close

Вход

Забыли?

вход по аккаунту

?

phys-2017-0017

код для вставкиСкачать
Open Phys. 2017; 15:160–174
Research Article
Open Access
Carmen Mota, Miguel A. López, and Arturo Martínez-Rodrigo*
A Mathematical Study of Accessibility and
Cohesion Degree in a High-Speed Rail Station
Connected to an Urban Bus Transport Network
DOI 10.1515/phys-2017-0017
Received Dec 27, 2016; accepted Feb 01, 2017
Abstract: In the last twenty years, the implementation of
High-Speed Rail (HSR) has been one of the major strategies for territorial structuring used by various countries.
This model has enhanced the development of countries
such as France, Spain, Germany and Japan. At present,
the United States and China are also starting to implement
this model. Nevertheless, the lack of social and economic
profitability of several networks is being increasingly analysed. Many networks located in particular regions serve
populations that are not large enough to recover the initial investment. For this reason, it is necessary to evaluate the population served by this transport mode, beyond
the number of users. In this sense, it is essential to identify the deficiencies and potentials of implementing a network linked to other secondary networks in a specific territory which can compensate for the so-called tunnel effect.
This article proposes to apply a mathematical approach
based on graph theory to measure the Degree Accessibility Node (DAN) in a constrained Geographic Information
System (GIS) model. Hence, it would be possible to compare regions, especially medium-sized cities, where the
implementation of HSR could represent a qualitative leap
due to incorporation into large transport networks. The
DAN function uses static and dynamic studies to evaluate
the level of connection of stations to secondary transport
networks—local public transport in this case. Thus, the impact of high-speed trains could be spread to greater territorial and population ranges. Four cases have been studied, two in Germany (one of them, Fulda, is analysed in
depth throughout this article) and two in Spain. These two
*Corresponding Author: Arturo Martínez-Rodrigo: Escuela
Politécnica de Cuenca, Universidad de Castilla-La Mancha, Cuenca,
Spain; Email: [email protected]
Carmen Mota: Escuela Politécnica de Cuenca, Universidad de
Castilla-La Mancha, Cuenca, Spain; Email: [email protected]
Miguel A. López: Escuela Politécnica de Cuenca, Universidad de
Castilla-La Mancha, Cuenca, Spain; Email: [email protected]
countries were selected since HSR was implemented in the
same relative period of time, in comparison with other European countries. Results show relevant differences, suggesting a review of inappropriate policies of transport integration in a city that could weaken the expansion of the
positive effects of HSR integration.
Keywords: High-speed rail; dynamic indexes; accessibility; centrality; graph theory
PACS: 89.75
1 Introduction
Nowadays, the expansion of High-Speed Rail (HSR) networks together with interconnected stops is raising the
challenge of integrating the high-speed railway stations
within urban dynamics [1]. The newly refurbished or built
stations that are to host HSR are conceived as an instrument to decrease travel times dramatically. Consequently,
HSR creates great expectations in terms of socio-economic
and territorial revitalisation [2]. This fact leads to certain
changes in the city, which are enhanced by public administrations in the framework of the pursuit of urban renewal [2].
The present study aims to analyse and compare the
accessibility levels of different stations through static and
dynamic mathematical procedures. It is worth noting that
these methodologies have been traditionally applied in
other fields such as road networks [3, 4]. The different local mobility policies analysed in the different cases are derived from the study of railway stations integration at a
local level, depending on their location within the public transport network. In this sense, the problems that are
normally related to the practical integration of the node
do not only show the importance of planning and implementing strategies, but also the necessity of joining urban
development and the appropriate implementation of this
infrastructure.
© 2017 C. Mota et al., published by De Gruyter Open.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree |
Moreover, the connection of stations with other secondary networks contributes to spreading the positive
effects of HSR to a greater population and territorial
range [5]. Consequently, situations where the station is located in a place lacking possible connections, omitting
the need to link the station to other secondary networks,
contribute to increasing the unfavorable effects of a transport mode that crosses large distances without stopping
in the aforementioned places [6]. For this reason, it is
necessary to study and analyse the HSR station together
with the different secondary networks in terms of cohesion and accessibility of the different nodes within the network. In this work, the mathematical approach is to compute the Degree Accessibility Node (DAN) for the study of
four European networks belonging to the same time period
and whose history is long enough to be studied. The DAN
function evaluates the accessibility of high-speed railway
stations through two different methodologies: on the one
hand, a static study to obtain the indexes describing the
node’s level of cohesion compared to the rest of the network, and on the other hand, a dynamic study that measures the connection of the stop evaluated compared to
other stops of the transport network, an urban bus transport network in this case.
Finally, it is worth noting that the networks under
study have to be comparable in order to provide conclusions about the development of the cities. Thus, different features were considered when the cities of Ulm-Neu
Ulm (conurbation) and Fulda in Germany and Lleida and
Toledo in Spain where selected among a wide range of possibilities. They are all medium-sized cities with comparable populations that range between 50 000 and 200 000
inhabitants, with the train station located in the inner city.
In these networks, the implications of HSR are more objective since they are not affected by the impact of other
transport modes such as air transport, and the implementation of HSR has a dramatic impact on their accessibility level globally [7]. Furthermore, the cities share structural similarities, where HSR has been implemented for
more than twenty years and HSR was commissioned at a
similar time—1991 in Germany and 1992 in Spain. Indeed,
these factors are necessary in order for transport system
dissimilarities to become observable. Moreover, these networks have a historical urban planning tradition administratively implemented in the fields of physical and spatial
planning, conceived as a link between economic and social planning. In the cases under study, the countries have
over a century of experience in urban planning, which is a
mandatory requirement for the comparison, according to
the European administration. This fact automatically rejects the possibility of considering other European coun-
161
tries such as Portugal or Italy within the analysis. Finally,
Germany and Spain share similarities in terms of territorial organisation into states—16 federal states in the case
of Germany, 17 autonomous communities in the case of
Spain. This also enables comparison between the different
administrative frameworks which make decisions about
city development.
1.1 The integration of high-speed rail in
Europe: a unique objective in a mixed
picture
The implantation of HSR in Europe was considered as an
attempt to promote railway as a transport system and articulate the territories of the European Union (EU). The initial idea was to offer a competitive alternative to air travel.
