Empirical Analysis on Flight Flow Network Survivability of China

JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY Volume 12, Issue 6, December 2012 Online English edition of the Chinese language journal Cite this article as: J Transpn Sys Eng & IT, 2012, 12(6), 177185.

RESEARCH PAPER

Empirical Analysis on Flight Flow Network Survivability of China DANG Yaru1,*, DING Feiya2, GAO Feng3 1 Civil Aviation S&T Educational Evaluation Research Center, Civil Aviation University of China, Tianjin 300300, China 2 Economics and Management College, Civil Aviation University of China, Tianjin 300300, China 3 Haikou College of Economics, Public Administration Faculty, Haikou 571127, China

Abstract: From the aspect of the complex network, this paper makes empirical analysis on the flight flow network structure of China from 2001 to 2010. The calculation of network statistical indicators reveals that the flight flow network has the small-world characteristics and the scale-free property. Then two indicators, the decline rate of the maximum connected sub-graph size and the decline rate of the overall efficiency are proposed to study the network survivability. Comparative analysis is conducted for different years, which indicates that the survivability of China flight flow network has an increasing trend and the network is more dependent on several key airports. Comparative analysis is also made for various attacks, which demonstrates that the flight flow network has strong robustness against random attack, but is vulnerable to deliberate attack. The reliability of the entire network is dominated by a few major airports, thus, the safe and effective operation of these airports should be ensured and it is essential to build some multi-hub systems in the future. Key Words: air transportation; survivability; complex network; flights; scale-free property

1

Introduction

In recent years, the complex network theory research has shown a sharp increase. Some complex systems in nature and the social fields can be described using the complex network theory, in which the nodes represent different individuals or organizations in the real systems, and the edges represent the relationships between them. As one of the most important research issues in complex network theory, complex network survivability has drawn extensive attention from researchers and scholars. Albert et al.[1] studied the complex network survivability at first. They focused on the influence of the topological structures on complex network survivability, and parted random networks and scale-free networks into two failure modes—random failure and deliberate attack. Their results showed that the scale-free network has stronger survivability than the random network in the random failure mode, but it is very vulnerable under deliberate attack, in other words, “robust butvulnerable.” Holme et al.[2] conducted a simulation analysis on the internet network under two attacks from nodes and edges, respectively, and verified the

conclusion of Albert et al.[1] At present, the complex network survivability researches have infiltrated into many fields; Dunne et al.[3] studied the food chain network; Shen[4] analyzed the U.S. western grid; Chen[5] studied the securities market network; Jin[6] argued the regional highway traffic network of China. Air transport is an important part of transportation; with the development and application of complex network theory, many scholars discussed the topology characteristic of air transport networks, and revealed that parts of air transport networks have scale-free characteristics[7–10]. It is extremely useful to study the air transport network function and efficiency. However, the issue of network reliability is seldom discussed. In 2008, due to the severe impact of natural disasters, civil aviation enterprises suffered huge losses, which made people pay more attention to the reliability of air transport networks in the event of natural disasters or hostile forces of deliberate attacks or various other uncertainties. Therefore, this paper establishes the flight-weighted network of China with flight data over 10 years. It then proposes the measurement indicators of survivability and makes

Received date: Jun 4, 2012; Revised date: Sep 7, 2012; Accepted date: Sep 12, 2012 *Corresponding author. E-mail: [email protected] Copyright © 2012, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(11)60239-0

DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185

comparative analyses, both of different years and of different attack modes on the basis of characteristics of the network structure analysis. It may provide a reference for the development of air transport in China.

2

Network construction and structure

2.1 Construction of flight flow network Considering that long-term historical data can better reflect the dynamic development trends of the flight flow network structure in China, this paper selects domestic airlines flight data records over 10 years from the Statistical Data on Civil Aviation of China (2002–2011) as samples. It chooses navigable cities as network nodes (if a city has more than one airport, then the corresponding data records will be merged), the direct routes as network edges, and the number of flights as the edge weight between two cities, so as to construct the flight flow network of China. The flight flow network can be denoted by a matrix (kij)n×n (n is the number of network nodes), in which kij represents the number of flights from city i to city j. 2.2 Structure of flight flow network By visualizing the flight data in China from 2001 to 2010, this paper provides diagrams of the structure of the flight flow network. Due to the length limitation, we provide pictures for the flight flow network in 2001, 2004, 2007, and 2010, as shown in Fig. 1. In these figures, the edge weight between the nodes reflects the degree of the flight crowd. From Fig. 1, we can clearly see that the scale of the flight flow network in China expands increasingly. Both the number of navigable cities and the number of air routes are increasing

