connectivity (𝑟𝑚𝑖𝑥𝑒𝑑/𝑎𝑙𝑙) is lower with better connected airports. Pearson’s correlation between 𝑟𝑚𝑖𝑥𝑒𝑑/𝑎𝑙𝑙 and overall connectivity is -0.571, with p-value at 0.000. Also, ratio of international connectivity against air connectivity (direct and indirect), 𝑟𝑖𝑛𝑡/𝑎𝑖𝑟, is higher with better connected airports. Pearson correlation between 𝑟𝑖𝑛𝑡/𝑎𝑖𝑟 and overall connectivity is 0.715, with p-value at 0.000. There is no clear correlation between domestic ratio (domestic air connectivity/air connectivity) and overall connectivity. This indicates that international flights are concentrated in mega airports. As a matter of fact, the top 4 airports, PEK, PVG, HKG, and CAN, contributed 46.55% of overall international connectivity and 69.41% of direct 0100002000030000400005000060000700008000090000100000PEKPVGHKGCANCTUKMGSZXURCCKGXMNXIYHRBHGHSHEHAKTAODLCNNGKWELHWFOCWUHNKGCSXSHACGOCGQTSNINCTYNXNNHETNGBTNAKHNHFELXASJWLYGNAYXUZOverall Connectivity of AirportsAirConnectivity MixedConnectivity29  international connectivity, while their contribution in domestic connectivity is only 15.63% of overall and 19.17% of direct domestic connectivity. The concentration of international flights, especially on transcontinental routes, in top ranking mega airports will continue in the foreseeable future. However, with the development of the national HSR network, we can expect increase of international connectivity in inland areas.  Figure 8 Airport connectivity components: direct, indirect and mixed 30   Figure 9 Airport connectivity components: domestic, international, and mixed Connectivity of the top 40 railway stations are presented in Figure 10. Nanjing South Railway Station (NKH), Hangzhou East Railway Station (HGHrail), Suzhou Railway Station (SZH), Shanghai Hongqiao Railway Station (AOH), Tianjin Railway Station (TJP), Shijiazhuang Railway Station (SJP), and Xuzhou East Railway Station (UUH), are the only 7 train terminals with connectivity over 35,000. NKH, AOH, HGHRail, UUH, and TJP are the top 5 considering only rail connectivity. SZH drops to the 8th position with rail connectivity only. 31   Figure 10 Top 20 railway stations of overall connectivity Figure 11 gives the distribution and components of railway connectivity. Mixed connectivity (air-rail, rail-air) is critical for railway stations. The correlation between 𝑟𝑚𝑖𝑥𝑒𝑑/𝑎𝑙𝑙 and overall connectivity for rail stations is 0.449, with p-value of 0.000. Mixed connectivity of a railway station represents the easiness of taking a train from the station to get close to an airport and then take a flight from the airport. For special cases like AOH, the railway station locates together with a well-connected airport, Shanghai Hongqiao International Airport (SHA), the mixed connectivity of AOH is not super high because passengers can just walk from AOH to SHA. However, this kind of colocation and cooperation between railway stations and airports is counted in the centrality of both terminals.  05000100001500020000250003000035000400004500050000550006000065000NKHHGHSZHAOHTJPSJPUUHIZQJGKCCTNGHSBTNJHVNPCWQWHNOHHSYTBXPCUWJNKZZFNXGZAFFZSXCHIOQSZQENHWCNXKSTIPICWGZQTXPSHHEAYVABHBBConnectivity of Top 40 Railway StationsRailConnectivity MixedConnectivity32   Figure 11 Components of railway station connectivity Connectivity of international terminals, which are all airports in this research, is also calculated. International terminals’ connectivity with China’s domestic terminals is presented in Figure 12, and their connectivity aggregated by country is showed in Figure 13. Detailed results for foreign airports and countries are presented in Appendix 4 and 5. Top-ranking international airports in connecting China are mainly distributed in South-east Asia, East Asia, Europe, and west-cost North America. Bangkok International Airport (BKK) is the airport best-connected with China, with connectivity of 15,999.63. Singapore Changi International Airport (SIN) follows closely with connectivity of 15,955.22. Seoul Incheon International Airport (ICN, 12,323.00), Kuala Lumpur International Airport (KUL, 12,208.43), Frankfurt Airport (FRA, 11,861.63), San 33  Francisco International Airport (SFO, 11,705.79), Don Mueang International Airport (DMK, 11,613.43), Los Angeles International Airport (LAX, 11,443.80), Tokyo Narita International Airport (NRT, 13,79028), and Paris Charles de Gaulle Airport (CDG, 10,494.39), take 3rd to 10th place.  Figure 12 Connectivity of international terminals When aggregated by country and region, United States (130,907) leads with big advantage to be the best-connected country with China. Thailand (52,890), Japan (50,978), Korea (28,980), Germany (25,484), Australia (23,275), Malaysia (21,973), and Canada (20,092) are the other 7 top-ranking countries and regions with connectivity higher than 20,000. For international airports and countries, high connectivity level with China represents the tight ties of economy, culture, politics, etc. between each other.                                                   28 Though ICN’s connectivity is higher than NRT, Tokyo is slightly better connected to China than Seoul when considering NRT and HND (Tokyo Haneda International Airport) for Tokyo and ICN and GMP (Seoul Gimpo International Airport) for Seoul. 34   Figure 13 Connectivity of international countries Compared with connectivity, centrality is more monopolistic. Figure 14 gives the centrality of top 40 terminals in centrality. PEK is the biggest hub, with centrality of 146985, while there are only 7 terminals beside PEK with centrality above 30000, which are PVG, CAN, SHA, HKG, AOH, HGHair and CTU. While looking at the composition of connectivity, PEK, PVG, CAN, and HKG are mostly air hub only. While SHA and AOH stands out as cross-mode hub, with cross-mode centrality accounting for 83.6% and 77.6% of their overall centrality respectively. As a matter of fact, SHA and AOH are currently the only mega airport and mega train station co-located in China. Constrained by land resource, it will be hard and expensive to connect HSR station with airports that are already built. But cities to build new airports are favoring the idea. Chengdu and Shenzhen have both reported plans of HSR-airport co-location in 2016 and 2017 respectively. Shanghai has also reported plan in 2016 to build Shanghai East Railway Station by the side of PVG. Air-rail transfer will be more common and convenient in the future. 35   Figure 14 Centrality of terminals Directional routes with connectivity higher than 100 are shown in Figure 15. A more detailed pattern of China’s domestic routes (connectivity higher than 200) is presented in Figure 16. We can see that well-connected routes are still concentrated in east part of China. Furthermore, international routes are mostly limited on PEK, PVG, CAN, and HKG.  At route level, rail route AOHNKH is the best-connected terminal-terminal route globally, with connectivity level 1079. All top 5 terminal-terminal routes are rail routes. The top 3 cross-mode routes between terminals are NKHURC (Urumqi Diwopu International Airport), NKHKMG, and NKHSYX (Sanya Phoenix International Airport). The top air route between terminals is HKG-LHR (London Heathrow Airport). HKG-LHR, HKG-LAX, and PVG-LAX are the top 3 international routes (nondirectional). The top international routes connecting mainland China are PVG-LAX, PEK-LAX, and PVG-CDG (Paris Charles de Gaulle Airport). 36  Surprisingly, none of routes connecting the top 4 foreign airports (BKK, SIN, ICN, and KUL), is on the very top. One reason could be that long routes benefit in the CUM for the high average speed. This is also a signal that these airports are less dependent on limited number of hub airports and have developed good connections with more airports in China.  Figure 15 Global routes (larger than 100) 37   Figure 16 Domestic Routes (larger than 200)  3.2 City and Region Connectivity It’s common for a city to have both railway station and airport, sometimes more than 1. Therefore, it is critical to look at connectivity aggregated at the level of city to see the overall inter-city transport service at the city. As the aggregation method has great effect on the result, city connectivity has been aggregated with 8 different radiation discount functions. The functions are listed in Table 3. The relationship between radiation discount and distance is presented in Figure 17. Results for cities under the 8 cases are presented in Appendix 6.   38  Table 3 Radiation discount experiments Case No Discount Benchmark (50 km, 100 km, 200 km) Function 1 NA Aggregate terminal connectivity by administration area. 2 (0.5, 0.25, 0.05) {  𝑒−𝑑𝑖𝑎70 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎31.84) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 3 (0.7, 0.35, 0.1) {  1.35×𝑒−𝑑𝑖𝑎75 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎42.4) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 4 (0.9, 0.45, 0.15) {  1.68×𝑒−𝑑𝑖𝑎79 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎76) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 5 (0.3, 0.15, 0.03) {  0.62×𝑒−𝑑𝑖𝑎70 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎25.25) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 6 (0.1, 0.05, 0.01) {  0.2×𝑒−𝑑𝑖𝑎71 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎20) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 7 (0.5, 0.35, 0.15) {  0.73×𝑒−𝑑𝑖𝑎130, 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎31.84) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50 8 (0.5, 0.15, 0.01) {  1.75×𝑒−𝑑𝑖𝑎40 , 𝑑𝑖𝑎 > 50cos(𝑑𝑖𝑎31.84) + 12, 0 ≤ 𝑑𝑖𝑎 ≤ 50    39  Case 1 has no radiation discount and aggregates terminal connectivity by administrative area. Case 6, Case 5, Case 2, Case 3, Case 4 changes the overall speed of decay, from fastest (10% at 50 km) to slowest (90% at 50 km). Case 7 and Case 8 changes the speed of decay for long-distance range (above 50 km), from slow (35% at 100 km, 15% at 200 km) to fast (15% at 100 km, 1% at 200 km). Case 2 is the same as the radiation function discussed in Section 2.3. It’s also considered as base case here.  Figure 17 Radiation Discount VS distance for all cases Connectivity of cities under all 8 cases are showed in Figure 18. Comparing city connectivity against Case 2, we see that Case 3, 4 and 7, where radiation discount decays slower, favours city connectivity, while in Case 5, 6, and 8, where radiation discount is more sensitive of distance, city connectivity is lower than Case 2. Some cities’ connectivity is even lower than Case 1 in Case 5, 6, and 8, because even terminals within their administrative area are “far” away from city centre in these cases. In cases except for 5, 6, and 8, connectivity for most cities is always higher 00.10.20.30.40.50.60.70.80.911 6111621263136414651566166717681869196101106111116121126131136141146151156161166171176181186191196Radiation Discount Case 2 to 8Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 840  than when there’s no radiation discount, because when connectivity decays slower with distance, terminals benefit a larger area of residents and terminals with different service are able to cooperate with each other. Mega airports will be able to provide good service for passengers not only in mega cities but also in their adjacent cities. Airports in smaller cities with unique routes or lower fare will also benefit large cities nearby. Crowded terminals can direct low-value connections to smaller terminals in the neighbourhood and focus on high-value routes. Therefore, by improving the short-distance transportation service to terminals from residency area both in the city and in adjacent cities, connectivity of all cities in the metropolitan area will be improved.   