Instead of that, it has become a new concept that emphasises the improvement of connectivity between territories
and cities. That continental network may contribute to the
territorial structuring process necessary to achieve a more
uniform and cohesive EU territory [8].
The main benefits of HSR are related to its high speed,
large capacity for passengers, punctuality, security, high
efficiency and comfort. For these reasons, HSR plays a key
role in the transport system between different European regions. One of the most direct effects of its implementation
is the improvement of accessibility [9, 10]. HSR represents
a key element of territorial structuring, enabling the development of new relationships between remote countries,
considerably shortening the distance between them [11]. It
promotes mobility and interaction in economic and social
aspects [12]. In this sense, different studies have reported
variations of accessibility after the implementation of HSR
at the European level [13–15].
Nevertheless, an evaluation prior to the multiannual renewal of the programme established in the TransEuropean Transport Network for the period between 20072013 was used to elaborate the report requested by the European Commission. This report emphasised the necessity
of continuing with the cohesion plan, establishing a costbenefit ratio of A
C1.6 for each euro invested. It also warned
that deficiencies in the execution of projects would imply
a loss of efficiency in terms of execution and financing. In
addition to the budgetary constraints, there are two big
areas where the evaluation identified deficiencies in the
preparation and implementation of the project. These deficiencies are along two critical lines:
Unauthenticated
Download Date | 10/27/17 9:11 PM
162 | C. Mota et al.
– The immaturity of the projects, lacking technical details, attention to the environment, public consultation and appropriate risk assessment.
– The poor technical-administrative coordination and
the lack of experience of the beneficiaries with requirements established in EU-funded programmes.
1.2 Evaluating accessibility by modelling
the real object: the local public
transport network
The implementation of HSR and the investment made in
Europe throughout the last twenty years have made it possible to link a large number of cities [6]. HSR’s competitiveness is based on the transport marketplace, service
quality and access time to the main centres of activity [16].
Nevertheless, due to the features of the mode (it needs to
travel long distances to reach the required speed [17]), if
the access node to the territory—the station—is not duly
linked to other secondary networks, its benefits will exclusively reach the surroundings thereof, exacerbating the effects commonly known as the tunnel effect [18] which consists of communicating those cores served by HSR only
while it creates serious imbalances in those locations that
are crossed but not served by it. This argument makes it
necessary to evaluate the level of connection of stations
with other secondary transport networks. In this case, the
DAN function makes it possible to evaluate the accessibility level of the station’s node by applying it to the local
public bus network, because only a smooth and efficient
connection to the city and any potential cores lends continuity to the positive effects of a transport mode based on
travel speed. Otherwise, the time saved thanks to the high
speed reached between those cities served by HSR is diluted when adding the time necessary to gain access to the
end of the route. In this case, the mode’s potential users
will no longer think the generally higher cost of HSR compared to other transport modes is justified, thus making
HSR less competitive.
On the other hand, in those countries with lower population density, the development of these secondary networks is even more necessary since they are essential to
serve a greater population range and to make network
implementation and maintenance costs sustainable. Finally, guaranteeing accessibility through public transport
is increasingly important due to the fluctuating price of
fuel [19] and due to congestion problems [20]. To evaluate accessibility, we usually find studies that are developed from the field of transport, economy or social policy planning [21]. Many of them introduce the accessibil-
ity conferred to the territory depending on the connection offered by public transport networks: in this sense, we
would like to emphasise how Burns and Inglis [22] evaluate
access cost to commercial areas depending on the transport means chosen; Yigitcanlar et al. [23] suggest a LUPTAI model (Land Use & Public Transport Accessibility Index), comparing access to different points depending on
whether the route is on foot or by bus, and Silva [24] develops the SAL system (Structural Accessibility Layer) which
measures the population affected by accessibility using
private, public and non-motorised transport.
The DAN function implies the evaluation of accessibility of a station node in comparison with the local public transport network through modelling of the real object on the basis of graph theory. By using a method that
has already been used by other network scholars such as
Garrison [3], each point can perfectly represent a city, a
station, a stop or a computer belonging to a network (or
any set linked to objects), and the lines that connect them
can represent roads, railways or wires (namely, the physical element that links said objects). A graph with these
features, integrated by nodes and lines, enable the modelling of a reality that can be a network of roads, of transport made up of different lines, the Internet or industrial
processes. Based on the foregoing, Kansky [25] was able
to study transport networks by abstracting them through
mathematical graph theory [26].
In our case, the graph is made up of trajectories that
link any pair of nodes linked by any local transport network, evaluating two perspectives: the static one, applied
by authors such as Seguí [27] to motorised road transport
to compare the cohesion level of the different nodes (populations in his case), and the dynamic one, to study the
accessibility of the different modes more specifically. Nevertheless, despite the fact that the latter has traditionally
been applied to the study of private road transport combined with the static perspective, its prior application to a
public transport network, as detailed below, has not been
found.
We next outline the evaluation process of these parameters in more details through application to one of the
four cases: Fulda, and deal with the results obtained in
Ulm-Neu Ulm, Toledo and Lleida subsequently. We close
with the required comparative valuation under final reflection in the form of conclusions, possible approaches in the
future and improvement of the situation under study.
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree |
2 Methodology
To find out the accessibility and cohesion degree in a transport network, it is crucial to calculate some features that
provide an objective point of view about the existing level
of interconnectivity and accessibility among the different
bus stops. To achieve this objective, the study of corresponding cartography together with the application of different georeferencing techniques, is essential in order to
build up the network model. Furthermore, it is necessary
to map the network into a set of vertexes and edges which
represent the connectivity and distance between the different bus stops within the model. It is important to remark that in this study, the network is analysed from two
different points of view: static and dynamic. On the one
hand, the numbers of vertexes and edges are computed in
the static study to quantify the cohesion degree in the network. On the other hand, graph theory is used to quantify
other aspects like connectivity and costs among different
nodes in the dynamic study. In the subsequent sections
both methodologies are described.
2.1 Static network study
Firstly, the generated graph was studied from a static point
of view. This allowed us to analyze the direct communication between the whole set of points of interest without taking into consideration the distances between the
diverse vertexes. This perspective reports the cohesion degree within the model where the connectivity between vertexes grows as the number of direct interconnections increases, i.e., the more direct connections between vertexes
in the model, the higher the cohesion degree. Therefore,
considering the graph under study where υ and ϵ correspond to the number of vertexes and the total number of
edges respectively, the maximum connection degree was
computed as shown in Eq. (1).
