DATA AND METHODS

In order to calculate accessibility changes associated with the development of HSR

networks in France in the 1982–1990, 1990–1999, and 1999–2009 time periods, 107 city

agglomerations with populations over 10,000 inhabits and served by HSR networks were

chosen as centers of economic activity. The population data for these agglomerations were

obtained from French National Institute of Statistics and Economic Studies (INSEE) census

data at the city (called commune in French) level.

Meanwhile, real scheduled travel time by HSR is considered an impedance factor

in calculating accessibility indicators. Travel time from these 107 agglomerations to/from

Paris, and the travel times between each agglomeration were individually calculated by

Thomas Cook Rail Timetables in 1982, 1990, 1999, and 2009. The calculation of train time

from a comprehensive and complex train timetable is intricate. To enable calculations and

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 Train times are based on timetables for the month of April for each year in

order to avoid the peak summer season and the winter off-season, and are averaged

according to daily time schedules to/from Paris and other cities.

 Average train time includes regular SNCF (French National Railway

Company) conventional train services (including rapid, express train, and inter-

city regional trains) and HSR service. However, in the present study, only direct

trains from one agglomeration to another, including both domestic and

international trains, are considered.

 Some cities have more than one train station. When assessing train

frequency, all stations in the same city were counted together if the same train

stopped at both stations. Otherwise, they were considered separately.

 When assessing daily rail service, only trains that run at least four days per

week were considered; trains that operate only on weekends were excluded.

 Trains that are scheduled temporarily, such as only for short periods during

the year or only on certain holidays, were also excluded.

In this study, average train times for both conventional rail services and HSR

service were considered, rather than the shortest travel time only from the latter service for

two reasons. First, using average train times more closely reflects reality, thereby providing

greater accuracy in establishing an accessibility index. Typically, HSR services provide the

shortest travel times between cities, but it doesn’t mean that the introduction of HSR service could replace all types of train service and immediately promote the overall

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rail service. Calculating average train time provides an opportunity to account for total train

frequencies to/from Paris. For example, Cannes has only five trains to/from Paris, with an

average travel time of 573 minutes. Among these five train frequencies, only one of them

is a TGV service with the shortest travel time of 390 minutes. It cuts the train time from

618 minutes to 573 minutes, which is almost the same as the average scheduled train time

in 1982. Thus, HSR service provide an option for traveler to save travel time, but whether

HSR service can generally reshape the time space linkage to/from Paris that depends on

the quality of HSR service.

In this chapter, the study focuses on evolution of two accessibility patterns: 1)

accessibility of 107 agglomerations to/from Paris, 2) accessibility pattern among 107

agglomerations.

To measure the accessibility of each agglomeration to/from Paris, this study

adopted a modified economic potential model in which travel time is main indicators.

However, the attractiveness of Paris to other cities is constant. Thus, this study set 𝑀_𝑗 in

equation 1 as 1. The indicator can be expressed as follows.

𝐴𝑖 = ∑

1 𝑇_𝑖𝑗𝑐 𝑛

𝑗=1

Similarly, where 𝐴_𝑖 is the economic potential of place i, 𝑇_𝑖𝑗is the transport cost

between place i and place j, c is a distance-decay parameter, assumed to equal 1.

In order to add frequencies as another impedance factor, a method from Bruinsma

and Rietveld (1995) are adopted here. This study mentions that the total travel T is consist

of three basic elements:

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Where V is penalty because one can not depart at the desired moment in rail service.

RT is real travel time, and I is time for checking in and checking out. However, the

checking in and checking out doesn’t fit rail service. This study assumes I as 0. The penalty V is estimated as follows.

V = 4E/F

Where E is the effective travel period. In this study, the effective travel period

covers 24 hours a day. Thus, E is equal to 24 hours in this study. F indicates the train

frequencies of that effective travel period.

To combine these equations together, the accessibility indicator can be calculated

by using the following expression;

Equation 2: Accessibility to/from Paris

, 1 1 E 4 i j i i j ij ij A T _tt F    





To calculate accessibility pattern on the national level, this study conduct a

107*107 time matrix among each agglomerations in the year of 1982, 1990, 1999 and 2009.

The standard economic potential model are used in this part, shown as follows.

Equation 3: Accessibility among 107 agglomerations

𝐴_𝑖 = ∑𝑀𝑗

𝑇_𝑖𝑗𝛼 𝑛

𝑗=1

Where 𝐴𝑖 is the economic potential of place i, 𝑀𝑗 is represented by the size of

population of place j, 𝑇_𝑖𝑗 is the rail travel time between place i and place j, 𝛼 is a distance-

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To display the evolution of accessibility pattern over time, this study use

Geographical Information System (GIS) to visualize the spatial and temporal pattern of

accessibility. In the recent existing studies, three approaches are used. One is using a time-

space map to visualize the impact of transport infrastructure on spatial structure (e.g.,

Vickerman, Spiekermann, & Wegener, 1999). The basic elements of this approach is using

travel time instead of physical distance to proportion their relative geographical location.

In other words, agglomeration centers are separated by travel time. The short travel time

between two agglomerations results in their presentation close together on the map. It is

straightforward to indicate that areas where rail service is performing well and other areas

where it is inefficient. However, this method is good at displaying the changes at the

boarder scale of view. The detailed of changes, especially changes in small agglomeration

may be fade out in this type of approach.

The second type of approach is to spread accessibility based from limited accessible

rail stations to the whole region (e.g., Gutiérrez & Urbano, 1996). This method interpolates

the isoaccessibility regions from accessible regions. However, given the context of France,

the whole region is not flat. If using this method, it may mislead and deviate enormously

from reality.

The last approach is building nodal accessibility (e.g., Bruinsma & Rietveld, 1998).

The size of points is proportional to their accessibility of that economic node. This study

is going to adopt this method. It is not only keeping this study rigorous, but also clearly

and directly ahead to appear the changes of accessibility for each agglomeration that

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