Figure 18 City Connectivity for All Cases When comparing cities under all cases, it is observed that Hong Kong, Lianyungang, Suzhou, Hangzhou, Ningbo, Guangzhou, Shanghai, and Shenzhen are the cities benefited the most in all 0300006000090000120000150000180000210000240000270000ShanghaiBeijingGuangzhouNanjingHangzhouShenzhenTianjinShenyangWuhanSuzhouChengduJinanHong KongZhengzhouXi'anChangchunChongqingChangshaHarbinShijiazhuangXuzhouKunmingFuzhouUrumqiXiamenGuiyangHefeiNingboQingdaoNanchangNanningDalianLanzhouTaiyuanHohhotHaikouXiningYinchuanLhasaLianyungangCity Connectivity for All CasesCom1 Com2 Com3 Com4 Com5 Com6 Com7 Com841  cases. While cities like Lanzhou, Kunming, and Lhasa always suffer with radiation discount. It seems that cities with other big cities in close neighbourhood benefit by accessing inter-city transport service of other cities. Distance is included in the radiation function to assess how easy it is to access terminals. Therefore, even though distances between cities would never change, when commute services are improved, e.g. when cities are connected with Maglev trains, or with faster highway, excellent inter-city transport service in mega cities will benefit a larger area of civilians.  Figure 19 City rankings with different cases The rankings of cities under different cases are presented in Figure 19. We can see that although some of the 8 cases are sensitive with distance while others are not, the ranking of cities are mostly consistent across all cases. For example, Ningbo’s ranking is always higher when radiation discount is enabled, so is Shijiazhuang, Suzhou, Shenzhen, etc. While cities like Urumqi, Changchun, Shenyang, etc., always rank lower with radiation discount. Shanghai ranks 051015202530354045ShanghaiBeijingGuangzhouNanjingHangzhouShenzhenTianjinShenyangWuhanSuzhouChengduJinanHong KongZhengzhouXi'anChangchunChongqingChangshaHarbinShijiazhuangXuzhouKunmingFuzhouUrumqiXiamenGuiyangHefeiNingboQingdaoNanchangNanningDalianLanzhouTaiyuanHohhotHaikouXiningYinchuanLhasaLianyungangCity rankings with different radiation discount casesCase_1 Case_2 Case_3 Case_4 Case_5 Case_6 Case_7 Case_842  1st in all cases except for Case 6. Distribution of cities with connectivity is presented in Figure 19, calculated with Case 2. It is observed that Yangtze-River Delta and Pearl-River Delta are better connected than Beijing-Tianjin-Hebei Economic Zone, a finding that is again consistent with the one in Zhang et al. (2004) and Hui et al. (2004) with respect to China’s air cargo connectivity.  Figure 20 City connectivity with Case 2 At the level of inter-city route, Beijing-Guangzhou (5,400) is the winner, followed closely by Beijing-Shanghai (4,882), and Beijing-Shenzhen (4,826). All the top 3 city pairs are benefited by high level of indirect connectivity. When 2 cities are far away from each other, and have a lot of big cities in between, it is easier for passengers to find indirect connections, because there are a lot of feasible transit cities. While in terms of direct connectivity, short-haul routes have better performance. Shanghai-Nanjing (3,942), Nanjing-Suzhou (3,138), Shanghai-Suzhou (2,601), 43  Beijing-Tianjin (2,435), and Shanghai-Hangzhou (2,306) are the top 5 routes. Rail connectivity, mostly HSR, contributes for more than 95% of direct connectivity for all top 10 routes in direct connectivity. Figure 20 presents connectivity of the top 20 non-directional inter-city routes.  Figure 21 Connectivity of city routes Figure 21 represents connectivity of inter-city routes between the 40 listed cities only. A diamond shape is observed with higher connectivity level within it, as marked with blue lines in Figure 22. Beijing-Tianjin-Hebei Economic Zone, Yangtze-River Economic Zone, Pearl-River Economic Zone, and Chengdu-Chongqing Economic Zone are the 4 vertices of the diamond. The strongest connections within this area are those connecting the 4 vertices. 0100020003000400050006000Connectivity of top 20 non-directional inter-city routesIndirectConn DirectConn44   Figure 22 Routes between listed cities The proportion of rail connectivity of routes29 is negatively correlated with route distance, with Pearson’s correlation of -0.610 (p-value 0.000). Rail connectivity accounts for larger share in short distance routes. The relationship between share of rail connectivity and route distance is showed in Figure 23. The line marked in blue shows the fitted values of rail’s share in terms of distance. Although the HSR has been well recognized as the dominant transport mode only for short- and medium-haul route with distance below 700 km (Adler et al., 2010; Fu et al., 2014; Wan et al., 2016; Yamaguchi et al., 2008; Xia and Zhang, 2016a), the HSR has become a better and popular option for both medium- and long-haul routes up to 1500 km, with people building in confidence in its safety and punctuality. For example, rail accounts for 64.94% for Urumqi-                                                 29 Proportion of rail connectivity is only calculated for routes with rail connections. 45  Xining, the great circle distance of which is 1443 km. Low cost may also be a critical advantage for rail transport. Rail has been a good complement for air transport on long-haul routes with insufficient air service.  Figure 23  Share of rail connectivity against route distance  3.3 Vulnerability Analysis Any kind of incident occurring on a city’s transport network will affect the connectivity of the city. Train breakdowns, electrical failures, road construction, aviation control, etc., would all result in connectivity decrease. In extreme situations, such as war and natural disaster, it is possible to lose one entire route, one terminal, or even a city. Vulnerability, which is defined by Berdica (2002) as the degree of susceptibility of a network to certain incidents that may lead to 46  reduced service or accessibility levels, is critical under these circumstances. When a city has a resistant transport network, which means that it will remain functional under extreme situations, it brings flexibility and easiness for government, companies, and individuals to rescue, rebuild, and balance back. Therefore, it is important to analyse vulnerability of city’s transport service for enterprises before locating, and for government because of security reasons.  A lot of research concerning how to define, evaluate, and handle vulnerability of cities’ transport system has been well-conducted (Berdica, 2002; Taylor et al., 2006; Taylor, 2008; Rodríguez and García, 2014). In this research, characteristics of incidents are not concerned. The focus is on the consequence in terms of connectivity, when the incident has already happened and destroyed a terminal or route. In this research, two kinds of vulnerability will be discussed. First, city impact, which is the loss of overall network connectivity when a city is lost. When a city is lost, not only the city’s connectivity but also connectivity of other cities connecting with it will be lost. City impact represents the importance of the city in the network. Figure 24 presents city impact of top 25 cities, in terms of overall connectivity and direct connectivity. Shanghai, Beijing, Guangzhou, and Nanjing are the top 4 cities in overall city impact. When Shanghai is lost, 9.6% of overall connectivity and 15.1% of direct connectivity in the whole city network will be lost. Nanjing surpasses Guangzhou to be the 3rd most important city in direct connectivity. Hangzhou, Wuhan, Zhengzhou, Changsha, Tianjin, and Xuzhou also rank higher in terms of direct city impact than overall city impact. These cities are extremely important because direct connections are more efficient and effective than indirect connections in extreme situations. 47   Figure 24 City impact Second, city resistance, which is the loss of the city’s remaining connectivity when a certain number of top ranking routes connecting it are lost, compared with original connectivity. If a city is only well connected with one city, it will be disconnected from the world when the only route is destroyed. However, if a city is well connected with multiple cities, the city will still be well-connected when one route is lost. Figure 25 presents city’s remaining connectivity when top 1, top 2, up to top 20 routes connecting the city are lost. Only cities ranking in the top 5 and the bottom 5 are presented. It is observed that Hong Kong, Shanghai, Beijing, Hangzhou, and Ningbo are more resistant of route loss. Hong Kong is the winner of resistance, keeping 88.94% of its original connectivity without the top 20 routes. While Lhasa would keep only 59.05% of its connectivity when top 20 routes are cut. 00.020.040.060.080.10.120.140.16ShanghaiBeijingGuangzhouNanjingHangzhouShenzhenTianjinShenyangWuhanSuzhouChengduJinanHong KongZhengzhouXi'anChangchunChongqingChangshaHarbinShijiazhuangXuzhouKunmingFuzhouUrumqiXiamenGuiyangHefeiNingboQingdaoNanningNanchangDalianLanzhouTaiyuanHohhotHaikouXiningYinchuanLhasaLianyungangCity ImpactLossOfDirectConn LossofConn48   Figure 25 City Resistance  3.4 Robustness Analysis All numeric results in previous parts of Chapter 3 are produced with the applied CUM, with equal weight for all quality factors. When the weight of quality factors changes, the result will be different. In this part, the robustness test will be performed for direct flights to see how the weight of quality factors will change the connectivity of applied CUM. As capacity and velocity are the only 2 quality factors that will affect direct flights, only weight of them will be changed.  