Dissertation framework

The framework and organization of this dissertation is shown as Figure 1.1, which depicts the content and key factors of each part of this dissertation, and shows the relationships among all parts. The research subjects at Chapters 4 and 6 are investigated based on the small-world airport network constructed at Chapter 3 and using the same flight database and airport traffic statistics as Chapter 3. On the other hand, the analysis from the perspective of passengers at Chapter 3 is further extended to investigate the perception of passengers about air travel services or products sold by airlines at Chapter 5 on the demand side, which focuses on the airline choice behavior of passengers and the influence of WOM.

Chapter 1 illustrates the overview of this dissertation with respect to the motivation and background, research objectives, spectrum and framework. Chapter 2 presents the review of literature in relevant topics and issues, and briefly discusses the key papers. The

discrimination of this dissertation from past studies is also discussed and identified in this chapter, in order to highlight the contributions of each part of this dissertation. Chapter 3 investigates one of positive influences of small-world properties, where the shortcut functions of complementary international airline alliances are discussed using the small-world theory. This dissertation considers travel time as a determinant to develop accessibility and mobility models, and the latter is further formulated at the global and local scales to analyze the global and local structure properties, respectively. For examining whether the alliance network is a small-world network or not, model normalization and degeneration are carried out. In the analysis of an actual case study of a complementary international airline alliance, the flight timetables of allied airlines and the worldwide flight data are collected for the real case and ideal case, respectively. The proposed models as well as the shortest path algorithm are then applied to compare the network connectivity and efficiency between the pre- and post-alliance situations, which enable us to evaluate the benefit of alliance routes and to examine the small-world properties of the airport network.

Chapter 4 investigates one of negative influences of small-world properties, which focuses on the transmission of influenza caused by air travel activities of passengers in a small-world airport network constructed at Chapter 3. The susceptible-infected epidemic model is applied to illustrate the influenza transmission, i.e. passengers are divided into the susceptible subpopulation and infected subpopulation. This dissertation develops two transmission models that illustrate the transmission behavior happened on scheduled flights and at airport terminals, respectively, with different values of infection parameters.

Furthermore, basic control measures are designed to be practiced at the departure and arrival procedures of passengers in order to constrain the transmission and pandemic of influenza. The start time and target of practice for control strategies differ from each other, which result in various control effectiveness in terms of cumulative number of infected

individuals and cumulative percentage of airports with infected cases. The relationship between the containment results of strategies and the level of connectivity of airports is also investigated, thereby providing helpful insights for the authorities.

Chapter 5 explores the other positive influence of small-world properties, which focuses on investigating the diffusion evolution of LCCs with WOM transmission and influence in small-world social networks. Passengers are allowed to revise their perceptions of LCCs over time as they receive more WOM information from social neighbors. The revision of perceptions will change the intensity of WOM information, and the level of the change is affected by passengers’ personal characteristics, such as the social connectivity and tie strength with other persons, and the number of neighbors who have adopted LCCs.

As soon as the intensity of WOM information is over the threshold value, the probability that a passenger adopts LCC will be increased. This dissertation also investigates how the dynamic structural properties of small-world networks and the dynamics in the perception revision affect the adoption timing and pattern of LCC. The influences of the culture difference on the diffusion of LCC are also analyzed, which may further affect the designs of management and marketing strategies for carriers.

Chapter 6 investigates the other negative influence of small-world properties, and applies the small-world airport network constructed at Chapter 3 to explore the problem of delay propagation. The level of connectivity of airports is affected by the small-world properties of the airport network. This dissertation uses a typical epidemic model, susceptible-infected-removed model, to illustrate the propagation of delay across flights and airports. There are several key factors are incorporated into the model, such as the delay duration and the level of connectivity of airports. This dissertation also considers the influences of weather conditions and probability of delay occurrence on the propagation

pattern. For solving the delay problem, the ground-holding policy, one of the short-term approaches, is applied. The policy holds flights on the ground before take-off, which involves how to efficiently and effectively allocate the limited capacity to flights. Several allocation strategies are proposed for mitigation and are evaluated for finding the optimal one. Furthermore, this dissertation investigates how the shortcut functions of specific flights facilitate the delay propagation using the small-world theory. Finally, Chapter 7 summarizes the important findings as well as some conclusions and management implications with respect to each part of this dissertation.

