應用小世界理論於航空網路之研究

(1)

國

立

交

通

大

學

運輸科技與管理學系

博

士

論

文

應用小世界理論於航空網路之研究

Small-World Theory in the Study of Air Transportation Network

研究生：施憲宏

指導教授：許巧鶯教授

(2)

應用小世界理論於航空網路之研究

Small-World Theory in the Study of Air Transportation Network

研究生：施憲宏 Student：Hsien-Hung Shih

指導教授：許巧鶯 Advisor：Chaug-Ing Hsu

國立交通大學

運輸科技與管理學系

博士論文

A Dissertation

Submitted to Department of Transportation Technology and Management College of Management

National Chiao Tung University in Partial Fulfillment of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

in

Transportation Technology and Management June 2008

Hsinchu, Taiwan, Republic of China

(3)

Small-World Theory in the Study of Air Transportation Network

Student: Hsien-Hung Shih Advisor: Dr. Chaug-Ing Hsu

Department of Transportation Technology and Management National Chiao Tung University

ABSTRACT

This dissertation aims to investigate the positive and negative influences that small-world properties have on an air transportation network as well as a social network of passengers. A series of models are systematically constructed in accordance with four important issues emphasized on: small-world network theory in the study of network connectivity and efficiency of complementary international airline alliances; transmission and control of an emerging influenza pandemic in a small-world airline network; word-of-mouth marketing in a small-world network for low-cost carriers; and the application of small-world theory to airport delay problem. The first part of this dissertation attempts to conceptually apply the shortcuts of a small-world network to explore the effects of international airline alliances on the connectivity of airline networks, and to examine whether the airline alliance network is a small-world network or not. The difference in the connectivity efficiency between pre- and post-alliance situations is also measured. The second part of this dissertation aims to explore the human-to-human transmission of emerging influenza via air travel activities. Two dynamic models that illustrate the transmission behaviors of the influenza virus on scheduled flights and at airport terminals are formulated so as to evaluate the expected burdens of the pandemic without and with control measures. The third part of this dissertation turns the emphasis on the first-purchase behavior of potential passengers for low-cost carriers (LCCs). It aims to explore how the WOM information is transmitted through the social connections in a small-world social network, how the perception of LCCs is revised over time, and how the WOM affects the adoption of LCCs by short-haul business passengers. The last part of this dissertation focuses on exploring the influences of small-world properties of an airport network on the delay propagation across flights and airports. An epidemic-like model is used to illustrate

(4)

the delay propagation over flights and airports. Several capacity-allocation strategies are proposed and are evaluated in terms of the total cost.

A series of case studies are performed to demonstrate the applications of this dissertation. The results show that the connectivity of the alliance network is better than before, and it exhibits small-world properties. The alliance effectively improves accessibility from high-medium traffic airports to low traffic airports. After the alliance, the shortest paths between origin-destination pairs will involve more transfers but less total travel time. The results also show that, as soon as the influenza is spread to the top 50 global airports, the transmission is greatly accelerated. Under the constraint of limited resources, a strategy that first applies control measures to the top 50 airports after day 13 and then soon afterwards to all other airports may result in remarkable containment effectiveness. As the infectiousness of the disease increases, it will expand the scale of the pandemic, and move the start time of the pandemic ahead. In addition, the results show that it may cause a mistaken forecast of adoption if without taking into account the influence of WOM. As soon as the ratio of the price of a LCC to the price of a FSC is over a half, the attractiveness of the LCC to business passengers is gradually diminished. The comparisons of different societies show that LCC may apply a slightly higher price to a lower risk-averse society, while this pricing strategy does not markedly affect its adoption pattern since LCC still has an advantage of price over FSC. In the average pattern for all 265 airports, the total cost and the total number of affected flights for a strategy that tends to allocate slots to long-haul flights are the lowest among all strategies, which is the same as those observations at past studies. When an airport has a high proportion of inter-regional flights scheduled to arrive and has low capacity due to weather condition, a strategy that uses the first-scheduled-first-served allocation principle will be an economic and equitable allocation strategy for this kind of airport. This strategy is also the best allocation strategy for those airports that are highly connected to other airports. Finally, based on the average patterns of all airports, a strategy that tends to allocate slots to long-haul flights not only decreases the total cost, but also indirectly reduces the occurrence and the scope of the inter-regional delay propagation.