𝐷𝐶𝑎𝑝𝑖𝑗𝑘 = (𝑆𝑒𝑎𝑡𝑖𝑗𝑘Seat0)𝑣1 (22)   D𝑉𝑒𝑙𝑖𝑗𝑘 = (Velocity𝑖𝑗𝑘Velocity0)𝑣2 (23)  0.550.60.650.70.750.80.850.90.951City ResistanceHong Kong Shanghai Hangzhou Beijing NingboXining Haikou Nanning Lianyungang Lhasa49  For a multiplicative model like CUM, to change the weight of a factor is to change the sensitivity of its discounting equation. Equation (22) and (23) present the generic capacity and velocity discount. In the applied CUM, 𝑣1 and 𝑣2 are both set to be 0.5. When 𝑣1 and 𝑣2 increase, the sensitivity of capacity discount and velocity discount will increase. When 𝑣1 and 𝑣2 decrease, the sensitivity will decrease. Especially, when 𝑣2 increases, the discrimination against short-haul flights increases. Here, as showed in Table 4, 4 different sensitivity levels are tested for capacity and velocity, which produces 16 sets of scenarios. Table 4 Robustness tests (V1, V2) Low Mid-low Mid-high High Low (0.25, 0.25) (0.25, 0.5) (0.25, 1) (0.25, 2) Mid-low (0.5, 0.25) (0.5, 0.5) (0.5, 1) (0.5, 2) Mid-high (1, 0.25) (1, 0.5) (1, 1) (1, 2) High (2, 0.25) (2, 0.5) (2, 1) (2, 2)   All 16 scenarios are tested for direct flights. Air connectivity of the 41 listed Chinese major airports for all scenarios are presented in Figure 26. Air connectivity is normalized with the highest connectivity under each scenario. We can see the normalized connectivity for most airports is consistent across scenarios. Generally, the more sensitive the scenario is, the more differentiated the connectivity will be. PEK, PVG, CAN, and HKG are still the 4 dominant airports. PEK is always the best-connected airport. Connectivity of PVG is also very stable under all scenarios. HKG always benefit from higher sensitivity, because flights connecting HKG have larger capacity and longer distance compared with other airports. URC also benefits from increased sensitivity on velocity discount because URC is far away from other airports in China 50  and flights serving URC are usually longer than other flights in distance. HET is similar as URC. Figure 27 presents the ranking of domestic airports under different scenarios. We can see that ranking is relatively robust across scenarios.   Figure 26  Robust test on domestic airports-normalized connectivity 00.10.20.30.40.50.60.70.80.91PEKPVGCANHKGKMGCTUSZXXIYCKGSHAHGHURCXMNCGOHRBNKGTAOCSXWUHSHEDLCTSNHAKKWELHWNNGFOCCGQTNATYNHETINCSJWNGBHFEKHNXNNWUXLXANAYXUZLYGNormalized Direct Air Connectivity of Domestic AirportsDir_Clw_Vlw Dir_Clw_Vmlw Dir_Clw_Vmhg Dir_Clw_VhgDir_Cmlw_Vlw Dir_Cmlw_Vmlw Dir_Cmlw_Vmhg Dir_Cmlw_VhgDir_Cmhg_Vlw Dir_Cmhg_Vmlw Dir_Cmhg_Vmhg Dir_Cmhg_VhgDir_Chg_Vlw Dir_Chg_Vmlw Dir_Chg_Vmhg Dir_Chg_Vhg51   Figure 27 Robust test on domestic airports-ranking Figure 28 gives the normalized connectivity with China of top 30 international airports. Compared with domestic airports, the connectivity between international airports and China’s domestic cities is less robust. Sensitivity of capacity has a slight favor for long-haul routes because airlines tend to serve long-haul routes with large aircraft. Sensitivity of velocity discount strongly support airports that are far away from China.  051015202530354045PEKPVGCANKMGHKGCTUSZXXIYCKGSHAHGHURCXMNCGOTAONKGHRBWUHCSXDLCSHETSNHAKKWELHWNNGFOCCGQTNAHETTYNINCSJWNGBHFEKHNXNNWUXLXANAYXUZLYGRanking of Direct Air ConnectivityDir_Clw_Vlw Dir_Clw_Vmlw Dir_Clw_Vmhg Dir_Clw_VhgDir_Cmlw_Vlw Dir_Cmlw_Vmlw Dir_Cmlw_Vmhg Dir_Cmlw_VhgDir_Cmhg_Vlw Dir_Cmhg_Vmlw Dir_Cmhg_Vmhg Dir_Cmhg_VhgDir_Chg_Vlw Dir_Chg_Vmlw Dir_Chg_Vmhg Dir_Chg_Vhg52   Figure 28  Robustness test on international airports (direct flights to China) The robustness shows that the weight of different discounting factors does have effect on results. It should be carefully chosen according to the objective before application.   00.10.20.30.40.50.60.70.80.91Robustness Test on International Airports (Direct Flights to China)Dir_Clw_Vlw Dir_Clw_Vmlw Dir_Clw_Vmhg Dir_Clw_VhgDir_Cmlw_Vlw Dir_Cmlw_Vmlw Dir_Cmlw_Vmhg Dir_Cmlw_VhgDir_Cmhg_Vlw Dir_Cmhg_Vmlw Dir_Cmhg_Vmhg Dir_Cmhg_VhgDir_Chg_Vlw Dir_Chg_Vmlw Dir_Chg_Vmhg Dir_Chg_Vhg53  4 Analysis for Drivers of Connectivity While a lot of research calculates connectivity, studies on the drivers of connectivity, and especially those on Chinese terminals connectivity remain sporadic. Although some literature (e.g., Li and Cai, 2004; Lin, 2012; Wang et al. 2014) has studied the evolution of air transport network of China and revealed a significant improvement in connectivity, the connectivity of individual airports has not been measured using a comprehensive approach that considers both quantity and quality elements.  In this Section, we run analysis on the drivers of connectivity30. The air connectivity of 69 Chinese airports, considering all the flights from and to these 69 airports for the period 2005-2016, is calculated, including both domestic and international flights. The results are in Appendix 7. These airports accounted for about 95% of the total passenger enplanements in the last few years. For each year, we use the flight data of two periods to construct the connectivity measure: April 16 to April 22, and Oct 16 to Oct 22. We hope that the use of two periods’ flight information will give a good representation of that year’s connectivity.  4.1 The Methodology and Data for Detecting the Drivers of Air Connectivity  We have obtained the connectivity performance scores for 69 airports (67 cities as Beijing and Shanghai have two airports each). In this section, we will investigate the economic and institutional drivers of the connectivity performance of these cities.31                                                   30 Only air connectivity is considered as historical schedule data for trains is not available. 31 The city of Lhasa is excluded from the second-stage regression analysis due to the lack of some macroeconomic indicator data for this city. 54  Although Burghouwt and Redondi (2013) note that connectivity is an important variable in passengers’ route choice and can be used in econometric models as an independent variable, little literature has studied the drivers of air connectivity as a dependent variable, although some studies have mentioned that connectivity is determined by a set of supply and demand components. They include land-use component (the characteristics of land uses at origins and destinations travellers), transport system component, the temporal component and the individual traveller component (e.g., demographic and income information) (Geurs and Van Wee, 2004; Taylor, 2008; Matisziw and Grubesic, 2010). In fact, many connectivity metrics are constructed based on this framework.  A relevant study is carried out by Maertens (2010) who examined the drivers of long haul flight supply at secondary airport in Europe. The author identified internal factors such as airport charges, semi-external factors such as the length of runway, and external factors including economic power, regional importance of inbound tourism, political importance of the catchment, etc.  The research suggests that economic power measured by GDP has a significantly positive impact on long haul flight supply. However, the author argued that sufficient runway length is only a condition sine qua non, which does not automatically increase the number of long haul flights. In fact, many long runways at many secondary airports are underutilised and thus not economically viable.  Macroeconomic condition matters. Wittman and Swelbar (2013) reported that in the period 2007-2012, the US air transportation system experienced a series of changes as a result of the global financial crisis, high fuel prices and airlines’ profit-focused capacity discipline strategies. Connectivity at medium-hub airports declined the most (15.6%) while large hub airports only lost 3.9% of their connectivity.  55  The gravity model might also be relevant. Our connectivity of a city (airport) is the aggregate of the connectivity of the city to and from all destinations. The connectivity performance of the city is driven by the economic significance of the city and its major trading partners as well as some impedance and facilitating variables. This is analogous to the gravity model which has been widely used in cross-country empirical analysis of international trade flows. The gravity model has also been applied to air transport to identify the determinants of bilateral air passenger or air cargo flows (Zhang and Zhang, 2016). Although our connectivity measure reflects the aggregate connectivity at an airport/city, which is not a flow between cities, the gravity model can still give us some guidance in revealing the economic drivers and cost/incentive factors for this performance indicator. Following the above discussion32, the regression model is specified as follows: Yit=α0+α1lnHHIit+α2lnYieldit+α3Locationi+α4lnPopit+α5lnGDPCapitait+α6lnFixedassetit +α7Touristi+α8Hubi+α9lnRunwayi+α10lnTerminalit+α11 Springit+α12HSRit +α13lnEconomyt+α14Crisist+α15 Olympicit+α16Expoit+τi+εit  where, • Yit is the connectivity (overall, domestic, and international) for city i in year t. • HHIit is the Herfindahl-Hirschman Index (HHI) of city i in year t. The HHI is calculated using the passenger share of each operating airline at the airport(s) of city i. • Yieldit is the average yield of all the flights out of the city i in the year t. Airline yield is calculated by dividing the airfare with the flight’s flying distance. The passenger number is used as the weight for the average.                                                   32 Apart from the factors mentioned above, non-aviation services at airport, such as shopping, car rental, hotel, etc., may also help airports to attract passengers and generate revenue. However, services are not included in the regression model because of data availability and endogeneity. 56  • Locationi is the sum of the reciprocal of distance from city i to its provincial capital city and its distance to the eight most-well connected airports in our sample. It is expected that if a city is closer to a larger city, its air connectivity will be lower. • Popit is the population of city i in year t.  • GDPCapitait is GDP per capita of city i in year t. • Fixedassetit is the value of the fixed asset investment of city i in year t. • Touristi is a dummy variable to control for the tourist cities.  • Hubi is equal to one if the city’s airport is one of the 11 hubs declared by the CAAC in 2010. • Runwayit is the airport runway length in city i in year t. If a city has multiple runways, the sum of the length of all runways is used. • Terminalit is the airport terminal size in city i in year t. • Springit is a dummy variable to control for the presence of the low-cost carrier (LCC), the Spring Airlines, in city i in year t.  • HSRit is a dummy variable to indicate whether city i has high-speed rail (HSR) service in year t. • Economyt is the sum of the GDP of Beijing, Shanghai and Guangzhou in year t. This variable is included following the guidance of the gravity model, which says that bilateral trade/passenger flows between two economies are proportional to the size measured by GDP or population of them. Beijing, Shanghai and Guangzhou represents three economic centres in North, East and South China, respectively, which are significant trading partners and travel destinations to almost all Chinese cities. For many airports, the first route that was launched should be the one linking to one of the three cities.   • Crisist is the variable to control for the global financial crisis in 2008 and 2009. •  Olympicit is the dummy variable to control for the effect of the 2008 Beijing Olympic game to Beijing.  • Expoit is the variable to control for the effect of the 2010 Shanghai World Expo to Shanghai. All continuous independent variables are taken logarithm in the estimation.  For the panel data regressions (random and fixed-effect models), the connectivity index is also taken the logarithm. We use one-year lagged values of all the time-variant variables for the estimation to avoid 57  potential endogeneity caused by the simultaneity between these variables and the air connectivity.   