year by year, with more flights and more complicated network structures. The flight flow network structure has obvious hierarchical levels. From the perspective of airline distribution, the domestic airlines are centralized on the east of the Harbin–Beijing–Xi’an–Chengdu–Kunming line, particularly in the triangular areas of Beijing, Shanghai, Guangzhou, and Shenzhen. They connect to most of the edges, especially the thick edges in the network, indicating that the number of flights on this route is large, which occurs due to China’s economic development. As a result, the flight flow network structure of China is quite imbalanced, with dense flight distribution to the east, and a centralization trend in the eastern and central areas. While in the western region, there are some cliques centered on Kunming, Chengdu, and Urumqi, which represent the effect of regional economic development, geographic conditions, and tourism functions on the flight flow network structure.

3

Structural statistic characteristics of flight flow network

In an undirected network, the basic statistical measures are normally the node degree (K), the average node degree (), the average path length (L), and the clustering coefficient (C), etc. Compared with the random network on the same scale, if the average path length of the network LLrand, the clustering coefficient CCr and where Lrand and Crand represent the average path length and the clustering coefficient of a random network, respectively, then the network has small world characteristics.

2001

2007

Fig. 1 Flight flow network structure of China in different years

2004

2010

DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185

Table 1 Statistical characteristics of flight flow network of China (2001–2010) Year

N

K



L

Lrand

C

Crand

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

61 64 75 83 87 92 98 102 116 135

488 580 632 746 814 908 1034 1076 1200 1368

8.000 9.063 8.427 8.988 9.356 9.870 10.551 10.549 10.345 10.133

2.192 2.091 2.280 2.251 2.231 2.233 2.222 2.230 2.256 2.259

1.977 1.887 2.026 2.012 1.997 1.975 1.946 1.963 2.034 2.118

0.698 0.691 0.700 0.726 0.733 0.760 0.748 0.764 0.760 0.795

0.131 0.142 0.112 0.108 0.108 0.107 0.108 0.103 0.089 0.075

obeys power-law distribution. The degree distribution of the flight flow network in China in different years is shown in Fig. 2 (as mentioned before, we only take four years as an example). We can observe that in the double logarithmic coordinate, the degree distributions are almost negative slope lines, both in the first and second stages of two-step-fitting scheme, demonstrating that the network is a scale-free network. Next, in the original coordinate, the degree distribution lines present a long tail characteristic, which illustrates that there are only a few high degree nodes in the network and most of the nodes have a low node degree. Such a network also fits the scale-free property. Scale-free networks have two properties—growth characteristics and properties of priority connections. Growth characteristics means that the network scale can expand freely, which matches the growing trend of both the number of nodes and the node degrees in the network. The priority connection property represents the difference of the connection priority of new nodes that is increasing with the expansion of the network, and the new nodes will be more likely to connect to the nodes with a higher node degree. This phenomenon is also known as the “Matthew Effect.” Hence, the newly launched flight route is always linked to the famous airports or hub airports in the air transport network, such as Beijing Captial International Airport. Intuitively, it somewhat causes an overload problem for the hub airports. As shown in Fig. 3, the maximum peak hour flight capacity of Beijing International Airport is 82 sorties/hour in 2010, but the planned flights are about 100 sorties/hour on average during peak hours. The flight density is far beyond the maximum flights capacity, making the airport overloaded during the whole day and resulting in flight delays, further affecting the efficiency of the entire network.

After calculating the structural statistical characteristic of the flight flow network of China from 2001 to 2010, (Table 1) we can find that both the number of network nodes and the node degrees are continuously increasing which indicates that the network scale is expanding and the network connectivity is improving. In addition, in each year, the average path length of arandom network with the same scale is less than that of the flight flow network, and the clustering coefficient is also much smaller than that of the flight flow network. Therefore, the Chinese flight flow network has small world characteristics, in which any two cities could be mutually arrived at after about 1.2 transits and the larger the clustering coefficient is, the better the aggregation feature is for the flight flow network. Not all the nodes in the network have the same node degree. If the distribution of node degree of the network, denoted as P(k), follows the power-law distribution, then this network is called a scale-free network[11–12]. In the double logarithmic coordinate, the power-law distribution is a line with a negative slope, which is the main basis for judging whether the network 100