(5)

ACKNOWLEDGEMENT

在交通大學待了十年光陰，今年終於可以光榮地從交通大學畢業了。在這漫長的日子裡，很感謝在學術研究及日常生活上都得到貴人的相助。首先，非常感謝恩師許巧鶯老師在我博士生涯中帶給我光明、輝煌及燦爛的學術體驗，讓我學習到許多學術研究上的精髓，瞭解從事研究所應堅持的理念與態度，恩師更帶領我從複雜問題中抽絲剝繭出重要的發現與價值，使我的研究不僅在學術上，也能在實務上對社會有所貢獻。學生謹言慎行遵從恩師的教導，並期許能傳授給後續學子以發揚恩師的教誨。在博士論文口試階段，感謝成功大學張有恆教授、中央大學顏上堯教授、本校馮正民教授及張新立教授能於口試與審查期間撥冗細審學生的博士論文，並提供寶貴意見與細心指正，使本論文於整體性上能更加完善，亦更能突顯論文的研究價值。而在就讀交通大學期間，非常感謝系上陳光華老師、張新立老師、韓復華老師、卓訓榮老師、任維廉老師、高凱老師、吳水威老師、吳宗修老師、謝尚行老師、王晉元老師、黃寬丞老師、黃家耀老師、郭秀貴老師、林貴璽老師及李明山老師於生活及課業上的關心與教誨，致上由衷的謝意，其中特別感謝高凱老師在學生課外之餘，給予學生平日生活上的關心與照顧，讓學生在就讀期間倍感溫馨，往昔與老師相處的珍貴畫面猶存在學生腦海中，特別致上無比的感激。另外，感謝系上的系辦助理秀蔭姊與幸榮姊，常常在學生處理課業上相關問題時適時地給予莫大的幫助，使許多瑣碎事務都能迎刃而解，讓學生能把握更多寶貴時間從事學術研究，謹致上誠心的祝福。在日常生活上，特別要感謝我的父母，施茂任與施許雪貞，對我的細心栽培及養育之恩，讓我能在無後顧之憂下，專心、幸福、穩定地完成博士學位，實現彼此的偉大夢想，同時亦感謝和藹可親、美麗動人、世上唯一的家妹曉君能在我沒有待在家裡的這段日子裡，全心全意、盡心盡力的侍奉我的父母，讓他們可以享有天倫之樂。也感謝家族中可愛的伯伯、姑姑、姑丈、叔叔及小嬸，帶給我充滿歡笑的人生。此外，特別要感謝我親愛的賢內助安秀讓我的人生更加精彩與充實，同天生日的機緣巧合讓我與她心心相惜、彼此相扶持，她總在天時地利人合下適時地能給我歡樂、驚喜、安慰、鼓舞、良言、幸福，帶給我的人生莫大的幫助。另外，要把我小小的謝意給我心愛的兩隻貓咪，BQ 與 Bogeot，雖然他們平時慵懶、生活愜意，但總在我熬夜趕報告、準備考試時能貼心地叮嚀我，要我好好照顧身體、盡快上床休息，著實感到小小的幸福。最後，除了感謝上天對我的關懷與照顧外，要再次感謝上述所有曾幫助我的貴人，讓我能順利完成博士學位這偉大夢想。

施憲宏

2008 年六月於新竹交大

(6)

LIST OF TABLES

Table 2.1 Characteristic path length and clustering coefficient for three real graphs ...30

Table 2.2 Main issues, features and results on small-world related literature...36

Table 2.2 (continued)...37

Table 2.3 Main issues, features and results on airline alliances related literature...42

Table 2.4 Main issues, features and results on mobility and accessibility related literature....49

Table 2.5 Main issues, features and results on disease related literature ...55

Table 2.6 Main issues, features and results on low-cost carriers related literature ...60

(9)

LIST OF FIGURES

Figure 1.1 Framework of this dissertation...20 Figure 1.2 Flowchart of research process...25

(10)

CHAPTER 1 Introduction

The main issues of interest in this dissertation are the positive and negative influences of small-world properties on air transportation network with respect to connectivity efficiency, disease pandemic, word-of-mouth marketing and flight delay. This chapter presents an overview of the motivation, problem specification, research objectives and methodology, and the framework of this dissertation.

1.1 Motivation and background

In recent years a series of new research studies have emerged that explored the issue of connectivity of a variety of networks. These studies mainly followed the work of Watts and Strogatz (1998) who developed a small-world theory to investigate distinctive characteristics in some real networks, such as social, technological and biological networks. Watts and Strogatz (1998) demonstrated that the structural properties of a small-world network are significantly different from the conventional assumptions of network property at past studies. Past studies ordinarily assumed the network as completely regular graphs, with highly clustered and highly separated, or as completely random graphs, with lowly clustered and lowly separated. However, the small-world network lies in between regular and random graphs, and has a distinctive combination of structure properties, high clustering at the local scale and low separation at the global scale, due to the function of introducing a few shortcuts (long-range links) into the network. Watts and Strogatz (1998) quantified the structural properties of networks by their clustering coefficient and characteristic path length, and showed that the small-world networks are highly clustered, like regular graphs, yet have small characteristic path lengths, like random graphs. This kind

(11)

of property combination does differ from those investigated by past research, and may play an important role in the study of the influence of the network property on the dynamics of social processes or any kind of communication. Watts and Strogatz (1998) also demonstrated that some social, technological and biological networks in the real world are all small-world networks.