We assume the error term to be consisted of a time-invariant airport-specific unobservable τi,  and a white-noise term εit, which is independent and identically distributed (i.i.d).33  We adopt both fixed-effect and random-effect.  Fixed-effect model help deal with the potential endogeneity problem if the error term τi is correlated to any independent variable. However, under this estimation method, the coefficients of all the time-invariant control variables, such as city tourism status, the airport hub status and other time-invariant variables cannot be identified.  Instead, the random-effect model is more efficient, and allows the identification of the time-invariant variables’ coefficients. But the endogeneity because of the correlation between  τi and controlled variables will have to be compromised.  Santos Silva and Tenreyro (2006) showed that the Jensen's inequality, E(𝑙𝑜𝑔(𝑦))  ≠ 𝑙𝑜𝑔 (𝐸(𝑦)), had been neglected for a long time in estimating the log-linearized gravity. Under heteroscedasticity (which is often the case in gravity studies and of course this study), parameters of log-linearized gravity models estimated by OLS will be highly misleading, which may distort the interpretation of the models. Santos Silva and Tenreyro (2006) thus recommended the use of the Poisson pseudo-maximum likelihood estimator (PPML) technique. This approach also has the advantage of dealing with the zero-flow problem in data (Zhang et al., 2017). Fally (2015) shows that PPML with fixed effects can produce reliable and consistent results for gravity                                                  33 The auto-correlation of the εit does not affect the estimation consistency and unbiasedness. It may only decrease the estimation efficiency. 58  models. Therefore, the PPML approach will be used in addition to the panel data estimation techniques. With PPML the level of connectivity is used instead of the logarithmic form. The airport HHI, and the average yield variables are calculated using the IATA AirportIS data. These are the air ticket booking data on the route and airline basis, with each airline’s passenger number, flight flying distance and the average ticket price reported monthly, quarterly and annually.34 The airport location index is calculated as the sum of reciprocal of the distances to major airports as discussed earlier. The distances between airports are retrieved by the GPS. The city population, GDP, total fixed asset investment data are available in China City Statistical Year Book (2005-2015). The 2015 and 2016 data of some these variables are not available, so our regression analysis only covers a period of 2005-2014. The city tourism status dummy equals one for the cities including Guilin, Haikou, Hangzhou, Huangshan, Kunming, Sanya, Wuyishan, Xi’an, Xiamen, Yichang and Zhangjiajie.35 The airport runway length and terminal size data can be found in CAAC published statistical data on civil aviation of China. The dummy of Spring Airlines’ presence is based on the IATA AirportIS data. The HSR dummy is constructed by referring to the news reports on the opening of HSR services at each city. Table 5 provides the summary statistics of our variables.                                                    34  We retrieve the prices of all the fare classes.  35  We chose these cities as tourism cities by referring to Zhang and Round (2009) and Fu et al. (2015).  59   Table 5 Descriptive statistics of the variables Variable No. of Obs Mean Std. Dev. Min Max Unit Connectivity (overall) 660 952 1,436 2.69 8,971 Unit Connectivity (domestic) 660 861 1,197 2.69 7,532 Unit Connectivity (international) 660 91 287 0 2,120 Unit HHI (1/10000) 660 2,658 1,515 865 9,831 Unit Airport Average yield 660 0.154 0.08 0.08 1.30 RMB Location Index 660 0.116 0.031 0.024 0.177 Unit City Population 660 596 450 52 3,375 Ten thousand City GDP per capita 660 52,034 42,974 5,303 481,638 RMB City Fixed Asset Investment 660 17,800,000 17,700,000 344,900 131,000,000 Ten thousand RMB Tourist 660 0.167 0.373 0 1 Unit Airport hub status 660 0.197 0.398 0 1 Unit Runway length 660 34,06 1,750 2,200 14,000 Meter Terminal size 660 13 22.54 0.2 140.85 Ten thousand m2 Spring Airlines’ share 660 0.009 0.02 0 0.23 Unit HSR 660 0.152 0.36 0 1.00 Dummy Economy 660 3.87 1.37 2.13 6.16 Hundred billion RMB    4.2 Results Analysis   4.2.1 Connectivity Results Analysis The overall connectivity scores (including both domestic and international connectivity) of all the cities under study are listed in Appendix 7. The total connectivity of the 69 airports increased from 40,330 in 2005 to 107,329 in 2016, an increase of 166%. Some small- and medium-sized 60  airports experienced the largest percentage increase. For example, Luzhou witnessed a 37-times increase and Wuxi 17-times. The airports of Beijing, Shanghai, and Guangzhou saw relatively slower growth rate. However, if we look at the absolute change, the top airports, Shanghai Pudong, Beijing, Kunming, Guangzhou, Xi’an, Chongqing, Chengdu, Shenzhen and Hangzhou, all experienced an increase of more than 200 connectivity points each year. The top 10 best connected airports in 2016 and 2005 are reported in Table 6. From 2005 to 2016, Beijing Capital, Guangzhou and Shanghai Pudong airports consistently remained the top three. Xi’an and Chongqing made into the top 10 while in 2016 Haikou and Urumqi dropped out. It should be noted that in 2016 the air connectivity of Shanghai as a city with two mega-airports surpassed Beijing as the best-connected city.    61  Table 6 Top ranked airports in 2005 and 2016 2016 2005 Rank Airport Connectivity Rank Airport Connectivity 1 Beijing Capital 8,762 1 Beijing Capital 5,643 2 Guangzhou 6,095 2 Guangzhou 3,216 3 Shanghai Pudong 5,693 3 Shanghai Pudong 2,947 4 Kunming 4,805 4 Shanghai Hongqiao 2,368 5 Shenzhen 4,729 5 Shenzhen 2,209 6 Chengdu 4,585 6 Chengdu 1,934 7 Xi’an 4,116 7 Kunming 1,473 8 Shanghai Hongqiao 3,980 8 Haikou 1,155 9 Chongqing 3,800 9 Hangzhou 1,149 10 Hangzhou 3,565 10 Urumqi 1,138  We put the airports into different groups based on their overall connectivity scores: over 3900, 400-3900, below 400. The evolution of the eight best connected airports in 2016 (overall connectivity score is greater than 3900) is presented in Figure 29. Almost all of them experienced very steady growth during 2005-2016. For the airports with connectivity scores between 400 and 3900 in 2016, we can also observe an upward growth pattern throughout the years. In general, we found that the higher the connectivity, the more stable the growth trend. This is especially the case for most provincial capital cities. The evolution of the least connected airports in 2016 is shown in Figure 30. Most of them are small and tourism cities. It can be seen that most of them suffered the loss of connectivity at some stage, indicating the vulnerability of the connectivity of small airports. It has been noticed that the HSR network has been extended to some of these cities including Taizhou, Wuyishan, and Yuncheng, which may have caused the 62  ups and downs of connectivity of these cities. In addition, their closeness and easy access to some large cities via highways may be another factor.     Figure 29  Connectivity of top connected airports 2005-2016  Figure 30 Connectivity of least connected airports 2005-2016 0100020003000400050006000700080009000100002005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016Beijing Guangzhou Pudong KunmingShenzhen Chengdu Xi'an Hongqiao0204060801001201402005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016Yuncheng Lianyungang Luzhou MudanjiangTaizhou Wuyishan Huangshan Jingdezhen63  Cities that heavily rely on the tourism industry should be more concerned about the airport connectivity. We examine five cities, Huangshan, Guilin, Sanya, Wuyishan, and Zhangjiajie. Except Guilin, the tourism industry contributes to more than 50% of the GDP for other four cities. Figure 31 shows that apart from Sanya, the situation is worrying for these cities as their airport connectivity performance exhibits stagnant or declining trends in some periods.  In fact, Wuyishan and Zhangjiajie recorded negative growth between 2005 and 2016.    Figure 31 Connectivity of some tourism routes The Civil Aviation Administration of China (CAAC) has partitioned China into several administrative regions: East China, Central and South China, North China, Northeast China, Southwest China, Northwest China and Xinjiang. Each region is administered by the CAAC regional administration. In this study, we combine Northwest China and Xinjiang. The distribution of the 69 airports is shown in Figure 32. The vast majority of the airports are located in the East, central, and south part of China. The connectivity at the region level can be seen in Figure 33, which clearly shows that East China, and Central & South China have much higher connectivity than other regions. Northeast and Northwest are at the bottom. The air connectivity 050010001500200025001 2 3 4 5 6 7 8 9 10 11 12Connectivity of tourism citiesWuyishan Sanya Zhangjiajie Huangshan Guilin64  within each region is shown in Figure 34, which shows how the airports in each region connect to each other. Again, cities are much better connected in East, Central and South China.   Figure 32 The distribution of airports across regions  Figure 33 Connectivity to the network outside the region 051015202530East China Central & SouthChinaNorth China Northeast China SouthwestChinaNorthwestChinaNumber of airports05000100001500020000250002005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016Connectivity beyond regionEast China Central & South China North ChinaNortheast China Southwest China Northwest China65   Figure 34 Connectivity inside the region The domestic connectivity follows the same pattern as the overall connectivity, which is not reported here. Figure 35 shows the top eight cities that have the highest international connectivity in 2016. Shanghai remained the best internationally connected city, followed by Hong Kong, Beijing, and Guangzhou. International connectivity of all other cities is almost negligible. It can be seen that the international connectivity of Shanghai and Beijing were severely affected by the 2008 global financial crisis. Beijing had not restored to its highest historical level by the end of 2016.  050010001500200025002005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016Connectivity within regionEast China Central & South China North ChinaNortheast China Southwest China Northwest China66   Figure 35 International connectivity of major cities  4.2.2 Regression Results Analysis  The regression results for the overall air connectivity are collated in Table 7. The results are largely consistent across models. As the PPML with fixed effects can produce more efficient estimation results in the presence of the heteroscedasticity problem, our discussion is mainly based on the findings of this model.  