υ(υ − 1)
Cd =
2
(1)
Furthermore, the relationship between the number
of possible edges within the graph and the real number
of observed edges, i.e., cohesion degree, was calculated
through Prihar’s index (P), which is defined as shown
in Eq. (2). It is interesting to remark that P ranges from
unity (when the cohesion degree is maximal) to υ/2 (corresponding to the minimum cohesion degree).
P=
υ(υ − 1)
2ϵ
(2)
163
Moreover, the cyclomatic number (µ) which represents the number of circuits within the network was computed as shown in Eq. (3). In this regard, the higher the
µ, the higher the cohesion level, with its minimum value
equal to zero and the maximum equal to (υ − 1)(υ − 2)/2.
µ = ϵ − (υ − 1)
(3)
In addition, the corrected cyclomatic numbers (Kansky’s indexes) were also computed. First, Kansky’s α index
was calculated by computing the relationship between the
number of existing circuits and the maximum possible circuits within the graph. This index is expressed mathematically as shown in Eq. (4).
α=
2µ
(υ − 1)(υ − 2)
(4)
Second, Kansky’s β index is defined as the rate between the number of edges and the number of vertexes,
such that the higher the number of edges, the higher the
connectivity among vertexes. The possible values for this
index range from zero to infinity based on the assumption of the number of connections between vertexes increasing faster than the number of vertexes when a network changes its structure and becomes more cohesive. Its
mathematical expression and maximum value for a given
number of vertexes can be observed in Eq. (5) and Eq. (6)
respectively.
ϵ
(5)
β=
υ
υ−1
(6)
2
Third, Kansky’s  index formulates the relationship
between the maximum number of edges in the graph and
the existing ones. This index ranges from zero to unity,
such that  increases when the model cohesion grows. It is
also frequently expressed as a percentage. This index can
be mathematically defined as shown in Eq. (7).
max(β) =
=
2ϵ
υ(υ − 1)
(7)
Finally, the Zagozdzon (Gp ) index was computed,
which indicates the existing development degree in the
graph by reporting the missing number of edges per vertex
needed to fill the graph completely. Its formula is shown in
Eq. (8).
υ2 − υ
−ϵ
2
Gp =
(8)
υ
2.2 Dynamic network study
The other major aspect of this work lies in the analysis of
the graph from a dynamic point of view. In this regard, this
Unauthenticated
Download Date | 10/27/17 9:11 PM
164 | C. Mota et al.
methodology allows enhancement of estimations regarding the accessibility and cohesion of the different vertexes
in the graph (in relation to the static study). The main reason for this lies in the fact that dynamic study of the graph
considers not only the number of vertexes and edges (υ,
ϵ), but also the cost value for each direct connection between the vertex or node i and vertex or node j within the
graph. Considering that accessibility is defined as the facility of access from any point within the network to another,
it seems appropriate to use the distance (d), measureed in
meters, to quantify the cost between two connected vertexes. Thus, the cost matrix for each connected vertex on
the graph was calculated as shown in Eq. (9).
⎧
⎪
⎪
⎨d(i, j) if (i, j)], are linked
C(i, j) =
0
⎪
⎪
⎩∞
if
i=j
if
(i, j) are not linked
(9)
Moreover, the assessment of whole dynamic markers
are based on computing the shortest path of the vertexes
in the graph, i.e., finding a path between two nodes in a
graph such that the sum of the costs of the edges forming
the path is minimized. To resolve the shortest path problem, there exist different algorithms (Dijkstra, BellmanFord, A*, Floyd-Warshall, etc.) which provide the minimum cost matrix defined by Θ ∈ ℜ υ×υ , where each number defined in the matrix by the pair of indexes (i, j) contains the shortest path between the node origin i and the
node destiny j.
Given the network proportions regarding the number
of vertexes involved, the Floyd-Warshall algorithm was
considered optimal to calculate Θ because of its simplicity and easy programming. This algorithm uses the matrix
C computed previously as its input argument and also uses
it to initialize the output matrix Θ such that Θ = C. Next,
in each interaction, the matrix Θ is recalculated so it contains costs of paths among all pairs of nodes (i, j), using
progressively enlarging sets of intermediate nodes defined
by the variable k. Thus, the matrix Θ is rewritten in the
first iteration, containing cost values among all the pairs
of nodes, using exactly only one intermediate predefined
node (k = 1). In the second iteration, the matrix Θ is redefined again with the resulting costs using two predefined
intermediate nodes (k = 2). Finally, the algorithm finishes when the number of intermediate predefined nodes
is equal to the total number of vertexes in the graph (k = υ).
This procedure can be summarized though the recursive
equation shown in Eq. (10).
k−1
k−1
Θki,j := min(Θk−1
i,j , Θ i,k + Θ k,j )
(10)
Once the matrix Θ is computed, several dynamic features found in the literature can be used to estimate the
accessibility and cohesion level in the network. In this regard, the graph’s diameter corresponds to the longest distance from one vertex to another anywhere in the shortest
path matrix. Moreover, the Shimbel index (Ψ), or the index
of actual accessibility, is defined as the summation of costs
between each vertex and the rest of the vertexes within
the shortest path matrix, and can be expressed mathematically as shown in Eq. (11). This index is useful for finding
out the core node in the network such that the lowest Ψ
values correspond with the most accessible vertexes and
the highest Ψ values correspond with the least accessible
nodes.
υ
∑︁
Ψi =
Θ i,j , i = 1, ..., υ
(11)
j=1
Given that the Ψ calculation depends on the number
of vertexes υ in the network, comparison with other networks is hardly possible. Consequently, the Shimbel index
is usually normalized for the number of nodes in the network, resulting in the relative accessibility index defined
mathematically as shown in Eq. (12). It is important to remark that the relative accessibility closest to zero corresponds to the core node.
Ωi =
Ψ i − min(Ψ)
× 100
max(Ψ) − min(Ψ)
(12)
Finally, to detect nodes with a low and high accessibility, mean and standard deviation are usually applied to
these indexes, such that indexes below the mean minus
once or twice the standard deviation have a high accessibility and those above the mean plus once or twice the
standard deviation are considered as poorly accessible.