These small-world phenomena also seem to exist at the air transportation network. Airlines can apply those inter-regional or inter-continental routes to enable passengers to fly between airports that are located at various geographic regions worldwide. At the same time, airlines can apply those intra-regional or short-haul routes to provide air travel services within one or more local regions. In other words, each destination or airport is highly connected to others that are located at the same local region, and is also inter-regionally connected to others that are located at distant and different regions in air transportation network. Those inter-regional routes indirectly reduce the separation between various geographic regions worldwide, and serve as an important bridge that allows passengers to travel from one region to another in an efficient way. As a result, these inter-regional routes mimic the shortcuts of a small-world network. Furthermore, the emergence of the airline alliances in recent years enables airlines to provide inter-regional air travel services by alliance routes at the global scale, and to retain intra-regional services by their own routes at the local scale. In other words, the airline alliances make the small-world phenomenon of air transportation network more obvious. However, this small-world phenomenon may easily cause the transmission and pandemics of infectious diseases by inter-regional air travel activities, and may also easily result in inter-regional delay propagation across airports that are located at various regions and their scheduled flights. In addition, on the demand side of air transportation, the word-of-mouth communication between passengers who form a small-world social network may affect the purchase decisions and adoption of a

(12)

given air services or products sold by airlines. Past studies have rarely explored the small-world properties of air transportation network, and thereby may have neglected some important results and observations that indeed exist in the network and may result in unexpected influences. To sum up, the important issues about the influences of small-world properties deserve further investigation, especially for air transportation network due to the lack of emphasis and theoretical formulation in the literature. In particular, it is necessary to explore the positive and negative influences that small-world properties have on the interaction among passengers, airlines and airports involved in air transportation network. The following paragraphs describe the developments associated with each research topic mentioned above up to the present.

International aviation markets have been globalized and have become increasingly competitive in recent years. There are more and more carriers using international airline alliances to access new markets, extend their networks and strengthen their competitive advantage under air traffic rights and resource limitations. The number of new alliance agreements has increased every year since 2001, and more than 110 new alliances were formed in 2004 (Kemp et al., 2005). Besides, the top three alliance groups, Star Alliance, Oneworld, and SkyTeam collectively account for over 80% of the North Atlantic traffic and for over half of world passenger traffic (Field, 2005). These data show that the emergence of international airline alliances has become mainstream in today’s international airline industry.

An international airline alliance is an agreement between two or more air carriers cooperating in a commercial relationship or jointly operating activities in various fields, such as integrated marketing strategies and reservation service, coordinated flight frequency and schedule, joint use of ground facilities, joint frequent flyer programs, and others. Alliances

(13)

provide opportunities for the partner carriers to extend their networks, service more parts of the world, increase the volume of passenger traffic and the load factor, and consequently strengthen their competitive positions and improve profitability. Code-sharing agreements are a mainstream practice of an alliance, whereby each carrier’s designator code is shown on his partner’s flights, such that carriers can offer services to destinations that they themselves do not physically serve. In the literature, Park (1997) and Oum et al. (2004) discussed the effects of airline alliances in detail.

Emerging infectious diseases, such as the avian influenza and severe acute respiratory syndrome (SARS), have rapidly caused numerous infected persons, negatively affecting human life and the economy. For instance, SARS led to an immediate economic loss of close to 2 percent of the GDP for the East Asian region in the second quarter of 2003 (Brahmbhatt, 2005). Avian influenza virus H5N1 may transform into a new human influenza virus through genetic reassortment, and develop the ability for increased and sustained transmission between humans (Capua and Alexander, 2002). H5N1 is showing a serious pandemic threat to the human population (Ferguson et al., 2005). Most people are easily infected with this new type of influenza because they have no immunity to the disease, thereby resulting in a serious pandemic.

Disease outbreak and pandemics will obstruct social and economic activities worldwide. In the past, the most noted influenza pandemic was the one beginning in 1918 with a mortality rate that resulted in the death of possibly 50 million people worldwide (Ligon, 2005). It shows that influenza pandemics are a serious health threat, and it is critical that one should understand how an emerging influenza spreads, how to predict the influences of a pandemic, and how to design control measures for mitigation. On the other hand, an empirical research indicated that passengers who took the same airplane flight with a SARS

(14)

patient would possibly become suspect or probable cases of SARS (Centers for Disease Control and Prevention, 2003). Another study also showed a high rate of transmission of SARS on aircraft (Olsen et al., 2003). These findings show that air travel facilitates the spread of infectious diseases, and plays an important role in the transmission of diseases worldwide and the appearance of serious pandemics with health and life threats. In particular, passengers of air transportation may infect with influenza during air travel activities, such as passenger consolidation, conveyance and distribution in airports and on scheduled flights.