According to all regression models, airline competition measured by HHI is conducive to overall air connectivity. Lower HHI indicates that the market has more airlines and more competition, which means that the market is more liberalized. Regression results also show that airports with lower average price have higher level of air connectivity, which means that the price that airports and airline charge is not only important for regulation reasons as discussed in Zhang and Czerny (2012), but it’s also an important factor affecting air connectivity. Zhang and Czerny (2012) discussed that a private and monopolistic airport tend to charge excessive prices to airlines and passengers. Therefore, the regression results show an insight that liberalization benefit air 0500100015002000250030002005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016International connectivityShanghai Hong Kong Beijing GuangzhouChengdu Hangzhou Tianjin Shenzhen67  connectivity by both increasing the competition and decreasing the airline price. This is consistent with conclusion of Fu et al. (2010), which showed empirical conclusion that liberalization led to substantial economic and traffic growth. It indicates the deregulation policies observed in Chinese airline market are effective and beneficial in promoting overall air connectivity. Fu et al. (2015) discussed the recent deregulation moves taking place in China, which empower airlines with more autonomy in route entry, network development and competition. Market mechanism for airport slot allocations have also been tried out in Shanghai and Guangzhou airports for a more efficient utilisation of scarce airport capacities. We would expect continuous deregulation in China’s air transport sector can further promote the air connectivity.  Table 7 The estimations of overall air connectivity  Panel data Fixed-effects Panel data Random-effects PPML Fixed-effects  PPML without fixed effects Airport HHI -0.437*** -0.455 *** -0.518***  - 0.211 ***  (0.063) (0.062) (0.045)  (0.062) Airport Average Yield -0.156*** -0.158*** -0.119***  -0.390***  (0.029) (0.028) (0.032)  (0.093) Location Index  -6.806**   -3.329***   (3.419)   (1.014) City Population 0.121 0.193** 0.097  0.418***  (0.104) (0.099) (0.106)  (0.103) City GDP per capita 0.009 0.091 -0.074  0.503***  (0.093) (0.097) (0.058)  (0.113) City Fixed Asset Investment  0.115** 0.105** 0.131***  -0.193**  (0.049) (0.048) (0.036)  (0.087) Tourist  0.681 **   0.506 ***   (0.274)   (0.081) Airport Hub Status  0.794***   0.186***   (0.245)   (0.067) Runway Length  1.893***   0.094 **   (0.502)   (0.057) Terminal Size -0.049 0.079 -0.025  0.574***  (0.071) (0.103) (0.040)  (0.032) 68  Spring Airlines 0.022 0.029 0.013  0.191***  (0.035) (0.034) (0.014)  (0.047) HSR -0.020 -0.020 -0.082***  -0.132***  (0.045) (0.041) (0.017)  (0.053) Economy 0.490*** 0.388 *** 0.463***  0.187***  (0.070) (0.076) (0.050)  (0.091) Global Financial Crisis -0.098*** -0.088*** -0.084***  -0.152 ***  (0.019) (0.019) (0.015)  (0.051) Beijing Olympic Games 0.081*** 0.059** 0.042*  -0.040  (0.026) (0.026) (0.025)  (0.052) World Expo 0.088*** 0.049** 0.077***  -0.125***  (0.022) (0.023) (0.020)  (0.052) Constant -3.173** -17.154*** -8.179  -3.484**  (1.549) (4.507) (1.569)  (1.922) No. of Obs 594 549 549  549 Note:  (1). The one-year lag values are used for each time-series control variable. (2) *, **, *** stand for the significance levels of 10%,5% and 1%. (3). The same notes also apply to the following Tables 8 and 9.  The random-effects estimations show that the closeness (“location index” variable) to the provincial capitals and to other mega airports can downgrade the airport connectivity, probably as a result of the airport competition and service substantiality. Similar to Bowers et al. (2015), the significantly positive effects of the length of runways, terminal and the amount of fixed asset investment in a city show that investment in airport facilities expansion and surface access to airports could produce the intended results, i.e., improving airport connectivity.    In addition, tourism, hub status, and cities with larger capacity have higher overall air connectivity.  Population and GDP per capita also have positive effects as expected.  In particular, the economic activities at the mega cities (the “economy” variable), i.e. Beijing, Shanghai, and Guangzhou, contribute to a better overall air connectivity for all our sampled cities. This is because, in China, most small-and-medium sized cities prefer to establish links with the mega-cities, Beijing, Shanghai, and Guangzhou (Li and Cai, 2004; Gong et al., 2017).   69  Our PPML model (without fixed effects) reveal that the presence of LCC (Spring Airlines) promotes air connectivity. Spring has opened many direct flights to Chinese secondary cities not normally served by the full-service carriers (Fu et al., 2015).  It is interesting to see that competition from HSR lowers overall air connectivity. On some short-and-medium haul routes in China, the launching of HSR services has forced airlines to withdraw capacity and reduce destinations (Wan et al.,2016). With plans to build more HSR, we would expect the HSR will impose more severe impacts on the air connectivity in China. Wang et al. (2017) highlights the importance of the coordination between air and HSR developments in China in order to avoid any investment redundancy.  Finally, we find that the global financial crisis adversely affects overall air connectivity in China, which is consistent with the findings in the US air transport market (Wittman and Swelbar, 2013).  The Beijing Olympics and Shanghai Expo had the effect of increasing air connectivity of Beijing and Shanghai in the respective years.  Table 8 summarises the regression results for the domestic air connectivity. The results and findings are quite similar to those for the overall air connectivity estimations. The regression results for the international air connectivity are shown in Table 9.  It is found that high airline price does not necessarily damage the international air connectivity. This might be because many international airline markets are still regulated by bilateral air service agreements (ASAs), and price competition is less relevant to the level of international connectivity.  Our location index variable is also insignificant for the international air connectivity estimation. This is probably because international air services are still concentrated in several major airports, such as Beijing, Shanghai and Guangzhou. The other findings of the international air connectivity are instead very similar to those of our overall and domestic connectivity estimations. 70  Table 8 The estimations of domestic air connectivity  Panel data Fixed-effects Panel data Random-effects PPML Fixed-effects PPML without fixed effects Airport HHI -0.430*** -0.451*** -0.506*** -0.211***  (0.065) (0.063) (0.044) (0.063) Airport Average Yield -0.165*** -0.168*** -0.153*** -0.460***  (0.029) (0.028) (0.036) (0.099) Location Index  -6.778**  -3.403***   (0.028)  (0.997) City Population 0.114 0.184** 0.089 0.417***  (0.102) (0.097) (0.100) (0.113) City GDP per capita 0.001 0.083 -0.069 0.494***  (0.096) (0.099) (0.057) (0.113) City Fixed Asset Investment 0.116** 0.106** 0.105*** -0.211**  (0.048) (0.047) (0.027) (0.090) Tourist  0.660**  0.491***   (0.273)  (0.077) Airport Hub Status  0.755***  0.093*   (0.219)  (0.057) Runway Length  1.777***  0.047   (0.524)  (0.083) Terminal Size -0.051 0.078 -0.032 0.579***  (0.070) (0.103) (0.039) (0.033) Spring Airlines 0.023 0.031 0.020 0.184***  (0.036) (0.035) (0.015) (0.049) HSR -0.020 -0.018 -0.078*** -0.121**  (0.046) (0.035) (0.018) (0.053) Economy 0.501*** 0.399*** 0.513*** 0.243***  (0.073) (0.079) (0.052) (0.093) Global Financial Crisis -0.096*** -0.087*** -0.092*** -0.166***  (0.019) (0.019) (0.016) (0.053) Beijing Olympic Games -0.004 -0.027 -0.036 -0.095*  (0.026) (0.026) (0.026) (0.055) World Expo 0.168*** 0.131*** 0.157*** -0.086  (0.022) (0.023) (0.022) (0.055) Constant -3.402** -15.738*** -0.999 -3.335  (1.606) (4.522) (1.053) (1.858) No. of Obs 594 594 594 594 71  Table 9 The estimations of international connectivity  Panel data Fixed-effects Panel data Random-effects PPML Fixed-effects PPML without fixed effects Airport HHI -0.524** -0.362** -0.439*** 0.071  (0.224) (0.193) (0.173) (0.110) Airport Yield 0.113 0.131 0.133 0.256*  (0.095) (0.098) (0.088) (0.149) Location Index  -4.217  -3.038   (4.277)  (2.466) City Population 0.705** 0.658*** 0.177 0.585***  (0.343) (0.234) (0.349) (0.191) City GDP per capita 0.038 0.408** -0.222 1.000***  (0.197) (0.203) (0.160) (0.278) City Fixed Asset Investment -0.018 -0.075 0.368** -0.057  (0.140) (0.126) (0.163) (0.089) Tourist  0.946***  0.831***   (0.346)  (0.133) Airport Hub Status  0.309  0.138   (0.355)  (0.099) Runway Length  1.131***  0.785***   (0.430)  (0.107) Terminal Size -0.737*** 0.696*** 0.246 0.610***  (0.142) (0.179) (0.376) (0.068) Spring Airlines -0.045 -0.055 -0.103* 0.219***  (0.088) (0.091) (0.051) (0.086) HSR 0.078 -0.001 -0.014 -0.149*  (0.141) (0.144) (0.069) (0.089) Economy 0.724*** 0.490** 0.162 -0.556***  (0.235) (0.227) (0.113) (0.203) Global Financial Crisis -0.158** -0.141** -0.023 -0.026  (0.062) (0.064) (0.063) (0.095) Beijing Olympic Games 0.595*** 0.588*** 0.355*** 0.161**  (0.084) (0.091) (0.063) (0.076) World Expo -0.002 -0.094 -0.171*** -0.396***  (0.055) (0.058) (0.066) (0.075) Constant -9.596* -21.025*** -20.191*** -6.592**  (5.034) (5.027) (5.982) (3.044) No. of Obs 594 594 594 594  72  5 Conclusion This research has proposed a connectivity model, CUM, to calculate connectivity and centrality involving multiple transport modes and multiple quality dimensions. Numeric results are produced with air and rail schedule data for 2016. A regression analysis on the drivers of connectivity is also conducted. CUM allows calculation of connectivity across modes and takes into consideration the effect of terminal locations on the connectivity a terminal contributes to the city, which enables the comparison of comprehensive connectivity level between cities. It has also included quality factors that would affect passengers’ utility and therefore reveals the connectivity felt by passengers. Furthermore, CUM has no constraint on the data’s time span or geographical range. Connectivity can be calculated for a day, a week, a month, or a year, for a city, a country, a continent, or the whole globe, which is useful for government and enterprises to monitor the up-to-date connectivity level of a customized transport network and make strategies accordingly. Besides, CUM also makes it easy to observe connectivity from different angles, terminal-wise, route-wise, city-wise, etc. The numeric results presented in Section 3 has shown that terminals in mega cities (Beijing, Shanghai, Guangzhou, Hong Kong, etc.) lead in connectivity. PEK, and NKH are the winner of airports and railway stations respectively. PEK is also the winner among all terminals. PVG is very close to PEK in terms of air connectivity. However, PVG’s cooperation with railway stations is not as good as PEK, resulting in a lower overall connectivity. SHA and AOH is a good example of air rail cooperation, ranking 4th and 5th in centrality. They are also the top 2 cross-73  mode hubs. Cooperation in location is a win-win game for both airports and train stations in terms of connectivity. Cooperation of schedules will help improve the connectivity even further.  