100

2001

2004 k=23

Slop=–0.48

p(k)

50

logp(k)

logp(k)

p(k)

k=15

50

Slop=–0.459 Slop=–2.341

Slop=–2.051 log k P(k)=50.738k–0.424

0

50

0

k

2

150

100

100

log k P(k)=65.701k–0.602

0

2007

0

k

50

100

100

p(k)

logp(k)

logp(k)

p(k)

50

50

Slop=–0.454

Slop=–2.008

Slop=–2.404

0

50

k

100

2 log k P(k)=109.925k–0.635

0

log k P(k)=81.701k–0.590

0

150

2010 k=31

k=26 Slop=–0.463

2

150

0

50

k

100

Fig. 2 Degree distribution of flight flow network of China in different years

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DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185 140 䅵ߦ㟾⧁˄‫ހ‬᯹˅ Planned flights (winter & spring)

䅵ߦ㟾⧁˄໣⾟˅ Planned flights (summer & autumn)

᳔໻ᆍ䞣/ ᇣᯊ Maximum capacity (h)

120

Numer of flights

100 80 60 40

20

00 :0 0 01 :0 0 02 :0 0 03 :0 0 04 :0 0 05 :0 0 06 :0 0 07 :0 0 08 :0 0 09 :0 0 10 :0 0 11 :0 0 12 :0 0 13 :0 0 14 :0 0 15 :0 0 16 :0 0 17 :0 0 18 :0 0 19 :0 0 20 :0 0 21 :0 0 22 :0 0 23 :0 0

0

Time

Fig. 3 Flight schedule numbers of Beijing Capital International Airport

4

Network survivability analysis

4.1 Network survivability metrics The survivability of a complex network is the quantified ability of the network to continue to function during and after a natural or man-made disturbance, especially under random or deliberate attacks. It is defined as the decline value of the overall network performance when the network is attacked[13]. Before evaluating the network survivability, we need to fix the measurement indicators. The average path length is a commonly used indicator to evaluate the efficiency, but it often increases first and then decreases with the increase in the amount of damage[6], which brings inconvenience to the research of survivability. Therefore, from the aspects of network topology and efficiency, we construct the decline rate of the maximum connected subgraph size and the decline rate of the overall network performance to analyze network survivability. The maximum connected subgraph size (S) is the number of nodes in the maximum connected subgraph (N’) to that in the original network (N), namely, S= N’/N. In this formula, N’ is the number of nodes in the maximum connected subgraph, while N is the total number of nodes in the original network. S represents the overall connectivity of the network. In the initial state, S0=1, which means that the initial network is a connected graph, with the best connectivity reliability. When the network is attacked continually, the network will separate into several connected components and the maximum connected subgraph size will gradually decrease, so that the network connectivity reliability will be worse. To eliminate the incomparability between indicators and describe the amount of damage for the network more accurately, this study constructs the decline rate of the maximum connected subgraph size (denoted by fS, where fS=ƸS/S×100%). In the formula, ƸS is equal to S of the original network size minus that after attack. The greater the fS is, the more reduction S has,

and the greater the damage of network is. Because the average path length has some shortcomings, we adopt the overall efficiency (E) as an indicator, where E

2 1 ¦ N ( N  1) i z jG d ij

In the formula, N is the number of nodes in network G, dij is the distance between node i and node j. E is the average value of the reciprocal of the distance between any two nodes in the network and it is between 0 and 1.When E=1, it means that the network is a full coupling network; when E=0, it means that all nodes in the network are isolated, and the distance between the nodes tends to infinity. Similarly, we also define the decline rate of the overall network performance expressed by fE, where fE=ƸE/E×100%. In the formula, ƸE is equal to the E of the original network minus that after attack. The greater the fE is, the more reduction E has, and the greater damage of network happens. Essentially, fS, fE and S, E are two different forms of the same group of indicators. 4.2 Network attack strategy Network attack strategy covers two aspects—attack targets and attack methods. Attack targets include the network nodes and edges. Because the flexibility of the edges in the network is large, we only consider the attack on the network nodes, namely, the attack on airports. Attack methods can be divided into random attacks and deliberate attacks. A random attack means that the network nodes (edges) will be destructed randomly according to a certain probability, with no exact target. A deliberate attack means that the network nodes (edges) will be destructed in the order of importance. The node degree and betweenness reflect the importance of the airport nodes in the network, Therefore, we would consider attacks according to the original value of the node degree and decreasing betweenness, so as to compare the effect on the survivability of the flight flow network. 4.3 Empirical analysis In the study of flight flow network survivability, two situations can occur—in case one, when one airport is

DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185

From the perspective of the overall efficiency, when we remove the first four nodes, fE is about 40% in each year, indicating that the overall network performance indicator drops faster than that of the maximum connected subgraph size. Similarly, the amount of damage increases fastest in 2010, and the gap between it and that in other years is wide, reflecting the high dependence degree for the first four airports. When we remove seven nodes, fE is the largest in 2001, which is close to 80%, but it is about 60% in other years. When we remove more nodes, the network survivability becomes worst in 2001 and best in 2010. When we remove 25 nodes, fE is nearly 100% and the network has almost crashed. In short, the flight flow network survivability of China increases year by year, but relies more and more on a few important hub airports. When these airports suffer larger man-made disturbances or natural disasters, the network survivability will drop very fast. Therefore, we should focus on strengthening protection for these important airports, meanwhile optimize airline network to improve overall network survivability. The following depicts the detailed research on the flight flow network in 2010. The comparative analyses of three attack methods, namely, random attack, degree-first attack, and betweenness-first attack, are made to discuss the network survivability. In random attacks, removing one edge node could make the maximum connected subgraph size or the overall efficiency indicator greater than that of the original network, so the value of ƸS or ƸE is negative and the curve of fS and fE will decrease below the axis. To visualize the effect of attacks better, we adopt two indices: S and E. Figs. 5 and 6 describe the relationship between S, E with respect to the number of removed nodes under various attacks.

100

100

80

80

60

60

fE

fE

attacked, we can open up new airlines, by passing this airport to form a new network, thus the survivability will be studied in this new flight flow network; while in case two, when one airport is attacked, all airlines connected to it will break because the airport is out of order, and we take into account the airflow direction, the flying range, and geographic location, etc. In this paper, we only consider the second case, that is, when one node is attacked, we will remove all its connected edges. The first case will be analyzed in the follow-up studies. Then, the decline rate of the maximum connected subgraph size and the decline rate of the overall network performance are calculated after each airport has been removed by Matlab. To analyze the overall development trends of the flight flow network survivability in China, we consider attacks based on degree-first order for each year. The variation curves of fS and fE in four different years are shown in Fig. 4. If we analyze from the perspective of the maximum connected subgraph size, when removing the first four nodes, fS is about 20% in each year, and the amount of damage increases fastest in 2010. This is because the scale-free property of the network in 2010 is more significant. The first four removed airports are Beijing, Guangzhou, Shanghai, and Shenzhen, all of which link to most of the other cities in the network. When we removes even nodes, fS in 2001 is the largest, which is up to 60%, while it is about 40% in other years. When we remove more nodes, the amount of damage is still largest in 2001, followed by 2004, 2007, and 2010, which validates that the flight flow network survivability has an increasing trend. When we remove 25 nodes, the network has nearly crashed and fS is more than 90% in each year, indicating that the network survivability is weak under a deliberate attack.

40

40

20

20

0

2

4

6 8 10 12 14 16 18 20 22 The number of removed nodes

24

0

2

4

6 8 10 12 14 16 18 20 The number of removed nodes

22

24

Fig.4 Relationship for fSǃfE with respect to number of removed nodes based on degree-first attack in different years 100

100 Random attack Betweenness-first attack

80

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60

60

S

S

S

100

Random attack Degree-first attack

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(a)

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Random attack Betweenness-first attack

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The number of removed nodes

(b) Fig. 5 Contrast curve of maximum connected subgraph size under different attacks

30

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The number of removed nodes

(c)

70

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DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185

Random attack Betweenness-first attack

Random attack Degree-first attack 0.4

Random attack Betweenness-first attack

0.4

E

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E

0.4

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0

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The number of removed nodes

(a)

30 40

50 60

70 80

90 100 110 120 130

The number of removed nodes

(b)

(c)

Fig. 6 Contrast curve of overall network performance indicator under different attacks