In the scope of consumer behavior, one of the most widely accepted notions is that word-of-mouth communication (hereafter WOM) plays an important role in shaping consumers’ attitudes and behaviors (Brown and Reingen, 1987). Many studies pointed out that WOM is the most powerful form of marketing on earth. The impact of WOM is ten times more effective than TV or print advertising, and four times as effective as personal selling in influencing consumers (Katz and Lazarsfeld, 1955; Hughes 2005). Rosen (2000) indicated that there are 53% moviegoers relying on a recommendation from someone they know; 70% Americans relying on the advice of others when selecting a new doctor; and 65% customers getting information about products from another person. So, WOM is the most important source of influence in the purchase of consumer products and services, as well as in determining the speed and shape of the diffusion process of a new product in a social system (Mahajan et al., 1990).

For passengers of air transportation, low-cost carriers (hereafter LCCs) can be seen as a new product since their rapid emergence at many aviation markets in recent years. LCCs have reshaped the competitive environment within liberalized markets and have made significant impacts in the world’s passenger markets, which had previously been dominated

(15)

by full-service carriers (hereafter FSCs) (O’Connell and Williams, 2005). LCCs accounted for a 43% share of the UK domestic market and 28% of the US, and the market share is predicted to grow further (Clarke, 2004). The characteristics of LCCs include a simplified fare structure, use of secondary airports, point-to-point direct flights, short turnaround time, a single type of aircraft, payment for in-flight service, and so on. The simplification of operations and high level of utilization enable LCCs to gain significant cost advantages and charge passengers low fare.

Although the original focus of LCCs was on leisure and tourism travelers, recent evidence indicated that 74% of UK business travelers said that they had used the service of LCCs for business trips (Company Barclaycard, 2005). Business travelers have increasingly used LCCs, while the number of short-haul European business trips that are taken in business class has dramatically dropped, where 79% of short-haul travelers thought that the business class service did not offer value for money (Mason, 2001). It suggested that LCCs were more likely to attract these short-haul business travelers.

Congestion problems are becoming increasingly serious in many major international airports due to the rapid growth of traffic demand. Such problems usually results in significant economic losses of airlines, passengers and airports (Janić, 2005). Traffic congestion arises when the traffic demand overcomes the airport capacity that is heavily influenced by weather conditions. One of solution approaches to the congestion problem is the ground-holding policy, termed as a short-term approach (Vranas et al., 1994). The task of the policy is that aircraft may be held on the ground before take-off whenever congestion is expected on its route, so that it can arrive at its destination airport without waiting in the air. The motivation of the policy is due to the fact that holding aircraft on the ground is safer than holding them in the air, and the delay cost of the former is less than that of the latter.

(16)

The problem of determining how much each aircraft must be held on the ground before take-off to minimize the total delay cost is referred to as the ground-holding problem (Vranas et al., 1994), which can be further divided into two categories, single-airport and multi-airports. The single-airport ground-holding problem is to decide the arrival slot allocation to various flights based on the landing capacity of a destination airport (Mukherjee and Hansen, 2007). The multi-airport ground-holding problem is shifted to consider an entire network of airports and incorporate the effect of delay propagation, in which when aircraft is delayed the next flight performed by the same aircraft will also be delayed. Hall (1999) pointed out that there was an average of 1.6 ground-holding programs implemented per day between September of 1998 and April of 1999, showing its high frequency of occurrence. Therefore, the ground-holding problem is an important topic for air traffic management research.

The literature on international airline alliances can be classified into three major categories: theoretical, empirical and comprehensive. Theoretical studies are focused on analyzing the economic benefits for alliances, such as outputs and profitability (Park, 1997; Wen and Hsu, 2006; Lin, 2004). The empirical studies collect data to investigate the current status of the alliances, the impact, features, strategies, and so on (Brueckner, 2003; Goh and Uncles, 2003; Albers et al., 2005; Iatrou and Alamdari, 2005). The comprehensive works not only developed theoretical models, but also conducted the empirical analyses of the effects of the alliances (Park et al., 2001; Chen and Chen, 2003). The majority of the above mentioned research investigated how alliances contributed to the economic outcomes of airlines. Little research, however, has been carried out on exploring the small-world properties of an alliance network as well as their effects on the connectivity efficiency of air transportation.