Connectivity of continental international routes are highly concentrated in the top four airports (PVG, PEK, CAN, and HKG). While, connectivity of short-haul international routes is more distributed. Bangkok International Airport (BKK) is the best-connected foreign airport for China. And United States leads with big advantage to be the best-connected country with China. High level of passenger connectivity also represents high level of interaction and economic dependency with each other. As the world’s 1st and 2nd largest economy, US and China are deeply connected. Rail transport, especially HSR, is recognized as dominant mode for short haul routes against air. However, the numeric results show that rail connectivity is also critical for mid and long-haul routes with distance up to 1500 km. Shanghai, Beijing, Guangzhou, and Nanjing are the most important cities in China’s city network. When Shanghai is lost, 9.6% of overall connectivity and 15.1% of direct connectivity in the whole city network will be lost. Hong Kong, Shanghai, Beijing, and Hangzhou, are more resistant of route loss in extreme situations, and therefore are better choices as warehouse, factory, etc., for security reasons. The regression analysis has shown that airline competition, investment in airport facilities expansion and surface access to airports, tourism, hub status, larger population and higher GDP per capita, economic activities, and presence of LCC help promoting air connectivity in China. However, being close to capital or mega cities downgrades air connectivity. The effect of being close to big airports might well become positive when the capacity of airports in capital and mega cities are in shorter supply. Global financial crisis adversely affects overall air connectivity in China. 74  The trends and patterns of the evolution of airport connectivity in China clearly demonstrate that China’s air transport market is a growth market. For example, major airports including most provincial capital cities experienced steady growth between 2005 and 2016. A number of non-capital cities such as Luzhou, Wuxi, Nantong, Luoyang, Shijiazhuang, Yuncheng and Mianyang increased by more than 10 times during this period.  However, for some tourism cities and small cities, the growth has been stagnant, although our regression results suggest that tourism cities tend to have higher connectivity levels than non-tourism cities, other things been equal. Several solutions can be considered according to our findings. First, tourism and small cities should develop a strategy to attract LCCs and ideally establish partnership with LCCs. Most LCCs are point-to-point airlines and thus the presence of them will increase the number of destinations and thus connectivity. The entry of LCCs is also expected to increase consumer choice airfare affordability, which will in turn lead to higher connectivity. Many studies including Olipra (2012) have confirmed that LCCs influence the development of tourism in smaller cities and less famous destinations.  Second, this research shows that infrastructure investment including upgrading and expanding airport facilities including development of passenger terminal facility will likely promote airport connectivity. Many big airports have become congested and many markets have been saturated in terms of frequency, which makes it hard for new airlines to enter these markets. Quite a few new airlines have emerged in China since 2013 and they are also looking for opportunities to grow themselves. A relatively new and modern airport will be a selling point for small airports to increase connectivity. When flight delay, long queues and high parking fees have become the norm at large airports, this implies an opportunity for nearby small airports. For example, the Director of the CAAC has recently announced that some flights from the second- and third-tier 75  cities to Beijing will be shifted to Tianjin and Shijiazhuang in the future and these airports will be linked to Beijing via HSR. This implies that on the one hand, HSR poses a threat to air connectivity, whereas on the other hand it can also be used to mitigate the congestion problem for mega-airports and increase the air connectivity of some cities in the neighbourhood. At the regional level, connectivity of Northwest China and Northeast China is substantially lower than other parts of China, although the performance of the provincial capitals is quite acceptable. The fundamental reason for the low connectivity in the two regions is the lack of airports and the failure of attracting air services to the non-capital airports. That is why National Development and Reform Commission and the CAAC jointly issued a notice in 2017 on national civil aviation airport network planning in which constructing new airports in West China is a top priority. Compared with Northwest China, Northeast China is more developed. It was the country’s heavy industrial base in the planned economy period with a focus on manufacturing, steel, automobile, oil extraction and refining. However, with the shift to a market-oriented economy and the gradual depletion of natural resources, Northeast China has lost its competitive position. In recent year, about two million people moved out of this region each year, which is a severe blow to its stagnant economy and the air transport sector. The central government put forward a strategy to invigorate Northeast China in 2003. However, this strategy has failed to regenerate the economy in the three Northeast provinces. It has been reported that in 2016 both private and government investment contracted in Northeast China (Yao, 2016). Our regression model has shown a significantly positive relationship between fixed asset investment, population and air connectivity. Unless the economic performance improves, we do not expect to see a significant increase in airport connectivity in the next few years for the Northeast China region.     76  Our results confirm that business cycle affects the airline industry and thus airport connectivity, while large events such as Olympic games and World Expo have the effects of promoting airport connectivity. Although these factors are largely beyond the control of most local governments, the central government should take them into consideration when offering financial assistance and choosing venues for hosting large sports and expo events.    The negative sign of the location index confirms our hypothesis that if there are two airports nearby, some passengers would be attracted to use the larger one. Without the support of local residents and businesses, it is difficult to increase the connectivity of the local airports. Advantages of large airports include cheaper prices and more frequency, which are unbeatable by smaller airports. Education campaign might be needed to convince the passenger that the benefit to them and to the local community is higher than driving hours to the nearest large airport. When the transit service between small airports and big cities in the neighbourhood is improved by using HSR, shuttle bus service, etc., we may expect the small airports to cooperate better with crowded mega airports and achieve progress in connectivity. A final warning is that although we have attempted to reveal a set of drivers behind the airport connectivity ranking which are undoubtedly useful for policy makers and airport management, the strategy of boosting connectivity should also be examined on a case-by-case basis. More research will be conducted on CUM and drivers of connectivity in the future. Numeric results involving more quality factors, e.g. cost, and more transport modes, will be useful to understand the overall connectivity and competition position of cities. CUM can be also used to calculate cargo connectivity when the quality factors are substituted by freight-related variables in equation (1).   77  Bibliography Adler, N., Pels, E., Nash, C., 2010. High-speed rail and air transport competition: game engineering as tool for cost-benefit analysis. Transportation Research Part B: Methodological 44(7), 812–833. Banno, M., Redondi, R., 2014. 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Available at SSRN 2897428.   85  Appendices Appendix 1: List of cities No City No City No City No City 1 Beijing 11 Hangzhou 21 Nanchang 31 Taiyuan 2 Changchun 12 Harbin 22 Nanjing 32 Tianjin 3 Changsha 13 Hefei 23 Nanning 33 Urumqi 4 Chengdu 14 Hohhot 24 Ningbo 34 Wuhan 5 Chongqing 15 Hong Kong 25 Qingdao 35 Xiamen 6 Dalian 16 Jinan 26 Shanghai 36 Xi'an 7 Fuzhou 17 Kunming 27 Shenyang 37 Xining 8 Guangzhou 18 Lanzhou 28 Shenzhen 38 Xuzhou 9 Guiyang 19 Lhasa 29 Shijiazhuang 39 Yinchuan 10 Haikou 20 Lianyungang 30 Suzhou 40 Zhengzhou    86  Appendix 2: List of terminals No Station Type City FULL Name 1 PEK Airport Beijing Beijing Capital International Airport 2 NAY Airport Beijing Beijing Nanyuan Airport 3 CGQ Airport Changchun Changchun Longjia International Airport 4 CSX Airport Changsha Changsha Huanghua International Airport 5 CTU Airport Chengdu Chengdu Shuangliu International Airport 6 CKG Airport Chongqing Chongqing Jiangbei Airport 7 DLC Airport Dalian Dalian Zhoushuizi International Airport 8 FOC Airport Fuzhou Fuzhou Changle Airport 9 CAN Airport Guangzhou Guangzhou Baiyuan International Airport 10 KWE Airport Guiyang Guiyang Longdongbao International Airpo 11 HAK Airport Haikou Haikou Meilan International Airport 12 HGH Airport Hangzhou Hangzhou Xiaoshan International Airport 13 HRB Airport Harbin Harbin Taiping International Airport 14 HFE Airport Hefei Hefei Xinqiao International Airport 15 HET Airport Hohhot HET Baita International Airport 16 HKG Airport Hong Kong Hong Kong International Airport 17 TNA Airport Jinan Jinan Yaoqiang International Airport 18 KMG Airport Kunming Kunming Changshui International Airport 19 LHW Airport Lanzhou Lanzhou Zhongchuan International Airport 20 LXA Airport Lhasa Lhasa Gonggar Airport 21 LYG Airport Lianyungang Lianyungang Baitabu Airport 22 KHN Airport Nanchang Nanchang Changbei International Airport 23 NKG Airport Nanjing Nanjing Lukou International Airport 24 NNG Airport Nanning Nanning Wuxu International Airport 25 NGB Airport Ningbo Ningbo Lishe International Airport 26 TAO Airport Qingdao Qingdao Liuting International Airport 27 PVG Airport Shanghai Shanghai Pudong International Airport 28 SHA Airport Shanghai Shanghai Hongqiao International Airport 29 SHE Airport Shenyang Shenyang Taoxian International Airport 30 SZX Airport Shenzhen Shenzhen Bao'an International Airport 31 SJW Airport Shijiazhuang Shijiazhuang Zhengding International Airport 32 TYN Airport Taiyuan Taiyuan Wusu International Airport 33 TSN Airport Tianjin Tianjin Binhai International Airport 34 URC Airport Urumqi Urumqi Diwopu International Airport 87  No Station Type City FULL Name 35 WUH Airport Wuhan Wuhan Tianhe International Airport 36 XMN Airport Xiamen Xiamen Gaoqi International Airport 37 XIY Airport Xi'an Xi'an Xianyang International Airport 38 XNN Airport Xining Xining Caojiabao Airport 39 XUZ Airport Xuzhou Xuzhou Guanyin International Airport 40 INC Airport Yinchuan Yinchuan Hedong International Airport 41 CGO Airport Zhengzhou