Figure 1.1 Framework of this dissertation

This dissertation depicts the flowchart of research process as Figure 1.2, and describes each step in detail as follows.

1. Define the research problems

Based on the motivation and background, this dissertation identifies the research issues, topics, scope, problems and objectives at first.

2. Literature review

To better understand the problems and identify the important objectives of research, this dissertation comprehensively and systematically reviews the existing literature on the relevant issues, such as the airline alliances, disease transmission and pandemics, airline choices of passengers, evolution of LCCs, airport congestion and delay, and so on. By doing so, this dissertation can clarify and highlight the contributions of this research, as well as can take into account the key factors when formulating models and designing management strategies.

3. Small-world theory and methodology

Next, the small-world theory and methodology are investigated in detail. The distinctive structure characteristics affecting the flow and spread of any communication or social process are identified. The understanding of the small world is the fundamentals of the model constructions.

4. Network connectivity analysis

Since the small-world properties affect the connectivity of components of a given network according to the understanding of the small world in Step 3, this dissertation

applies several quantitative variables for evaluating the network connectivity. Travel time is one of them, and is also one of the most significant measures of performance in an air transportation system. From the perspective of passengers, mobility and accessibility are used to evaluate, respectively, the ease of movement for passengers to and from cities, and the extent to which passengers can reach their destinations for accomplishing socioeconomic activities.

5. Network of international airline alliances

For evaluating the connectivity and efficiency of an alliance network, this dissertation defines the nodes and links of the network in advance. The mobility and accessibility models are then used to evaluate the network connectivity and efficiency before and after the alliance, and investigate the benefits contributed from the alliance. The small-world properties of the network are also examined.

6. Disease transmission model

This dissertation discusses how the influenza spreads to other regions of the world via the air travel activities of passengers, and develops the transmission models. The small-world properties and travel time between two airports are critical factors affecting the influenza transmission. This dissertation also investigates the transmission behavior of the influenza virus within the airport terminals, which have different infection parameters from that on scheduled flights.

7. Control strategies

This dissertation further designs several control strategies to mitigate the pandemic of influenza. There exist differences in the time that a strategy is carried out and in the target

which carries out the strategy across all strategies. This variation affects the containment results of strategies.

8. Ground-holding policy

This dissertation focuses on investigating the practice of ground-holding policies, involving how to effectively allocate the limited arrival capacity of an airport to flights. The issues that the policies affect the delay cost and duration of flights are also discussed in this dissertation.

9. Airport delay model

A typical epidemic model is applied to explore the airport delay problem and to formulate a delay model. This model can be used to examine how a given delay is propagated to other relevant flights and airports via shortcuts of a small-world network.

Based on the policies in Step 8, this dissertation further uses the model to evaluate the effectiveness of each allocation strategy.

10. Social influence and perception revision

This dissertation turns the emphasis on the airline choice behavior of passengers, in which the LCC is the subject of analysis. In a social network that has been demonstrated as a small-world network, the issue how the social influence results in the adoption decisions of potential passengers is discussed in detail. The social influence comes from the social neighbors who have adopted the LCC before and pass WOM information to potential passengers. This dissertation also develops the scheme of the perception revision of potential passengers, which dynamically affects the adoption behavior of passengers.

11. Word-of-mouth intensity model

Based on Step 10, this dissertation further proposes an intensity model, incorporating the tie strength of social relationship between persons and the adoption decisions of social neighbors, to analyze that how much the intensity of WOM information is will increase the adoption probability of potential passengers. Several key factors affecting the adoption probability are also discussed.

12. Dynamic structure of network

Since the dynamic properties of network structure have been demonstrated as a factor of influencing the spread of any communication, this dissertation dynamically change the structure of the social network with partial randomness. The influence of dynamic properties is evaluated in terms of the diffusion evolution of adoption at a two-dimensional space.