In order to calculate both static and dynamic indexes,
mathematical software (Matlab) was used for programming the DAN function. Given the dimension of the transport networks (249 rows and 249 columns), automation of
this process is required. A fragment of the DAN function is
shown in Listing 1.
Listing 1: A fragment of DAN function programmed with Matlab
%G l o b a l v a r i a b l e s ;
C = Cost_Matrix ( ) ;
max1 = 0 ;
maxn = 0 ;
node1 = 0 ;
node2 = 0 ;
noden1 = 0 ;
t a b l e _ a c c e s k m = zeros ( length ( C ) , 6 ) ;
f o r i = 1 : length ( C )
f o r j = 1 : length ( C )
i f C ( i , j ) == i n f
C ( i , j ) = 0; % f i l t e r i n g
Unauthenticated
Download Date | 10/27/17 9:11 PM
...
A Mathematical Study of Accessibility and Cohesion Degree |
end
% max d i a m e t e r i n t h e n e t w o r k
i f C ( i , j ) > max1
max1 = C ( i , j ) ;
nodo1 = i ;
nodo2 = j ;
end
% max d i a m e t e r f o r each node
i f C ( i , j ) > maxn
maxn = C ( i , j ) ;
end
end
%A c c e s s i b i l i t y i n d e x e s
table_acceskm ( i , 1 ) = i ;
% vertexes
t a b l e _ a c c e s k m ( i , 2 ) = sum( C ( i , : ) ) ;
% Shimbel index
t a b l e _ a c c e s k m ( i , 3 ) = maxn ;
% Diam eter
t a b l e _ a c c e s k m ( i , 4 ) = sum( C ( i , : ) ) /
N;
% Average l e n g t h
maxn=0;
nodon1 =0;
end
%
M
%
m
%
R e l a t i v e a c c e s s i b i l i t y ( Omega %100)
= max( tabla_a c c es k m ( : , 2 ) ) ;
max S h i m b e l i n d e x ;
= min ( tabla_a c c es k m ( : , 2 ) ) ;
min S h i m b e l i n d e x ;
f o r i = 1 : length ( C )
tabla_acce s k m ( i , 5 ) = . . .
( ( t a b l e _ a c c e s k m ( i , 2 ) − m) / . . .
(M − m) ) * 1 0 0 ;
end
.
.
.
3 Static and dynamic analysis of a
German city: Fulda
In order to apply the methodology described in Section 2
to different networks, cities under study have to be structurally analogous. This prerequisite makes possible extrapolation of the results and comparison between the dif-
165
ferent locations. In this regard, four singular cases of intervention in urban projects around European stations in
medium-size cities with no more than half a million population were chosen for this analysis. More concretely, Fulda
(Germany), Ulm-Neu Ulm (Germany), Lleida (Spain) and
Toledo (Spain) were included in the study, given that these
cities share structural similarities and adopted very different solutions in the integration of HSR within the urban
area. Given that the effects provoked by the integration
of HSR is more considerable in medium-sized locations,
some authors have reported the suitability of these cities
as urban impact indicators [28].
To analyze the cohesion and accessibility of the main
attractions through the urban transport network and its relationship with the HSR, it is necessary to carry out a cartographic representation of the local public transport network at an urban level with respect to the surroundings of
the HSR stations. This process was accomplished by using
a Geographic Information System (GIS), which allowed us
to build up the graph of Fulda, consisting of vertexes and
edges formed by the public transport network and its interconnectivity, respectively. Moreover, local agents were
interviewed to locate the city’s main attractions as can be
appreciated in Fig. 1. Thus, the objective is to embed points
corresponding to bus stops into the graph to perform a further study of accessibility and centrality regarding the HSR
station and the city’s main attractions, as well as the assessment of the relationship with elements of the mobility policy such as public car parks, taxi ranks or other stations. In the case under study, the HSR station is located
at city center and a complex bus stop network, taxi rank
and public car parks can be found within a 1-kilometer radius (see Fig. 2), thus reinforcing the hypothesis of their
relationship.
3.1 Generating the connection matrix
In the case of Fulda, the public transport network is composed exclusively of the public bus network, consisting
of nine urban bus lines and 312 bus stops which cover a
length of 88.67 km within an area of 60.01 km2 . Eight out
of nine bus lines have a bus stop at the HSR station. Only
bus line number 4 has no match with this station. Given
that many of the bus stops coincide, the total number of
vertexes considered in the graph was 249, such that two
coincident nodes were labeled with the same identification. Moreover, the number of total interconnections between them was 292. It is noteworthy that distances were
calculated as the minimum path in meters necessary to go
from i to j if they were directly connected, 0 in cases where
Unauthenticated
Download Date | 10/27/17 9:11 PM
166 | C. Mota et al.
13
10
11
12
1
4
2
Central
Station
3
15
5
7
6
8
14
9
Figure 1: Fulda’s city centre and main attractors: 1. Cathedral, 2. Old Market, 3. Town Hall, 4. Planetarium, 5. Trade Fair, 6. Shopping Center, 7. Johannisau Stadium, 8. Aueweiher Park, 9. Geisküppel Park, 10. Natural Reserve, 11. Fulda’s University, 12. Public Services, 13. Food
Factory, 14. Paper Factory, 15. Tyres Factory.
i = j and ∞ if the pair (i, j) was not directly connected,
as iexplained in Eq. (9). Thus, the graph corresponding
with Fulda’s valued public transport network was generated (see Fig. 3) and the connection matrix was computed.
In this regard, the connection matrix for up to the first 10
vertexes (bus stops) and their corresponding edges (direct
interconnections) are presented in Table 1. As can be observed, the matrix diagonal is always 0, since in these elements i = j. Moreover, in the case of the urban bus transport network, the distance from node i to nodej is not necessarily the same to go from j to i since they can use different routes or be unconnected, as can be observed in the
pair (i, j) = (2, 3) where d(2, 3) = 272.60 but d(3, 2) = ∞.