Zhengzhou Xinzheng International Airport 42 VAP Train Station Beijing Beijing North Railway Station 43 BXP Train Station Beijing Beijing West Railway Station 44 BJP Train Station Beijing Beijing Railway Station 45 VNP Train Station Beijing Beijing South Railway Station 46 BOP Train Station Beijing Beijing East Railway Station 47 CRT Train Station Changchun Changchun West Railway Station 48 CCT Train Station Changchun Changchun Railway Station 49 CSQ Train Station Changsha Changsha Railway Station 50 CWQ Train Station Changsha Changsha South Railway Station 51 CNW Train Station Chengdu Chengdu South Railway Station 52 CDW Train Station Chengdu Chengdu Railway Station 53 ICW Train Station Chengdu Chengdu East Railway Station 54 CQW Train Station Chongqing Chongqing Railway Station 55 CUW Train Station Chongqing Chongqing North Railway Station 56 BPW Train Station Chongqing Beibei Railway Station 57 DLT Train Station Dalian Dalian Railway Station 58 DFT Train Station Dalian Dalian North Railway Station 59 FZS Train Station Fuzhou Fuzhou Railway Station 60 FYS Train Station Fuzhou Fuzhou South Railway Station 61 GBQ Train Station Guangzhou Guangzhou North Railway Station 62 GZQ Train Station Guangzhou Guangzhou Railway Station 63 GGQ Train Station Guangzhou Guangzhou East Railway Station 64 IZQ Train Station Guangzhou Guangzhou South Railway Station 65 GIW Train Station Guiyang Guiyang Railway Station 66 KQW Train Station Guiyang Guiyang North Railway Station 67 VUQ Train Station Haikou Haikou Railway Station 68 HZH Train Station Hangzhou Hangzhou Railway Station 69 HGH Train Station Hangzhou Hangzhou East Railway Station 88  No Station Type City FULL Name 70 BJB Train Station Harbin Binjiang Railway Station 71 HBB Train Station Harbin Harbin Railway Station 72 XFB Train Station Harbin Xiangfang Railway Station 73 VAB Train Station Harbin Harbin West Railway Station 74 HTB Train Station Harbin Harbin North Railway Station 75 ENH Train Station Hefei Hefei South Railway Station 76 HFH Train Station Hefei Hefei Railway Station 77 HHC Train Station Hohhot Hohhot Railway Station 78 NDC Train Station Hohhot Hohhot East Railway Station 79 JAK Train Station Jinan Jinan East Railway Station 80 JNK Train Station Jinan Jinan Railway Station 81 JGK Train Station Jinan Jinan West Railway Station 82 KMM Train Station Kunming Kunming Railway Station 83 LZJ Train Station Lanzhou Lanzhou Railway Station 84 LAJ Train Station Lanzhou Lanzhou West Railway Station 85 LSO Train Station Lhasa Lhasa Railway Station 86 UKH Train Station Lianyungang Lianyungang East Railway Station 87 NCG Train Station Nanchang Nanchang Railway Station 88 NXG Train Station Nanchang Nanchang West Railway Station 89 NJH Train Station Nanjing Nanjing Railway Station 90 NKH Train Station Nanjing Nanjing South Railway Station 91 NNZ Train Station Nanning Nanning Railway Station 92 NFZ Train Station Nanning Nanning East Railway Station 93 NGH Train Station Ningbo Ningbo Railway Station 94 QHK Train Station Qingdao Qingdao North Railway Station 95 QDK Train Station Qingdao Qingdao Railway Station 96 JXK Train Station Qingdao Jiaozhou Railway Station 97 SHH Train Station Shanghai Shanghai Railway Station 98 SNH Train Station Shanghai Shanghai South Railway Station 99 AOH Train Station Shanghai Shanghai Hongqiao Railway Station 100 SYT Train Station Shenyang Shenyang Railway Station 101 SOT Train Station Shenyang Shenyang South Railway Station 102 SBT Train Station Shenyang Shenyang North Railway Station 103 IOQ Train Station Shenzhen Shenzhen North Railway Station 104 BJQ Train Station Shenzhen Shenzhen East Railway Station 89  No Station Type City FULL Name 105 OSQ Train Station Shenzhen Shenzhen West Railway Station 106 NZQ Train Station Shenzhen Futian Railway Station 107 SZQ Train Station Shenzhen Shenzhen Railway Station 108 SJP Train Station Shijiazhuang Shijiazhuang Railway Station 109 VVP Train Station Shijiazhuang Shijiazhuang North Railway Station 110 SZH Train Station Suzhou Suzhou Railway Station 111 OHH Train Station Suzhou Suzhou North Railway Station 112 KAH Train Station Suzhou Suzhou Industry Zone Railway Station 113 TYV Train Station Taiyuan Taiyuan Railway Station 114 TNV Train Station Taiyuan Taiyuan South Railway Station 115 JMP Train Station Tianjin Junliangcheng North Railway Station 116 TXP Train Station Tianjin Tianjin West Railway Station 117 TIP Train Station Tianjin Tianjin South Railway Station 118 FHP Train Station Tianjin Binhai Raiway Station 119 YKP Train Station Tianjin Yujiabao Railway Station 120 TJP Train Station Tianjin Tianjin Railway Station 121 WAR Train Station Urumqi Urumqi Railway Station 122 HKN Train Station Wuhan Hankou Railway Station 123 WCN Train Station Wuhan Wuchang Railway Station 124 WHN Train Station Wuhan Wuhan Railway Station 125 XMS Train Station Xiamen Xiamen Railway Station 126 XKS Train Station Xiamen Xiamen North Railway Station 127 XAY Train Station Xi'an Xi'an Railway Station 128 EAY Train Station Xi'an Xi'an North Railway Station 129 CAY Train Station Xi'an Xi'an South Railway Station 130 XNO Train Station Xining Xining Railway Station 131 UUH Train Station Xuzhou Xuzhou East Railway Station 132 XCH Train Station Xuzhou Xuzhou Railway Station 133 YIJ Train Station Yinchuan Yinchuan Railway Station 134 XPF Train Station Zhengzhou Zhengzhou West Railway Station 135 ZZF Train Station Zhengzhou Zhengzhou Railway Station 136 ZAF Train Station Zhengzhou Zhengzhou East Railway Station   90  Appendix 3: Terminal connectivity No Station Type Admin City Connectivity Air Rail Across Mode Overall 1 PEK Air Beijing 75227.83 0.00 17225.23 92453.06 2 PVG Air Shanghai 73653.93 0.00 9023.39 82677.32 3 HKG Air Hong Kong 67914.57 0.00 8036.81 75951.37 4 CAN Air Guangzhou 48538.14 0.00 19335.60 67873.74 5 NKH Rail Nanjing 0.00 18958.53 42542.87 61501.40 6 HGH Rail Hangzhou 0.00 16459.75 38991.53 55451.28 7 SZH Rail Suzhou 0.00 13164.05 37945.43 51109.49 8 CTU Air Chengdu 28933.44 0.00 17773.86 46707.31 9 AOH Rail Shanghai 0.00 18927.13 27616.24 46543.37 10 KMG Air Kunming 24056.81 0.00 22244.55 46301.36 11 SZX Air Shenzhen 24311.56 0.00 19838.17 44149.73 12 TJP Rail Tianjin 0.00 13629.77 26819.12 40448.89 13 URC Air Urumqi 19382.82 0.00 20795.04 40177.86 14 SJP Rail Shijiazhuang 0.00 13384.41 26510.55 39894.96 15 CKG Air Chongqing 20728.43 0.00 14896.53 35624.96 16 UUH Rail Xuzhou 0.00 14064.39 21537.16 35601.56 17 XMN Air Xiamen 20237.85 0.00 15134.88 35372.73 18 XIY Air Xi'an 21372.38 0.00 12632.68 34005.07 19 IZQ Rail Guangzhou 0.00 10322.96 22156.06 32479.02 20 JGK Rail Jinan 0.00 11300.96 20837.73 32138.69 21 CCT Rail Changchun 0.00 12964.45 19030.65 31995.10 22 NGH Rail Ningbo 0.00 11985.64 19456.52 31442.15 23 HRB Air Harbin 17184.18 0.00 13793.71 30977.89 24 SBT Rail Shenyang 0.00 13559.63 16987.30 30546.93 25 NJH Rail Nanjing 0.00 10583.80 18379.43 28963.23 26 HGH Air Hangzhou 21049.38 0.00 7872.80 28922.18 27 SHE Air Shenyang 17358.21 0.00 11344.54 28702.75 28 VNP Rail Beijing 0.00 12819.85 15768.74 28588.59 29 CWQ Rail Changsha 0.00 11759.93 16519.94 28279.87 30 WHN Rail Wuhan 0.00 10500.88 17296.56 27797.44 31 HAK Air Haikou 13476.26 0.00 14164.38 27640.65 32 TAO Air Qingdao 16731.09 0.00 10577.55 27308.65 33 DLC Air Dalian 16219.65 0.00 10605.47 26825.12 91  No Station Type Admin City Connectivity Air Rail Across Mode Overall 34 OHH Rail Suzhou 0.00 7944.63 18115.85 26060.49 35 SYT Rail Shenyang 0.00 8528.78 16753.34 25282.11 36 NNG Air Nanning 12801.60 0.00 12099.56 24901.17 37 BXP Rail Beijing 0.00 12904.98 11967.35 24872.33 38 KWE Air Guiyang 12808.83 0.00 11959.53 24768.36 39 LHW Air Lanzhou 13345.98 0.00 11338.31 24684.28 40 CUW Rail Chongqing 0.00 10908.38 13505.57 24413.95 41 JNK Rail Jinan 0.00 10386.10 13689.85 24075.95 42 FOC Air Fuzhou 14355.77 0.00 9669.21 24024.98 43 ZZF Rail Zhengzhou 0.00 9647.28 14169.57 23816.84 44 NXG Rail Nanchang 0.00 8802.61 14883.90 23686.51 45 ZAF Rail Zhengzhou 0.00 9458.96 14088.94 23547.90 46 WUH Air Wuhan 17093.15 0.00 6299.08 23392.23 47 NKG Air Nanjing 17320.07 0.00 5874.34 23194.41 48 CSX Air Changsha 15197.88 0.00 7802.97 23000.84 49 SHA Air Shanghai 14232.11 0.00 8386.54 22618.65 50 CGO Air Zhengzhou 15655.53 0.00 6694.21 22349.74 51 CGQ Air Changchun 13099.79 0.00 8770.05 21869.84 52 FZS Rail Fuzhou 0.00 7881.48 13964.01 21845.49 53 XCH Rail Xuzhou 0.00 8884.55 12782.37 21666.92 54 IOQ Rail Shenzhen 0.00 9128.74 12287.50 21416.23 55 SZQ Rail Shenzhen 0.00 5097.87 16099.67 21197.53 56 ENH Rail Hefei 0.00 8565.16 12351.78 20916.94 57 TSN Air Tianjin 13051.46 0.00 7370.60 20422.06 58 WCN Rail Wuhan 0.00 7284.11 11418.68 18702.79 59 INC Air Yinchuan 10013.62 0.00 8391.89 18405.51 60 XKS Rail Xiamen 0.00 8104.21 10046.96 18151.17 61 TIP Rail Tianjin 0.00 5877.66 11494.30 17371.96 62 ICW Rail Chengdu 0.00 7816.02 9541.29 17357.31 63 GZQ Rail Guangzhou 0.00 8223.34 9021.46 17244.80 64 TXP Rail Tianjin 0.00 7196.72 9932.96 17129.67 65 SHH Rail Shanghai 0.00 9697.04 7396.82 17093.85 66 TYN Air Taiyuan 9134.77 0.00 7455.10 16589.87 67 XNN Air Xining 8731.52 0.00 7784.52 16516.03 68 HET Air Hohhot 8610.05 0.00 7765.20 16375.26 92  No Station Type Admin City Connectivity Air Rail Across Mode Overall 69 EAY Rail Xi'an 0.00 7714.60 8512.38 16226.98 70 VAB Rail Harbin 0.00 7574.26 8358.19 15932.45 71 HBB Rail Harbin 0.00 7567.57 8250.33 15817.91 72 XAY Rail Xi'an 0.00 7469.57 8148.72 15618.29 73 LZJ Rail Lanzhou 0.00 7552.01 7928.84 15480.85 74 HZH Rail Hangzhou 0.00 5984.47 9460.42 15444.89 75 WAR Rail Urumqi 0.00 9197.00 5826.00 15023.00 76 NGB Air Ningbo 10053.95 0.00 4899.72 14953.67 77 CSQ Rail Changsha 0.00 6139.61 8789.48 14929.09 78 BJP Rail Beijing 0.00 7183.60 7743.04 14926.63 79 GIW Rail Guiyang 0.00 6862.55 7818.82 14681.37 80 CRT Rail Changchun 0.00 5483.60 9166.81 14650.41 81 HKN Rail Wuhan 0.00 6099.49 8127.59 14227.08 82 FYS Rail Fuzhou 0.00 4200.57 9863.59 14064.16 83 KMM Rail Kunming 0.00 6736.43 7020.61 13757.04 84 TNA Air Jinan 8864.36 0.00 4577.36 13441.72 85 HFH Rail Hefei 0.00 6492.67 6884.55 13377.21 86 VVP Rail Shijiazhuang 0.00 5132.37 7959.73 13092.10 87 KHN Air Nanchang 7673.00 0.00 5174.56 12847.55 88 HFE Air Hefei 9735.66 0.00 3111.03 12846.69 89 CDW Rail Chengdu 0.00 7090.59 5641.59 12732.18 90 LXA Air Lhasa 5808.74 0.00 6715.79 12524.53 91 QDK Rail Qingdao 0.00 5675.38 6785.55 12460.93 92 KQW Rail Guiyang 0.00 5767.92 6520.25 12288.18 93 SNH Rail Shanghai 0.00 5270.69 6968.98 12239.66 94 TYV Rail Taiyuan 0.00 5546.04 6251.55 11797.59 95 TNV Rail Taiyuan 0.00 4121.13 7520.41 11641.54 96 NNZ Rail Nanning 0.00 6918.39 4722.75 11641.15 97 XNO Rail Xining 0.00 6290.57 5216.00 11506.57 98 SJW Air Shijiazhuang 5280.89 0.00 5806.48 11087.38 99 GGQ Rail Guangzhou 0.00 4840.37 5577.73 10418.10 100 DFT Rail Dalian 0.00 4087.71 5511.33 9599.04 101 NCG Rail Nanchang 0.00 4833.24 4684.13 9517.37 102 HHC Rail Hohhot 0.00 4660.32 4857.04 9517.36 103 NFZ Rail Nanning 0.00 4762.32 4747.74 9510.06 93  No Station Type Admin City Connectivity Air Rail Across Mode Overall 104 DLT Rail Dalian 0.00 3996.50 5462.63 9459.13 105 NDC Rail Hohhot 0.00 4630.74 4747.73 9378.47 106 YIJ Rail Yinchuan 0.00 4730.46 4441.55 9172.00 107 JAK Rail Jinan 0.00 2741.85 3909.21 6651.06 108 