(17)

There are several studies have focused on reviewing infectious diseases and analyzing their impacts (Brahmbhatt, 2005; Capua and Alexander, 2002; Donnelly et al., 2003; Ligon, 2005; Meijer et al., 2004), as well as the design and evaluation of control measures (Ferguson et al., 2005; King et al., 2004). For example, Ferguson et al. (2005) modeled the spread of a pandemic in Thailand by incorporating random contacts associated with day-to-day movements to work within the country, and then evaluated the potential effectiveness of containment strategies. In addition, numerous studies have proposed mathematical epidemic models to evaluate and describe the dynamic evolution and the severity of epidemics in the population (e.g. Allen and Burgin, 2000; Colizza et al., 2006, 2007; Massad et al., 2005; Méndez and Fort, 2000). For example, Colizza et al. (2006, 2007) developed a metapopulation stochastic epidemic model on a global scale, and used a stochastic transport operator to describe the dynamics of individuals based on travels between cities. They concluded that a cooperative strategy where countries with large antiviral stockpiles share a part of their resources with other countries results in a global deceleration of the pandemics. However, few of the previous studies have discussed the influences of passenger consolidation, conveyance and distribution as well as small-world properties of an air transportation network on the spatiotemporal evolution of an influenza pandemic.

Attracting passengers is one of the most important goals for the operation of airlines. A number of studies have applied the utility function to investigate the airline choices of passengers, and found that there exists preference heterogeneity among passengers (e.g. Espino et al., in press; Rose et al., 2005). However, few of these studies have considered that passengers may change their perceptions of a product over time in their learning process, in which they receive additional WOM information about the product from other people. The dynamics in the perceptions may thus change passengers’ purchase decisions

(18)

and adoption timing of the product. If one neglects the changing perceptions of passengers, then it will result in a mistaken forecast of product adoption.

The literature of ground-holding problem can mainly be divided into four categories, static, dynamic, deterministic and stochastic versions. The static version of ground-holding problem makes the hold decisions once at the beginning of daily operations (Vranas et al., 1994), whereas the dynamic version makes the decisions within time of the day as better capacity estimates become available (Richetta and Odoni, 1994). The deterministic version considers airport capacities as fixed (Janić, 2005), whereas the stochastic version takes into account the uncertainty in airport capacities (Mukherjee and Hansen, 2007). These models conventionally minimized the total (ground plus airborne) delay cost to decide the number of time periods that each flight is held on the ground before take-off, with various heuristic algorithms for integer solutions from the linear programming (LP) relaxation. In the ground-holding problem, the use of linear cost functions tends to assign the arrival slot to flights with high delay cost. Recently, the model of Mukherjee and Hansen (2007) allows for applying nonlinear cost functions, showing it tends to obtain more equitable slot allocation across flights than linear cost functions. In the field of multiairport ground-holding problem, the research was restricted to the case when aircraft is delayed, the next flight performed by the same aircraft will also be delayed. Few studies, however, have explored the influences of small-world properties of air transportation network on the duration and propagation of flight delay.

Following Watts and Strogatz (1998), there are several studies investigating whether specific real-world networks reveal small-world properties or not (Sen et al., 2003; Guimerà and Amaral, 2004; Jiang and Claramunt, 2004). In particular, Latora and Marchiori (2001, 2002) found that the model of Watts and Strogatz (1998) has some problems regarding its

(19)

application to transportation systems, and then proposed global and local efficiency models to overcome problems. These studies have considered the physical distance between two nodes for weighted networks, but few studies have taken travel time between two nodes into account. Unfortunately, travel time is one of the most significant measures of performance in the air transportation system. More importantly, for transportation systems, it has been well recognized that mobility and accessibility are more appropriate for measuring system performance and effectiveness than the efficiency models proposed by Latora and Marchiori (2001, 2002). In the literature, there are also some studies proposing epidemic models to evaluate the dynamics of epidemics in small-world networks (Kuperman and Abramson, 2001; Saramäki and Kaski, 2005; Small and Tse, 2005), but not incorporating the influence of air travel activities into model formulation. On the other hand, the effects of small-world properties on the diffusion process of new products or services within a social network and on the flight delay of air transportation network have rarely been explored in the literature (Jun et al., 2006).

To sum up, several important issues about the influences of small-world properties on air transportation network deserve further investigation. However, these issues have been rarely emphasized and theoretically formulated in the literature. This dissertation aims to explore the positive and negative influences of small-world properties on air transportation network with respect to connectivity efficiency, disease pandemic, word-of-mouth marketing and flight delay. A series of models are formulated to systematically investigate the connectivity efficiency with and without alliances, influenza transmission via air travel activities, and duration and propagation of flight delay within an air transportation network with small-world properties. Furthermore, the scope of this dissertation is also extended to the aspect of passengers of air transportation, exploring how the WOM information affects the adoption of LCCs by short-haul business passengers on dynamic small-world social

(20)

networks at the micro level, where the changing revision of perception, dynamic properties of network structure and social heterogeneity are together incorporated.