3.2 Static study of the Fulda’s network:
cohesion
Static indexes are useful to assess the cohesion degree of
different networks, as well as to track the network development degree through time. Therefore, static features defined in Section 2 were applied over the whole graph of
Fulda and results are shown in Table 2. The geographical
global area under study consists of 249 vertexes and 292
edges, which represents only 0.95% of the total number of
possible direct connections among the network, defined
by the maximum connection degree index (30876). Consequently, results obtained through Prihar’s index indicated
a low cohesion degree with a value of 105.74, the maximum
and minimum cohesion levels being 1 and 124.5 respectively. Similarly, the µ index reported a low number of pos-
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree |
167
P
P
P
P
P
P
P
P
P
P
CentralP
Station
P
P
P P
P
P
Tx
Tx
P
P
P
P
P
P P
P
Tx
Bus
Station
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
Figure 2: Elements of mobility policy in Fulda. P. Public car park; Tx. Taxi rank.
Table 1: Connection matrix.
i/j
1
2
3
4
5
6
7
8
9
10
1
0
162.10
∞
∞
∞
∞
∞
∞
∞
∞
2
162.10
0
∞
∞
∞
∞
∞
∞
∞
∞
3
∞
272.60
0
263.50
∞
∞
∞
∞
∞
∞
4
∞
∞
263.50
0
179.90
∞
∞
∞
∞
∞
5
∞
∞
∞
179.90
0
∞
∞
∞
∞
∞
6
∞
∞
∞
∞
392.70
0
∞
∞
∞
∞
7
∞
∞
∞
∞
∞
351.05
0
180.70
∞
∞
8
∞
∞
∞
∞
∞
∞
180.70
0
185.10
∞
9
∞
∞
∞
∞
∞
∞
∞
185.10
0
176.20
10
∞
∞
∞
∞
∞
∞
∞
∞
176.20
0
Unauthenticated
Download Date | 10/27/17 9:11 PM
168 | C. Mota et al.
Table 2: Static indexes applied to Fulda’s graph.
Index
Number of vertexes
Number of edges
Maximum connection degree
Prihar’s index / interval
µ index /interval
Kansky’s α index
Kansky’s β index / interval
Kansky’s  index / interval
G p index
Global
249
292
30876
Area1
25
35
300
Area2
25
27
300
105.74 / [1,124.5]
44 / [0, 30628]
0.14%
1.17 / [0, 124]
0.0095 / [0, 1]
122.83
8.57 / [1, 14.5]
11 / [0, 276]
3.98%
1.4 / [0, 14]
0.12 / [0, 1]
10.60
11.11 / [1, 14.5]
3 / [0, 276]
1.08%
1.08 / [0, 14]
0.09 / [0, 1]
10.92
sible circuits, which is indicative of a low cohesion degree
in the network. Moreover, the Kansky’s indexes reinforced
this result, showing the same trend. More concretely, Kansky’s α index reported a value of 0.14% of the maximum
possible cohesion level and Kansky’s β value indicated the
low complexity existing in the network, given that the obtained value for this parameter was 1.17, far away from its
maximum possible value. Similarly, Kansky’s  index indicated that only 0.95% of the possible edges were presented
in the graph. Finally, the graph’s development index (Gp)
reported that the number of edges left for each node to
achieve the maximum cohesion level was 123, which is a
significant number considering the nodes presented in the
network.
Although a low cohesion degree was observed considering the entire network, the study of the cohesion degree
from different areas within the network is more interesting from a city’s development point of view. Therefore, two
geographical areas corresponding with the surroundings
of the HSR station, and a peripheral industrial area were
assessed. To facilitate this comparison, each area was defined by a cluster formed from the nearest 25 nodes around
for each zone, as can be appreciated in Fig. 4. It is important to remark that the connection matrix was recalculated
for each area under study, and only direct paths among
the involved nodes were considered. Then, the number of
edges was taken into account and static markers were applied over both areas. The results of this comparison are
shown in Table 2, Columns 2 and 3. Thus, while the number of direct connections in Area 1 represents 11.67% of
its specific network, Area 2 reported only 9% of the possible direct connections within its specific network. Consequently, Prihar’s index showed better cohesion degree for
Area 1 than Area 2, achieving values of 8.57 against 11.11,
where 14.5 represents the worst possible cohesion. Similarly, the number of possible circuits within the graph was
higher in Area 1 than in Area 2. Regarding Kansky’s indexes, the three parameters showed the same trend, showing that Area 1 has better cohesion than Area 2. More concretely, Kansky’s α index showed that the number of completed circuits within Area 1 was more than three times
higher than in Area 2. Also, Kansky’s β index reported a
better relationship between number of edges and vertexes
in Area 1 than Area 2. Futhermore, regarding the existing and maximum number of edges in the network, Area
1 presented much better cohesion, achieving 12% while
Area 2 presented a 9% cohesion. Finally, the graph’s development index (Gp) reported that Area 1 needs a slightly
lesser number of edges than Area 2 in order to complete
the graph.
3.3 Dynamic study of the Fulda network:
accessibility and centrality
To carry out the dynamic study regarding Fulda’s graph,
the Floyd algorithm was applied over the connection matrix and the first ten nodes are shown in Table 3. Observing the results, it is noteworthy that all the nodes
are connected between them, i.e., it is possible to reach
any node from any other within the network. Afterwards,
the Shimbel index (Ψ) and the normalized Shimbel index
(Ω) were computed, together with the network diameter
and average length. The results for the most interesting
nodes, given their location and accessibility, can be observed in Table 4. Thus, the highest accessibility was for
node 92, which corresponds to the historic quarter surroundings near the Council area. In contrast, the less accessible nodes can be found outside the urban core, next
to the industrial zone. Regarding the HSR station, it is the
fourth most accessible node, with Ω equal to 1.89, thus
achieving a high accessibility degree as shown in Table 4.
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree |
13
13
91
7
8,
8
8,
8
8,
81
91
71
3
8,
12
8
9,
91
2
1,
02
9
8,
91
7
8,
1
2,
61
13
5,
9
46
8
9,
9,
6
47
74
2,
1
8
8,
71
12
7,
7
6
8,
2
7,
34
2
8,
03
351,05
298,7
,1731
5, 6
5
8,
94
5
8,
67
67
8
0,
765,9
,6052
765,6
7,12
3
51
27
2
2,
8,
9
8,
248,9
232,6
17
24
251,6
5
9,
9
432,8
318,8
8,
2,
18
2
26
3,
15
2
9
3,
5 3
3, 2
220,1 9
2 1 8.