QHK Rail Qingdao 0.00 3734.11 2510.96 6245.06 109 CQW Rail Chongqing 0.00 2995.90 3232.18 6228.09 110 LSO Rail Lhasa 0.00 3057.76 1794.96 4852.72 111 BJQ Rail Shenzhen 0.00 3501.64 1335.17 4836.80 112 UKH Rail Lianyungang 0.00 2670.83 2144.03 4814.86 113 LYG Air Lianyungang 2360.79 0.00 2236.19 4596.98 114 VUQ Rail Haikou 0.00 2488.76 1899.47 4388.23 115 CAY Rail Xi'an 0.00 2113.74 2077.98 4191.72 116 OSQ Rail Shenzhen 0.00 2086.50 1795.74 3882.24 117 NAY Air Beijing 1751.31 0.00 1800.13 3551.44 118 XUZ Air Xuzhou 2073.66 0.00 1166.02 3239.68 119 NZQ Rail Shenzhen 0.00 505.12 2599.26 3104.38 120 GBQ Rail Guangzhou 0.00 1224.22 1353.22 2577.44 121 SOT Rail Shenyang 0.00 746.36 1176.70 1923.06 122 KAH Rail Suzhou 0.00 518.04 871.37 1389.41 123 CNW Rail Chengdu 0.00 449.89 909.75 1359.64 124 LAJ Rail Lanzhou 0.00 497.99 820.16 1318.15 125 XPF Rail Zhengzhou 0.00 548.68 668.66 1217.34 126 BPW Rail Chongqing 0.00 559.25 644.73 1203.98 127 HTB Rail Harbin 0.00 573.89 604.29 1178.17 128 YKP Rail Tianjin 0.00 164.37 861.30 1025.67 129 XMS Rail Xiamen 0.00 634.06 317.27 951.33 130 JMP Rail Tianjin 0.00 371.18 467.80 838.98 131 FHP Rail Tianjin 0.00 569.53 243.33 812.86 132 XFB Rail Harbin 0.00 594.02 93.29 687.31 133 BOP Rail Beijing 0.00 380.19 61.49 441.68 134 VAP Rail Beijing 0.00 177.44 260.94 438.38 135 BJB Rail Harbin 0.00 339.87 86.75 426.62 136 JXK Rail Qingdao 0.00 117.12 187.18 304.29  94  Appendix 4: Connectivity of international airports (with China), top 50. No IATA Code Country Connectivity No IATA Code Country Connectivity 1 BKK TH 15999.63 26 IST TR 6278.75 2 SIN SG 15955.22 27 ORD US 6077.06 3 ICN KR 12323.00 28 HND JP 6052.31 4 KUL MY 12208.43 29 MEL AU 5981.90 5 FRA DE 11861.63 30 YYZ CA 5905.65 6 SFO US 11705.79 31 SEA US 5662.42 7 DMK TH 11613.43 32 HEL FI 5294.42 8 LAX US 11443.80 33 KBV TH 5273.15 9 NRT JP 10591.14 34 ADD ET 5199.93 10 CDG FR 10494.39 35 EWR US 5185.78 11 KIX JP 9853.24 36 AKL NZ 5071.76 12 TPE TW 9817.51 37 MUC DE 5043.62 13 HKT TH 9674.60 38 CJU KR 4879.29 14 AMS NL 8979.78 39 DTW US 4810.62 15 SYD AU 8939.75 40 CNX TH 4790.64 16 YVR CA 8738.79 41 GMP KR 4637.21 17 LHR GB 8329.41 42 DFW US 4587.44 18 JFK US 7964.67 43 ZRH CH 4437.04 19 DXB AE 7695.06 44 MXP IT 4368.69 20 SVO RU 7633.26 45 HNL US 4189.41 21 DOH QA 6802.27 46 PUS KR 4087.90 22 FCO IT 6467.09 47 MNL PH 4077.22 23 DPS ID 6449.95 48 CPH DK 3973.45 24 NGO JP 6436.61 49 IAD US 3932.50 25 CGK ID 6282.82 50 BOS US 3918.73    95  Appendix 5: Connectivity of foreign countries (with China), top 80. No Country Connectivity No Country Connectivity 1 US 130906.82 41 CZ 2737.77 2 TH 52889.50 42 PK 2696.36 3 JP 50977.87 43 BE 2589.23 4 KR 28980.19 44 GR 2541.56 5 DE 25483.90 45 KE 2238.44 6 AU 23274.81 46 NP 2152.15 7 MY 21973.46 47 KZ 2125.47 8 CA 20092.10 48 UA 1833.40 9 ID 19340.50 49 BD 1789.49 10 RU 19184.89 50 IL 1745.46 11 TW 17166.97 51 NO 1708.08 12 IT 16077.64 52 PT 1700.30 13 SG 15955.22 53 HU 1685.49 14 GB 15069.49 54 JO 1465.81 15 FR 14328.14 55 NG 1418.43 16 IN 13463.61 56 IQ 1401.32 17 VN 13063.69 57 DZ 1334.86 18 AE 11298.23 58 LA 1285.04 19 ES 10073.00 59 HR 1207.73 20 TR 9535.90 60 AZ 1064.28 21 NL 9071.59 61 RO 1030.09 22 QA 6802.27 62 UZ 969.21 23 NZ 6772.18 63 TZ 961.65 24 CH 6514.77 64 MU 950.70 25 PH 6466.71 65 IE 947.44 26 KH 6421.09 66 MA 850.30 27 FI 6276.02 67 MN 813.03 28 ET 5922.31 68 LB 798.91 29 SA 5408.57 69 BH 795.85 30 MX 4818.96 70 GE 739.38 31 DK 4568.51 71 OM 737.06 32 AT 4519.33 72 BY 730.44 33 SE 3956.73 73 RS 724.13 34 LK 3789.62 74 KW 715.29 35 PL 3584.65 75 CY 651.20 36 ZA 3578.83 76 BG 642.79 37 EG 3306.07 77 TN 553.71 38 MM 3147.82 78 BN 518.17 39 MV 3101.07 79 GH 515.26 40 IR 3057.66 80 TM 502.67 96  Appendix 6: City connectivity with different radiation discount functions No City Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 1 Shanghai 177,254 195,426 227,168 259,318 167,088 132,324 229,539 176,157 2 Beijing 161,048 166,171 182,304 198,655 151,626 132,923 189,057 155,540 3 Guangzhou 127,702 153,538 179,989 206,398 129,727 100,861 173,207 137,672 4 Nanjing 110,391 122,060 137,501 154,254 111,140 98,183 166,723 107,240 5 Hangzhou 96,358 131,360 156,344 182,719 113,519 93,109 181,034 105,011 6 Tianjin 95,018 102,048 128,224 155,164 81,760 59,041 137,708 82,040 7 Shenzhen 94,314 174,632 197,810 220,773 152,121 123,347 190,604 162,569 8 Shenyang 82,187 81,371 83,583 85,964 79,510 76,922 90,373 79,992 9 Wuhan 81,333 80,445 84,482 88,877 77,191 72,745 98,231 77,739 10 Suzhou 78,559 154,496 194,180 234,927 124,072 90,366 203,144 121,798 11 Hong Kong 77,407 140,884 169,431 197,808 113,339 79,097 158,457 129,938 12 Jinan 74,322 74,761 82,204 90,405 69,201 61,825 105,794 69,041 13 Chengdu 72,641 71,857 73,994 76,223 69,953 67,244 78,276 70,497 14 Zhengzhou 66,397 62,887 66,804 71,060 59,423 54,729 80,222 61,159 15 Xi'an 65,552 61,529 63,613 65,668 59,104 55,526 66,967 61,300 16 Changchun 63,844 61,690 66,993 72,564 57,076 51,114 73,043 58,279 17 Chongqing 62,994 61,743 64,663 67,744 59,192 55,653 70,869 59,938 18 Changsha 62,953 59,505 63,409 67,485 55,813 50,655 72,096 57,684 19 Shijiazhuang 61,915 70,155 78,416 87,688 65,092 59,251 102,818 61,359 20 Xuzhou 59,593 63,999 69,827 76,528 60,494 56,218 95,737 58,289 21 Harbin 58,583 54,242 58,493 62,826 50,152 44,636 61,194 52,009 22 Fuzhou 57,192 52,039 57,431 63,108 47,001 40,738 64,573 49,578 23 Kunming 54,565 46,896 50,320 53,565 42,644 36,430 49,075 46,780 24 Xiamen 49,545 50,533 53,339 56,403 48,433 45,679 62,686 48,150 25 Urumqi 48,705 46,766 47,604 48,360 45,652 43,913 46,767 46,766 26 Guiyang 47,622 45,652 47,581 49,601 43,793 41,099 52,864 44,884 27 Hefei 44,415 61,219 72,720 85,448 54,121 46,213 102,510 48,402 28 Ningbo 44,016 87,035 111,342 137,049 70,431 52,271 134,314 59,702 29 Nanchang 43,928 46,142 49,952 54,323 43,748 40,749 68,119 42,618 97  No City Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 30 Qingdao 42,649 42,153 45,817 49,928 39,386 35,677 62,700 39,696 31 Nanning 42,550 38,186 40,539 42,930 35,599 31,998 44,136 37,841 32 Dalian 41,725 42,924 45,012 47,514 41,764 40,308 58,868 41,070 33 Lanzhou 38,614 29,082 34,801 40,599 24,362 19,169 35,217 27,181 34 Taiyuan 37,204 42,744 47,734 53,304 39,574 35,840 64,222 37,549 35 Hohhot 32,841 33,597 34,716 36,107 33,051 32,389 44,132 32,601 36 Haikou 27,567 23,423 26,029 28,721 20,714 16,965 30,712 22,831 37 Yinchuan 25,383 24,350 25,440 26,592 23,321 21,832 28,981 23,894 38 Xining 25,075 26,088 28,884 31,780 23,751 20,778 31,393 23,784 39 Lhasa 16,134 10,948 12,970 15,079 8,735 6,267 10,957 10,948 40 Lianyungang 8,304 17,279 25,012 33,827 12,812 7,777 53,783 8,763    98  Appendix 7: Airport connectivity from 2005 to 2016 Airport Y2005 Y2006 Y2007 Y2008 Y2009 Y2010 Y2011 Y2012 Y2013 Y2014 Y2015 Y2016 Beijing Capital 5,643 5,943 6,240 6,608 7,157 7,243 7,475 7,909 8,187 8,489 8,552 8,762 Guangzhou 3,216 3,395 3,869 4,032 4,383 4,607 4,815 5,219 5,489 5,746 5,680 6,095 Shanghai Pudong 2,947 3,236 3,308 3,529 3,568 3,849 3,924 4,292 4,389 4,721 5,334 5,693 Kunming 1,473 1,845 2,071 2,194 2,653 2,730 2,836 2,957 3,956 4,001 4,456 4,805 Shenzhen 2,209 2,335 2,542 2,669 3,043 3,192 3,219 3,497 3,860 4,296 4,594 4,729 Chengdu 1,934 2,247 2,364 2,333 2,727 2,945 3,211 3,406 3,603 3,868 4,389 4,585 Xi'an 806 1,257 1,579 1,392 2,040 2,240 2,742 2,977 3,280 3,609 3,829 4,116 Shanghai Hongqiao 2,368 2,281 2,464 2,670 2,727 3,232 3,420 3,619 3,727 3,907 3,900 3,980 Chongqing 995 1,119 1,345 1,522 1,928 2,034 2,280 2,746 3,012 3,339 3,582 3,800 Hangzhou 1,149 1,302 1,520 1,683 1,895 2,045 2,139 2,362 2,786 2,960 3,286 3,565 Urumqi 1,138 769 901 845 1,044 1,499 1,703 2,079 2,467 2,508 2,663 3,071 Xiamen 1,019 997 1,186 1,279 1,650 1,734 2,023 2,260 2,609 2,789 2,839 2,965 Harbin 638 583 746 890 1,080 1,130 1,171 1,380 1,643 1,909 2,063 2,508 Nanjing 795 742 1,063 1,185 1,490 1,554 1,624 1,769 1,840 1,900 2,199 2,484 Zhengzhou 508 576 736 797 1,064 1,170 1,186 1,392 1,717 2,043 2,027 2,392 Qingdao 993 918 1,107 1,084 1,327 1,440 1,521 1,685 1,880 2,032 2,267 2,370 Changsha 575 851 1,087 1,150 1,465 1,583 1,566 1,818 1,913 2,063 2,035 2,320 Shenyang 804 789 1,001 1,030 1,199 1,226 1,318 1,436 1,717 1,822 1,825 2,225 Wuhan 780 724 1,061 1,081 1,309 1,368 1,413 1,578 1,799 1,930 2,066 2,200 Dalian 861 767 868 980 1,225 1,383 1,396 1,508 1,623 1,847 1,813 2,157 Sanya 479 417 518 676 816 1,004 1,083 1,288 1,435 1,724 2,004 2,148 Haikou 1,155 746 786 946 957 912 1,114 1,163 1,375 1,514 1,760 2,124 Tianjin 388 389 531 668 826 953 1,007 1,151 1,340 1,535 1,763 2,083 Guiyang 487 550 649 582 785 829 957 1,125 1,293 1,554 1,568 1,736 Nanning 367 384 474 535 714 809 1,027 1,063 1,217 1,365 1,407 1,588 Fuzhou 621 565 623 651 830 909 964 1,080 1,296 1,310 1,455 1,523 Lanzhou 268 308 395 341 456 553 501 628 780 923 1,063 1,495 Changchun 375 325 395 525 670 774 735 911 1,092 1,159 1,304 1,433 Jinan 598 618 704 814 931 994 1,129 1,118 1,189 1,204 1,232 1,393 99  Airport Y2005 Y2006 Y2007 Y2008 Y2009 Y2010 Y2011 Y2012 Y2013 Y2014 Y2015 Y2016 Taiyuan 423 384 473 570 712 754 837 936 1,090 1,056 1,123 1,148 Hohhot 181 197 217 224 353 437 563 717 795 824 896 1,077 Wenzhou 446 355 436 470 621 671 695 666 814 833 827 926 Yinchuan 190 179 199 226 381 465 495 582 668 709 823 894 Guilin 482 570 678 565 727 697 663 725 745 943 839 889 Ningbo 428 433 450 483 560 585 622 615 659 824 784 869 Nanchang 325 334 371 413 460 584 611 677 794 810 810 867 Shijiazhuang 78 105 121 154 209 361 472 482 609 647 630 859 Zhuhai 144 109 158 145 208 244 255 275 385 626 634 857 Hefei 216 259 308 324 422 482 554 661 714 732 780 819 Xining 150 112 159 157 208 283 307 387 464 569 526 677 Lijiang 123 186 220 232 270 257 249 315 419 530 550 615 Wuxi 33 78 164 200 226 264 311 343 392 456 490 608 Yantai 183 182 207 213 275 317 281 379 505 496 536 607 Shantou 163 145 167 181 178 196 230 279 376 367 448 543 Lhasa 100 154 184 116 171 215 230 241 289 419 466 516 Quanzhou 90 118 172 254 274 279 287 282 344 344 417 470 Beijing Nanyuan 0 0 113 146 162 242 288 364 437 481 521 461 Baotou 57 54 44 81 113 127 140 185 188 240 236 236 Xuzhou 46 54 74 68 85 97 137 153 168 189 212 225 Zhangjiajie 221 223 219 157 162 137 153 154 143 151 188 214 Changzhou 48 67 76 111 90 87 132 150 213 226 203 209 Mianyang 19 16 21 29 35 50 78 67 92 123 148 206 Zhanjiang 65 58 54 43 57 76 60 64 82 113 148 206 Beihai 57 37 45 29 68 90 94 90 132 155 169 200 Yiwu 39 51 101 72 95 92 110 135 167 168 179 193 Nantong 13 19 32 25 26 31 42 57 105 130 149 189 Yichang 71 86 85 87 90 90 80 103 124 134 132 161 Weihai 32 43 63 62 68 79 97 90 116 85 138 158 Linyi 19 28 33 38 55 82 98 106 115 133 138 153 Liuzhou 15 26 47 44 36 35 71 101 95 88 95 123 100  Airport Y2005 Y2006 Y2007 Y2008 Y2009 Y2010 Y2011 Y2012 Y2013 Y2014 Y2015 Y2016 Luoyang 9 23 23 22 41 34 44 92 87 68 82 110 Yuncheng 10 22 33 38 68 64 81 96 105 125 113 108 Lianyungang 21 26 32 30 44 52 65 70 84 86 93 105 Luzhou 3 15 20 23 22 30 35 37 48 78 94 100 Mudanjiang 42 28 27 33 48 51 55 63 66 81 94 94 Taizhou 30 37 42 60 72 82 90 42 82 95 86 92 Wuyishan 88 79 66 77 64 81 81 89 110 102 71 78 Huangshan 63 48 46 44 36 45 68 71 81 94 71 71 Jingdezhen 20 9 26 28 28 31 37 45 42 44 43 50   

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