1.2 Research objectives

The overall goal of this dissertation is to explore the influences of small-world properties in detail, and to make contributions in providing guideline of management strategies for responding to the influences. Specifically, the purpose of this dissertation is to investigate the positive and negative impacts small-world properties have on an air transportation network as well as a social network of passengers. The positive impacts are referred to the improvement in connectivity efficiency of network and the high level of penetration of LCCs, whereas the negative impacts are referred to the pandemic of influenza and the propagation of flight delay. In view of these topics, a series of models are constructed in accordance with issues emphasized. Based on the characteristics and significance of issues, there are four distinct parts involved in this dissertation: small-world network theory in the study of network connectivity and efficiency of complementary international airline alliances; transmission and control of an emerging influenza pandemic in a small-world airline network; word-of-mouth marketing in a small-world network for low-cost carriers; and application of small-world theory to airport delay problem. These four parts are illustrated more explicitly as follows.

In the first part of this dissertation, this study attempts to conceptually apply the shortcuts of small-world networks in order to explore the effects of international airline alliances on the connectivity of airline networks. In particular, the mobility and accessibility are used to investigate the effects of alliances by taking travel time into consideration, which allow us to quantify the difference of the connectivity between pre- and post-alliance situations. Mobility at the global and local scales is further used to examine whether the

(21)

airline alliance network is a small-world network or not. The connection between the proposed models and the economic benefits of airlines is also discussed in order to provide practical applications.

The second part of this dissertation aims to explore the human-to-human transmission of emerging influenza via air travel. The effects of air travel activities (i.e. passenger consolidation, conveyance and distribution in airports and scheduled flights) on the influenza pandemic are investigated in terms of the spatiotemporal evolution in a small-world airline network. This study also attempts to investigate how the influenza spreads to different geographic regions worldwide based on the connectivity properties of the small-world network. The transmission behaviors of the influenza virus on scheduled flights and at airport terminals are discussed, respectively, in order to evaluate the expected burdens of the influenza pandemic without and with control measures.

The third part of this dissertation turns the emphasis on the first-purchase behavior of potential passengers for LCCs in an aviation market dominated by FSCs before. This study aims to explore how the WOM information affects the adoption of LCCs by short-haul business passengers in dynamic small-world social network at the micro level. A dynamic approach is used to investigate the first-purchase behavior of potential passengers, where we allow passengers to revise their perceptions of LCCs over time based on the receipt of updated WOM information from their social neighbors. This revision in turn affects the dynamics of each passenger’s adoption probability and LCC’s adoption timing. Furthermore, the dynamic properties of network structure and the social heterogeneity are together incorporated into the modeling of passenger adoption behavior.

In the last part of this dissertation, this study focuses on exploring the influences of structural properties of an airport network on the delay propagation. When the arrival

(22)

capacity of an airport is reduced due to the weather condition, it may result in the delay of flights scheduled to land the airport. These delayed flights will be held on the ground for the cost and safety considerations, which is referred to the ground-holding policy. This study applies the small-world theory to explore the structural properties of the airport network, and uses the concept of shortcuts to analyze the characteristics of various flights, which in turn affect the delay propagation over scheduled flights and airports. This study further analyzes the influence of delay on scheduled flights with different length of haul. Other factors influencing the pattern of propagation, including the duration of delay and its probability of occurrence, the impacts of inter-regional long-haul flights and the level of connectivity of airports, are also investigated in the study.

Specifically, the objectives and contributions of each part of this dissertation are discussed as follows, respectively.

(1) This study explores the effects of international airline alliances on the connectivity of airline networks by conceptually applying the shortcuts of small-world networks, and develops the mobility and accessibility models to investigate the effects of alliances based on travel time. This study defines a traveler’s travel time between airports as the sum of his/her flying time on the flights and transfer time incurred at intermediate airports. The mobility model is constructed at the global and local scales, respectively, and is shown that it is more appropriate for measuring the system performance and effectiveness than the efficiency model proposed in the literature. The global and local structural properties of the alliance network are evaluated using mobility model, so as to examine whether it is a small-world network or not. This study also shows the degeneration and normalization of models, and discusses the connection between the models and the economic benefits of airlines in order to provide practical applications.

(23)

(2) This paper develops dynamic transmission models that illustrate the transmission behaviors of an influenza virus on scheduled flights and at airport terminals where air travel activities consisting of passenger consolidation, conveyance and distribution are carried out. The transmission of influenza via air travel is evaluated in terms of the dynamical evolution and spatial distribution in a small-world airline network. For the realism of our models, links of the network were weighted by the flying time and the number of passengers, and different values of the infection parameters were designed for flights and airports, respectively. The influences of small-world properties of an air transportation network on the pandemic evolution are also investigated. Furthermore, this study not only predicts the patterns of the influenza pandemic under various situations, but also proposes several control measures to mitigate the pandemic and further evaluates the effectiveness of performing these measures.