6, 2 17
173,2
21
8
5,
24
5,
7
2
19
6,
16
2
413,8
232,9 221,5 247,8
7,
2
392,7
,9252
607,3
1,4
75
272,6
5
4
1,
162,1
9
1
2,
8,
24
19
231,8
213,8
1
358,61
25
265,1
3
4,
278,7
25
243,8
7
4,
246,8 287,8
298,7 198,7 199.8
21
212,8
2
3,
405,9
3
5,
56
5
8,
2
3,
13
2
9,
68
5
7,
3
2,
41
42
203,5
289,7
4,
3
14
34
4
8,
2
8,
52
4
8,
5
9,
13
11
62
212,4
26
02
7,
5
265,9
232,7
141,2
198,8
231,7
201,8
11
8
9,
6
9,
67
71
6
9,
71
9,
7
5
312,3
12
315,8
4
209,8
4,
7
4,
7
201,2 187,8
7,
9
209,7
3
2,
5
9,
61
82
156,7
178.9
198,8
345,6
8
323,4
25
259,6
5,14
6
232,5
312,3
30
5
176,2 185,1 180,7
16
231,2
231,4
365,9
354,6
8,
82
8,
0
376,7
314,8 378.3
312,5
27
62
342,3
279,9
436,7
343,3
3
325,8
468,7
612,8
6,8
37
458,8
314,4
5
165,8
312,3
22
32
165,8
278,9
9,
1
7,
4
312,8
449,8
432,7
285,9
3,
9
81
8,
6
72
271,2
6,78
6
412,1
2
308,18, 7 212,3
165,9 67 198,4
312,2
2
325,4
36
41 6,3
6,
7
1,
187,9
265,8
312,3
206,9
2,3
31
310,2 354,1
40
12
0,
89
5,
65
432,1
262,3
2,1
43
332,2
9
8,
2
06 ,9
5
26
6
4,
287,8
703,2
265,9
Central Station
8,
5
22
4
312,7
12
6
4,
2,
1
51
2,
7
6
7,
31
21
4,
3
4,
63
245,9
302,3
221.2
8
23
3
9,
2,
4
367,4
587,7
11
20
262,5
231,4
231,4
234,2
7,
6,
4
8
8,
231,1
48
354,8
29
378,6
9
323,9
,8
34
48
0,
77
1,
5,
8
432,8
787,6
356,8
06
2
259,08 ,4
02
7
311,4
31
8,
5
13
2
46
323,8
214,2
208,9
206,53
1
5,
8
412,3
449,8
449,8
273,71
8,
56
16
421,2
326,8
216,7
214,6
167,8
343,7
154,8 167,4
201,2 167,8 167,7
187,8
176,8
0,6
25
4,
5
165,8
867,8
165,36
6,1
46
125,4
314,8
250,6
265,9 113,8
13
6,9
35
231,7
220,6
220,6
5,
8
2,3
33
298,7
236,6
4,1
23
301,8
220,6
16
298,2
7,2
34
7,2
17
345,6
3
879,8
13
1,4
34
247,9
4,8
14
347,9
1
389,56
268,9
217,9
232,2
212,3
453,8
267,8
301,3
231,2
203,4
165,8
209,4
222,1
238,9
165,8
8
2
3,
6
2
169
176,8
6
7
Figure 3: Representation of the Fulda’s network of local public buses by means of a graph.
Table 3: Minimum paths computed throughout Floyd algorithm.
i/j
1
2
3
4
5
6
7
8
9
10
1
0
162.10
712.43
975.93
1155.83
4319.38
3968.33
3787.63
3602.53
3433.63
2
162.10
0
550.33
813.83
993.73
4157.28
3806.23
3625.53
3440.43
3271.53
3
434.70
272.60
0
263.50
443.40
3606.95
3255.90
3075.20
2890.10
2721.20
4
698.20
536.10
263.50
0
179.90
3343.50
2992.40
2811.70
2626.60
2457.70
5
878.10
716
443.40
179.90
0
3163.55
2812.50
2631.80
2446.70
2277.80
6
1270.80
1108.70
836.10
572.60
392.70
0
3205.20
3024.50
2839.40
2670.50
7
1621.85
1459.75
1187.15
923.65
743.75
351.05
0
180.70
365.80
542
8
1802.55
1640.45
1367.85
1104.35
924.45
531.75
180.70
0
185.10
361.30
9
1987.65
1825.55
1552.95
1289.45
1109.55
716.85
365.80
185.10
0
176.20
10
2163.85
2001.75
1729.15
1465.65
1285.75
893.05
542.00
361.30
176.20
0
Unauthenticated
Download Date | 10/27/17 9:11 PM
170 | C. Mota et al.
3
4,
12
13
2
8,
13
6
8,
03
13
91
7
8,
8
8,
8
8,
81
91
71
3
8,
12
8
9,
91
2
1,
02
9
8,
91
1
2,
7
8,
61
13
5,9
46
587,7
9,6
8
47
8
9,
74
2,1
12
71
8
8,
7,7
2
7,
34
9
8,
214,6
354,8
176,2 185,1 180,7
259,6
351,05
298,7
,1731
5, 6
5
8,
5
8,
94
67
67
8
0,
765,9
187,9
,6052
5,14
6
765,6
251,6
248,9
232,6
5
17
24
432,8
318,8
8,
2,
18
2
9,
9
9
26
3,
15
2
3,
4
1,
5
272,6
162,1
9
1
2,
8,
24
19
213,8
1
358,61
25
3
4,
25
243,8
7
4,
21
212,8
2
3,
209,7
9
8,
56
5
8,
2
3,
13
2
9,
68
14
5
7,
34
4
8,
52
405,9
3
5,
3
2,
41
42
4
8,
13
265,9
232,7
5
312,3
231,7
156,7
198,8
178.9
176,8
6
141,2
315,8
4
209,8
198,8
8
9,
11
6
9,
71
6
9,
12 4, 7
201,8
4,
7
5
9,
11
62
203,5
289,7
4,
3
7,
5
212,4
26
2
8,
2
201,2 187,8
287,8
199.8
246,8
298,7 198,7
265,1
278,7
231,8
312,3
232,5
231,2
5 3
3, 2
220,1 9
2 1 8.