(a) Original network

(b) Remove 5 nodes

(c) Remove 20 nodes

(d) Remove 30 nodes

Fig. 7 Variation of network structure based on the degree-first attack

(a) Original network

(b) Remove 5 nodes

(c) Remove 20 nodes

(d) Remove 30 nodes

Fig. 8 Variation of network structure based on the betweenness-first attack

From Figs. 5(a) and 5(b), compared with the random attack, S drops faster under the deliberate attack based on degree-first or betweenness-first mode. When we remove 10 nodes, S declines nearly by half; when we remove 40 nodes, S is close to 0, and the network almost cannot be connected. In Fig. 5(c), when we remove less than 20 nodes, S falls slightly faster based on the betweenness-first attack than that based on the degree-first attack; when we remove around 20–40 nodes, S falls faster based on the degree-first attack. From Figs. 6(a) and 6(b), E is observed as fluctuating and tends to descend slowly in a random attack. There are several jump points occasionally because some important nodes may be removed. E declines sharply under deliberate attacks based on degree-first and betweenness-first mode. When we remove about five nodes, E declines by half; when we remove 30 nodes, E is close to 0, and the network is almost disconnected. From Fig. 6(c), there is a little difference of E in two deliberate attacks. In conclusion, the flight flow network of China has robustness under a random attack, but is very vulnerable under a deliberate attack due to the non-homogeneous network structure.

To observe the changes of the network structure more clearly under deliberate attacks, the original network is visualized after removing 5, 20, and 30 nodes, as shown in Figs. 7 and 8. Before the attacks, the original network contained 135 nodes and 1368 edges. After removing five nodes (Beijing, Shanghai, Guangzhou, Chengdu, Shenzhen) based on degree-first attack, 97 nodes and 766 edges remain and the network becomes very sparse since the connected edges decline sharply. After removing five nodes (Beijing, Kunming, Shanghai, Urumqi, Guangzhou) based on the betweenness-first attacks, 88 nodes and 814 edges remain while the network scale diminishes quickly. In particular, after removing Urumqi and Kunming airports, there are almost no connections in the western region, and the network is hugely damaged. When we remove 20 nodes based on degree-first attack, the network decomposes into several components, centered at Urumqi, Hohhot, Guilin, etc. The network scale is very small with limited scope of reach ability, as the southwest, the central and the northeast areas of China are almost impossible to reach. When we remove 20 nodes based on betweenness-first attacks, only some coastal cities are

DANG Yaru et al. / J Transpn Sys Eng & IT, 2012, 12(6), 177185

connected and other areas are nearly in a state of blank. It can be found that the network connectivity is damaged more severely when based on a betweenness-first attack than when based on degree-first attack. The larger the betweenness of a node is, the greater the role it enacts as a bridge in the network. Therefore, once we remove such kind of nodes, the network bridge will be interrupted, resulting in the rapid decline of the network connectivity. When we remove 30 nodes, whether under degree-first attack or betweenness-first attack, there are only a few connections among nodes and the network is almost broken down, which further proves that the flight flow network of China is vulnerable to deliberate attacks.

5

Conclusions

Using the complex network theory, this paper develops the flight flow network model of China and analyzes the networks tructure. By calculating the network statistical indicators, we prove that the flight flow network has small world and scale-free characteristics, which will definitely affect the running status of the flight flow network. According to this analysis, we set two indicators, namely, the decline rate of the maximum connected subgraph size and the overall efficiency indicator, to analyze the network survivability. From the development trend of the flight flow network of China in the last decade, we can find that the survivability has an overall yearly improving trend. However, the hub airports are increasingly crowded, indicating that the scale-free property of the network is more distinguishable. From the comparison among various attacks, when we deliberately remove 5 to 10 nodes from the network, the overall performance of the network drops almost in half, and it drops faster under betweenness-first attack than that under degree-first attack, which means that the damage is greater under betweenness-first attack. When we deliberately remove more than 30 nodes in the network, the network almost crashes. However, the damage is weaker under random attacks, and the network structure is almost not destroyed. This means that the development of the flight network in China is over-reliant on a few important airports due to the rapid development of its economy. When hub airports are affected by natural disasters or man-made failures, the entire flight flow network would be severely affected. Thus, the airports with high degree should be guaranteed to operate safely and effectively, especially for those with high betweenness feature, such as Shanghai, Guangzhou, Kunming, and Urumqi airports, etc. Meanwhile, we should optimize the overall airline organization, improve the management of the airline network, and develop multi-hub

systems so as to enhance the reliability and connectivity of the flight flow network of China fundamentally.

Acknowledgements This research was funded by the Science and Technology Foundation of Civil Aviation Administration of China (No. RKXZY0820, MHRD201214).

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