(3) This study uses a dynamic approach to investigate the first-purchase behavior of potential passengers, which allows passengers to change their perceptions of LCCs over time as they learn more information about LCCs from WOM communication in the diffusion process. The WOM information is transmitted through interpersonal channels where the strength of social ties with other people is different across all population and is affected by the connections of a small-world network with dynamic structural properties. This study develops an intensity model of WOM information to determine whether or not a passenger adopts LCCs based on the receipt of updated WOM information and his/her own perceived utility. In contrast to past studies, social heterogeneity with respect to the size of company that passengers work for, the level of connectivity with other people, the tie strength between persons and the adoption timing of LCCs are together incorporated into our model. In addition, this study investigates

(24)

how the dynamic properties of the small-world network resulting from its partially random structure affects the temporal pattern of adoption of LCCs.

(4) This study develops an epidemic-like model, which can be interpreted as the propagation of delay across flights and airports in a small-world network. In the model, two kinds of state transition occur. One is when a flight or an airport is delayed due to severe weather, and the other is when the delay of the flight or airport is eliminated or the flight is cancelled due to its delay over the maximum allowed delay. This study applies the concept of shortcuts of a small-world network to investigate the characteristics of various flights, and further analyzes the influence of flights with shortcut functions on the propagation pattern of delay. The influences that the duration of delay, the inter-regional long-haul flights and the level of connectivity of airports have on the propagation are also investigated. Furthermore, this study proposes several allocation strategies of the limited airport capacity to flights, and then evaluates their effectiveness in terms of the total cost.

1.3 Research scope

This dissertation aims at exploring a series of important issues with respect to the positive and negative influences of small-world properties on the field of air transportation. The networks investigated in this dissertation include a transportation network comprising scheduled passenger-flights and airports located at different regions, and a social network consisting of passengers who have various personal characteristics and social neighbors. The research scope of each part of this dissertation is different from each other, and is described as follows. The research scope of the first part of this dissertation is on an airport network constructed by the allied airlines of an international alliance, in which this dissertation will show this network is a small-world network. Based on the small-world

(25)

network of the first part mentioned above, the research scope of the second part is further extended to the influenza transmission on the scheduled passenger-flights and the airports within the network, and that of the fourth part is to the delay propagation along with ground-holding policies. However, the research scope of the third part is on the choice behavior of short-haul business passengers between FSCs and LCCs, in which passengers form a small-world social network and the WOM information is passed through interpersonal relationships. The study objects of this dissertation are the international airlines (FSCs and LCCs) and airline alliances, airports worldwide, and passengers who have social relationships with other people. Furthermore, this dissertation investigates the airline choices of passengers in an aviation market that is previously dominated by FSCs and now has a new entrant, LCCs. The interrelations among the study objects are also incorporated in this dissertation.

1.4 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

(26)

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

(27)

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

(28)

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.

(29)

(30)

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

(31)

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

(32)

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.

(33)

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.

(34)

(35)

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

(36)

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 kv (kv -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

(37)

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).

(38)

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.

(39)

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

(40)

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. εij =1dij. When there was

no path in the graph between nodes i and j, dij =+∞ and, consistently, εij =0. The global

efficiency of a generic weighted (and possibly even nonconnected) graph G , is formulated as ( )=

∑

1 ( ( −1)) ∈ ≠ N N G G j i ij glob d

E , where N is the total number of nodes in G . The

local efficiency of G is formulated as

∑ ∑

∈ ≠ ∈ ⎟⎟⎠ ⎞ ⎜⎜ ⎝ ⎛ − = G G N G i i i m l lm loc V V d E i )) 1 ( ( 1 1 ) ( , where i

V is the number of nodes that connect to node i, and G is the subgraph of node i. Latora _i

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.

(41)

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 number of non-stop connections to a given city, and the betweenness centrality, defined as the number of shortest paths going through a given city. They found that the degree and betweenness centrality of the airport network both distributed as those patterns with truncated power-law decay. A surprising finding is that the most connected cities that have the largest degree are typically not the most central cities that have the largest betweenness centrality. It led the authors to propose a model that can explain this finding in terms of the geo-political constraints. They also showed that the world-wide airport network is a small-world network. Jiang and Claramunt (2004) carried out a topological analysis of large urban street networks, and wanted to examine which streets are important for a city in terms of connectivity and how each given street intersects with every other. Therefore, they focused on a ‘named-streets’-oriented view for topological analysis. ‘Named streets’ represented a functional modeling element of large urban street networks whose structure should be retained by a structural analysis. For evaluating the degree to which streets are interconnected versus segregated in a given city, they designed a graph at a modeling level, in which the nodes denoted those named streets and edges denoted connections between those named streets (note that in such a view a node denoted not a street segment but an entire named street). Without loss of generality, a named street that was separated into two

(42)

or more parts (for example, South Queen Street and North Queen Street) was semantically aggregated. One of the objectives in the study of Jiang and Claramunt (2004) was to explore such an alternative graph model. This named-street-centred network model was denoted as a topological network model. The urban street networks of three cities (Gävle, Munich and San Francisco) located at different countries were used, and the result showed that these networks are small-world networks.