6, 2 17
173,2
21
8
5,
24
5,7
19
6,
16
2
6,8
37
,2
413,8
232,9 221,5 247,8
7,
2
392,7
8
27
7,12
3 2,2
51
449,8
,9252
607,3
1,4
75
212,3
432,7
612,8
323,4
36
6,3
7
25
6,78
6
198,4
37
2, , 90
56
9,
71
67
1
82
345,6
308,1
8,
165,9767
165,8
365,9
30
Area 2
6,
16
314,8 378.3
231,4
5
82
8,
0
376,7
312,5
8,
62
9,
7
342,3
279,9
436,7
343,3
3
325,8
468,7
354,6
27
2
312,3
458,8
314,4
5
265,8
22
32
165,8
278,9
9,
1
7,
4
312,8
41
1,
312,3
72
1
285,9
3,
98
8,
6
271,2
52
412,1
40
432,1
312,2
5,
6
325,4
206,9
2,3
31
310,2 354,1
262,3
2,1
43
332,2
12
0,
89
8,
4,6
287,8
703,2
265,9
Central Station
2
50
65,9
26
22
4
221.2
312,7
323,9
4,6
2,
367,4
1
51
7,6
31
21
7
2,
9,3
4,
9
8
23
11
20
63
Area 1
245,9
231,4
234,2
302,3
7,
6,
4
8,8
262,5
2,
4
231,4
432,8
787,6
48
48
0,
77
378,6
29
231,1
214,2
356,8
06
2
259,08 ,4
,8
32
34
323,8
449,8
208,9
206,53
02
7
311,4
31
8,
5
1,
1
5,
8
412,3
449,8
167,4
273,71
176,8
0,6
25
61
5,
8
46
421,2
326,8
216,7
201,2 167,8 167,7
167,8
343,7
154,8
165,36
187,8
6,1
46
125,4
314,8
250,6
8,
5
16
867,8
6,9
35
231,7
220,6
265,9 113,8
4,
5
165,8
2,3
33
298,7
236,6
4,1
23
220,6
5,
8
13
298,2
7,2
34
7,2
17
345,6
301,8
220,6
16
879,8
2
3,
1,4
34
247,9
4,8
14
347,9
3
1
389,56
268,9
217,9
232,2
212,3
267,8
453,8
203,4
301,3
231,2
222,1
6
165,8
209,4
8
238,9
165,8
2
7
Figure 4: Area 1 and Area 2 used in the static study.
Among the most accessible bus stops can be found those
belonging to the historic Baroque center and public services (nodes 12, 90, 92, and 94), the HSR central station
(node 11), the university (nodes 53, 123 and 124), the administrative center (node 50 and 52), the hospital (node
47) and the congressional palace (node 185). It is noteworthy that these points of interest were identified by the local agents as the most interesting locations within the city.
Indeed, considering locations with high accessibility as
those nodes with Ω below the mean minus once the standard deviation, i.e., those vertexes with Ω ≤ 14.95, all the
aforementioned nodes lie in that range. On the contrary, if
nodes with Ω above the mean plus once the standard deviation are considered as nodes with low accessibility, i.e.,
vertexes with Ω ≥ 59.52, we find locations corresponding
with nodes away from the urban center, usually located in
industrial areas. Thus, nodes 57, 58, 72, 73 and 135 are the
most marginal vertexes in terms of accessibility. In this re-
gard, the two most relevant industrial nodes (node 77 and
84) achieved Ω values equal to 62.52 and 37.85 respectively,
showing a low accessibility within the network.
3.4 Comparison of Fulda with others
European cities
In Table 5 can be observed a dynamic comparison between
German and Spanish cities regarding their HSR stations
and characteristics. More concretely, the Spanish stations
are located in Toledo and Lleida, and the German stations
are located in Fulda and Ulm-Neu Ulm. These stations
were chosen after a preliminary study considering their urban characteristics and population, where all of them are
categorized as medium-sized cities with not more that half
a million in population.
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree | 171
Table 4: Dynamic indexes applied to Fulda’s graph.
Location
Hospital
Historic Quarter
HSR Central Station
Historic Quarter
Hospital
Public Services
Public Services
University
Industry Area
Industry Area
Industry Area
Industry Area
Industry Area
Industry Area
Historic Quarter
Historic Quarter
Town Hall
Public Services
University
University
Industry Area
Congress Palace
Node Id
Diameter(m)
Ψ
Ω
7618.45
6615.60
6249.30
Average
length(m)
3930.22
3077.66
2828.37
5
10
11
978624.17
766338.49
704264.79
27.20
7.62
1.89
12
47
50
52
53
57
58
72
73
77
84
90
91
92
94
123
124
135
185
5801.10
7149.50
6363.90
5964.80
5755.50
10443.17
10206.57
10727.90
10402.10
9056.70
7871.80
5993.50
6393.82
5545.80
5713.60
5811.70
5808.10
10308.00
6728.20
2811.70
3327.20
2898.79
2915.40
2872.48
6988.37
6769.01
7099.76
6776.58
5468.14
4393.70
2946.31
3040.90
2746.03
2783.58
2878.11
2835.69
6796.69
3163.50
700113.41
828473.23
721798.59
725934.87
715248.67
1740104.21
1685482.48
1767840.87
1687368.27
1357103.17
1094031.87
733630.31
757185.31
683761.31
693111.41
716648.21
706086.51
1692376.31
787712.21
1.51
13.35
3.51
3.89
2.90
97.44
92.40
100
92.58
62.52
37.85
4.60
6.77
0.00
0.86
3.03
2.06
93.04
9.59
Table 5: Dynamic comparative study among different networks from HSR station point of view.
Population
Density of population (inh/Km2 )
Network length (Km)
Number of vertexes
Number of lines
Ψ
Ω
Hierarchical position (HSR station)
Fulda
64177
617
88.67
249
9
704264.79
1.89
4th
Some topological aspects were studied in order to
check the comparability and reliability of this study. In
this regard, some differences were found: while Fulda and
Toledo have a quite similar number of inhabitants, Lleida
and Ulm-Neu Ulm are relatively higher in population. Another difference, in terms of the bus lines configuration,
lies in the fact that Lleida has the highest number of bus
lines (18 lines) among all the cases under study, and consequently the highest network length. However, the aforementioned line characteristics do not affect proportionally
Ulm-Neu Ulm
177986
894
76.38
177
13
538681.94
0.00
1st
Toledo
83108
359
53.37
73
12
270644.15
5.04
8th
Lleida
138416
654
106.88
226
18
798273.90
2.56
10th
to the number of vertexes within the network. Indeed, the
number of vertexes is quite similar among all the cities
(249 in Fulda, 177 in Ulm-Neu Ulm, and 226 in Lleida), with
Toledo being the city presenting the lowest density of vertexes (73) with reference to its population.