13. Case studies and sensitivity analyses

Case studies are provided at each part of this dissertation to illustrate the application and to demonstrate the effectiveness of the proposed models. This dissertation also applied the sensitivity analyses of models to evaluate the results and patterns under various scenarios.

14. Conclusions and suggestions

Finally, this dissertation presents the concluding remarks, management suggestions and recommendations for future research.

Figure 1.2 Flowchart of research process

CHAPTER 2 Literature review

This chapter reviews the literature on related areas and issues. The following subsections are organized as: 2.1 Small-world related issues; 2.2 Airline alliances related issues; 2.3 Mobility and accessibility models; 2.4 Disease related issues; 2.5 Low-cost carriers related issues; and 2.6 airport delay problems. The research issues, methodology and important findings of the related studies are also discussed and summarized in this chapter. The final subsection identifies and highlights the contributions of this dissertation.

2.1 Small-world related issues

The small-world phenomenon was first observed by Stanley Milgram (1967) of Harvard University. In the late 1960’s, he distributed a number of letters to a random selection of people in Nebraska and Kansas, and asked these people to send the letters to a stockbroker in Boston by passing letters from person to person. For each person, the strategy of passing the letter was that the person would pass his/her letter to someone he/she presumed was more likely to know the Boston stockbroker. The receivers of letters would also subsequently pass letters based on the same strategy. Milgram kept track of the letters and the demographic characteristics of the letter receivers, by requiring each intermediary to report their receipt of the letter. A reasonable number of letters eventually reached their destination, i.e. the Boston stockbroker, with a medium chain length of about six. Therefore, Milgram concluded that six was the average number of acquaintances separating any two people in the world. This situation has been labeled as “six degrees of separation”, a popular phrase in the social network. There were certainly possible sources of error in Milgram’s experiment, and the number six is probably not very accurate. However, the important result

that any two randomly chosen persons can be connected by only a short chain of intermediate acquaintances has been subsequently verified and is now widely accepted. This result is referred to as the small-world phenomenon.

In the late 1990’s, Watts and Strogatz (1998) pointed out that the connection topology was ordinarily assumed to be either completely regular or completely random, but many biological, technological and social networks lay somewhere between these two extremes.

Therefore, they explore simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder. They found that these networks can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. They called them ‘small-world’ networks, by analogy with the small-world phenomenon (Milgram, 1967). To interpolate between regular and random networks, they considered the following random rewiring procedure.

They started from a ring lattice with n vertices and k edges per vertex, and then rewired each edge at random with probability p. This construction allowed them to ‘tune’ the graph between regularity (p=0) and disorder (p=1), and thereby to probe the intermediate region 0<p<1, about which little was known. They further quantified the structural properties of these graphs by their characteristic path length L(p) and clustering coefficient C(p). L(p) was defined as the number of edges in the shortest path between two vertices, averaged over all pairs of vertices. And C(p) was defined as follows. Suppose that a vertex v has kv

neighbors, then at most k_v (k_v -1)/2 edges can exist between them (this occurs when every neighbor of v is connected to every other neighbor of v). Let Cv denote the fraction of these allowable edges that actually exist. Define C(p) as the average of Cv over all v. For friendship networks, these statistics had intuitive meanings: L(p) was the average number of friendships in the shortest chain connecting two people; Cv reflected the extent to which friends of v are also friends of each other; and thus C(p) measured the cliquishness of a

typical friendship circle. In other words, L(p) measured the typical separation between two vertices in the graph (a global property), whereas C(p) measured the cliquishness of a typical neighborhood (a local property).