There are several studies applying the small-world network to explore the spread of diseases or rumors. Kuperman and Abramson (2001) proposed a model to analyze the spread of an infection at different population structures. The interactions between the elements of the population were described by a small-world network, ranging from ordered lattices to random graphs. The links represented the contact between subjects, and infection can proceed only through them. The result showed a transition at a finite value of a disorder parameter in a small-world network. The epidemic behavior changed from an irregular and low-amplitude evolution at a small value of the parameter to a spontaneous state of wide amplitude oscillations at a large value of the parameter. Zanette (2001) developed an epidemiclike model to interpret the propagation of a rumor. The result exhibited critical behavior at a finite randomness of the underlying small-world network. That is, the transition occurred between a regime where the rumor dies within a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the entire population. The influence of the network connectivity on the critical randomness was also discussed, showing that the critical randomness decreases as the connectivity grows, and that the dependence of the critical randomness on the connectivity is distributed as a pattern with power-law decay.

(43)

Zanette and Kuperman (2002) investigated the propagation of epidemics on a small-world network under the action of immunization, and focused on the combined effect of the structure of the small-world network and the immunization process. They showed that the infection level decreases monotonically as the fraction of vaccinated individuals grows, and that the threshold for the propagation of the disease grows with the fraction of vaccinated individuals. Furthermore, the targeted immunization, where the individuals chosen to be vaccinated are those with the highest number of social connections, produced a substantial improvement in disease control. Saramäki and Kaski (2005) proposed a model for the spread of randomly contagious diseases such as influenza. The model was based on a stochastic susceptible-infected-removed mechanism on small-world networks, where randomly occurring long-range links were introduced in order to take into account the inherent randomness of spreading. The equations for the epidemic threshold and spreading dynamics were derived, and were used to examine how the epidemic saturation time, defined as the time when 95% of the susceptible population has become infected, scales with the system size and initial conditions. The comparison of the numerical result from the model with real-world data showed a good agreement.

Small and Tse (2005) developed a four-state model for disease transmission, in which the community was modeled as a small-world network of interconnected nodes, and transmission could only propagate between linked nodes. They used the model to exhibit two typical features of an epidemic, geographically localized outbreaks and super-spreaders, and showed that super-spreaders may occur even if the infectiousness of all infected individuals is constant. The result also showed that large-scale transmission occurs when a large number of clusters are exhibited, and indicated that quarantine, travel restrictions and closure of schools and work places are all effective control strategies for the epidemic.

(44)

Table 2.2 summarizes main issues and features as well as important results in the existing literature on small-world networks.

(45)

Table 2.2 Main issues, features and results on small-world related literature Authors Main issues and features Important results Watts and Strogatz

(1998)

First propose the small-world theory

Clustering coefficient and characteristic path length can measure the distinctive properties of small-world networks Kuperman and

Abramson (2001)

Propose a model to analyze the spread of an infection at different structures

A transition at a finite value of a disorder parameter is shown in a small-world network

Latora and Marchiori (2001, 2002)

Propose the global and local efficiency models

The proposed models can drop all restrictions of previous models, and an extended transportation system embracing the MBTA is a small-world network, with both high global and high local efficiency

Zanette (2001) Develop an epidemiclike model to interpret the propagation of a rumor

The transition occurs between a regime where the rumor dies within a small neighborhood of its origin, and a regime where it spreads over a finite fraction of the entire population.

Zanette and Kuperman (2002)

Investigate the propagation of epidemics on a small-world network under the action of immunization

The infection level decreases monotonically as the fraction of vaccinated individuals grows, and the targeted immunization produces a substantial improvement in disease control

Sen et al. (2003) Investigate the structural properties of the Indian railroad network (IRN)

The IRN behaves like a small-world network and is typical of the railroad network of any other country

(46)

Table 2.2 (continued)

Authors Main issues and features Important results Guimerà and

Amaral (2004)

Use the degree and betweenness centrality to investigate the world-wide airport network

The world-wide airport network is a small-world network, and the most connected cities are typically not the most central cities

Jiang and

Claramunt (2004)

Carry out a topological analysis of large urban street networks

The urban street networks of three cities located at different countries are small-world networks

Saramäki and Kaski (2005)

Propose a model for the spread of randomly contagious diseases

The numerical results of the proposed models match the real-world data well

Small and Tse (2005)

Develop a four-state model for disease transmission in a small-world network

Super-spreaders may occur even if the infectiousness of all infected individuals is constant, and that large-scale transmission occurs when a large number of clusters are exhibited