From a numerical example, Watts and Strogatz (1998) found that the regular lattice at p=0 was a highly clustered, large world where L(0) grew linearly with n, whereas the random network at p=1 was a poorly clustered, small world where L(1) grew only logarithmically with n. These limiting cases might lead one to suspect that large C(p) is always associated with large L(p), and small C(p) with small L(p). On the contrary, there was a broad interval of p over which L(p) was almost as small as L(1) but C(p) was much larger than C(1) in the example. These small-world networks resulted from the immediate drop in L(p) caused by the introduction of a few long-range edges. For small p, each of such

‘shortcuts’ had a highly nonlinear effect on L(p), contracting the distance not just between the pair of vertices that it connected, but between their immediate neighborhoods, neighborhoods of neighborhoods and so on. By contrast, an edge removed from a clustered neighborhood to make a shortcut had, at most, a linear effect on C(p). Hence, C(p) remained practically unchanged for small p even though L(p) dropped rapidly. To test the above ideas obtained from a numerical example, Watts and Strogatz (1998) had computed L and C for the collaboration graph of actors in feature films, the electrical power grid of the Western United States, and the neural network of the nematode worm Caenorhabditis elegans. The graph of film actors was a surrogate for a social network. The graph of the power grid was relevant to the efficiency and robustness of power networks. And Caenorhabditis elegans was the sole example of a completely mapped neural network. The L and C for three graphs compared to random graphs with the same number of vertices (n) and average number of edges per vertex (k) were shown in Table 2.1. All three real graphs showed the small-world phenomenon, in which their L were as small as L(1) but C were much larger than C(1).

These examples were not hand-picked; they were chosen because of their inherent interest and because complete wiring diagrams were available. Thus the small-world phenomenon was not merely a curiosity of social networks nor an artifact of an idealized model. It was probably generic for many networks.

Table 2.1 Characteristic path length and clustering coefficient for three real graphs

n k Lactual L(1) Cactual C(1)

Film actors 225,226 61 3.65 2.99 0.79 0.00027

Power grid 4,941 2.67 18.7 12.4 0.080 0.005

Caenorhabditis elegans 282 14 2.65 2.25 0.28 0.05

Following Watts and Strogatz (1998), some studies were proposed to investigate whether specific real-world networks reveal small-world properties or not. In particular, Latora and Marchiori (2001, 2002) pointed out that the mathematical formalism of Watts and Strogatz (1998) suffered from severe limitations: (1) it applied only to some cases, whereas in general the two quantities L and C were ill-defined; (2) it worked only in the topological abstraction, where the only information retained was about the existence or the absence of a like, and nothing was known about the physical length of the link. Therefore, Latora and Marchiori (2001, 2002) proposed global and local efficiency models, and confirmed that their models can drop all restrictions in the model of Watts and Strogatz (1998). They defined the shortest path length d between two generic nodes i and j as the _ij smallest sum of the physical distances throughout all the possible paths in the graph from i to j. The efficiency ε_ij in the communication between nodes i and j was then defined to be inversely proportional to the shortest distance between them, i.e. ε_ij =1d_ij. When there was no path in the graph between nodes i and j, d_ij =+∞ and, consistently, ε_ij =0. The global efficiency of a generic weighted (and possibly even nonconnected) graph G , is formulated

as 1 ( ( 1)) and Marchiori (2001, 2002) confirmed that a small-world network is a network with both high global and high local efficiency. They also showed that if the Boston subway transportation system (MBTA) is combined with its bus system, then this extended system is a small-world network.

Sen et al. (2003) investigated the structural properties of the Indian railroad network (IRN) to examine whether or not some of the general behavior obtained for many complex networks may also be present in IRN. Stations are considered as nodes, and an arbitrary pair of stations is considered as connected by a link when at least one train stops at both stations.

With the definition of links, the mean distance of the network is a measure of how good is the connectivity of the network. They found that IRN behaves like a small-world network and believed that it is typical of the railroad network of any other country. Guimerà and Amaral (2004) investigated the world-wide airport network using the degree, defined as the

With the definition of links, the mean distance of the network is a measure of how good is the connectivity of the network. They found that IRN behaves like a small-world network and believed that it is typical of the railroad network of any other country. Guimerà and Amaral (2004) investigated the world-wide airport network using the degree, defined as the