Regarding relative accessibility, it is noteworthy that
while the Fulda HSR station ranks in the fourth position
out of 249 nodes, and the HSR station in Ulm-Neu Ulm
ranks the first position out of 177, the Toledo HSR station
and Lleida HSR station rank the eighth position out of
Unauthenticated
Download Date | 10/27/17 9:11 PM
172 | C. Mota et al.
Table 6: Static comparison study among different networks: Fulda, Ulm-Neu Ulm, Toledo and Lleida.
Index
Number of vertexes
Number of edges
Maximum connection
degree
Prihar’s index / interval
µ’s index /interval
Kansky’s α index
Kansky’s β index / interval
Kansky’s  index / interval
G p index
Fulda
249
292
30876
Ulm-Neu Ulm
177
196
15576
Toledo
73
89
2628
Lleida
226
271
25425
105.74 / [1,124.5]
79.47 / [1, 88.5]
29.52 / [1, 36.5]
93.82 / [1, 113]
44 / [0, 30628]
0.14%
1.17 / [0, 124]
20 / [0, 15400]
0.13%
1.11 / [0, 88]
17 / [0, 2556]
0.67%
1.22 / [0, 36]
46 / [0, 25200]
0.18%
1.20 / [0, 112.5]
0.0095 / [0, 1]
0.0126 / [0, 1]
0.0339 / [0, 1]
0.0107 / [0, 1]
122.83
86.89
34.78
111.30
73 and tenth position out 226, respectively. This fact reinforces the hypothesis that degree of connectivity and development of the surroundings of the HSR station are better for the German than for the Spanish stations. This difference is exacerbated when contrasting the different population densities. Thus the Ulm-Neu Ulm station which
has the best connection among all the networks, serves
a population of 177986 inhabitants with a density of 894
inhabitant per km2 . In the most adverse case (Toledo),
whose station ranks in the eight position out of 73, there
are 83108 inhabitants with a low density population of 359
inhabitants per km2 . Certainly, the Toledo station rank in
relation to its secondary transport network limits accessibility for potential customers and fails to guarantee the
sustainability and profitability of the HSR network.
With respect to static indexes (see Table 6), all the networks a have similar number of vertexes except Toledo,
which presents one-third the number of nodes compared
to the rest of the networks. Nevertheless, there exist differences mainly in two markers: maximum degree of connexion and the Zagozdzon index which increase proportionally as the number of vertexes in the network grow. Thus,
Toledo network has the lowest maximum degree connection and Zagozdzon index among all the networks studied.
Furthermore all the public bus transport networks show
a cohesion degree pretty low within their respective intervals, as reported by the rest of the static indexes used in
this study. Therefore, both German and Spanish stations
have a low cohesion degree and all of them need a high
level of development in order to improve connection and
cohesion. However, it is important to remark that the networks are hardly comparable given their differences regarding the number of vertexes.
4 Conclusions
4.1 Conclusions regarding the static
assessment
In the case of the static study of the network, applied to
Fulda first, it was found that the cohesion level reported
by all indexes showed the same low cohesion. The result is
logical, since they measure the relation between the number of vertexes in the graph and the potential direct interconnections between them. The more stops are added to
the network, the more potential connections appear.
As described in Section 3.2, the static method, which
has been widely applied when assessing cohesion, does
in fact provide incomplete information in the case of the
global study of the network. This method, which is useful when analysing the connection of town by roads that
link each one of them with the others, is less reliable when
analysing networks such as those of local buses, since they
have a large number of nodes (identified by stops in this
case). Given that it has a greater number of nodes distributed in the same area, instead of contributing to something that would in principle be deemed to be a network
with a higher level of cohesion, the static study penalises
this fact, since the figures resulting therefrom to calculate
the number of connections needed to link all the stops
directly are not compatible with the spatial configuration
inherent to transport networks that are like those we are
analysing. This way, the results of those networks with
a greater number of stops as Fulda (249), Ulm-Neu Ulm
(177) or Lleida(226) are comparatively negative in comparison with other networks with a lower number of stops as
Unauthenticated
Download Date | 10/27/17 9:11 PM
A Mathematical Study of Accessibility and Cohesion Degree | 173
Toledo (73), where fewer edges would be necessary to link
a lower number of vertexes.
The deficiencies of direct extrapolation in a method
traditionally utilized in road networks should be taken
into account, since the number of nodes is much lower in
the case of road networks and the connections have a radial trend rather than linear, which does not happen in the
case of public transport networks. For this reason, applying static studies to two different places in the same city
seemed appropriate: one in the city center, Area 1, and
a more outlying zone, Area 2. Thus, upon extrapolation
based on these two areas, the method becomes interesting again. In the case of Fulda, the comparative analysis
of two areas belonging to the same city and served by the
same network, the first one having a more central location and the second one having a more outlying location,
shows results differing from the level of cohesion of those
nodes belonging to the area with better location and consistently linked to a greater number of nodes, in comparison to the area whose nodes coincide with a lower number
of lines, which is more valid when diagnosing those areas
with greater cohesion deficit within the networks serving
them.
4.2 Conclusions regarding the dynamic
assessment
The severity and the scope of the conclusions seems to be
logical, making it necessary to take into account any national, regional and local policies that may, in fact, prepare and execute what has been planned under the right
conditions. Analyses like that of this research show very
different trajectories in the policies affecting the location
of HSR stations and their integration in the local mobility.
Two ideas are noteworthy:
– The difference in the accessibility level of the
stop that corresponds to the HSR station has very
favourable values in the German cases, and not so
much in the Spanish cases, being especially unfavourable in Toledo case. The necessary territorial spread from the station guaranteed by a suitable link to secondary transport networks is as commonly accepted theoretically as variable in its practical application.
– Different connection levels between the HSR station
and those locations that, from the study of the city
that has been envisaged by interviewee local agents,
are deemed to be poles of generation of activity
within local dynamics. In this regard, Fulda presents
good levels of accessibility to locations identified as
main attractors. This good station accessibility and
aforementioned attractors guarantee access of travellers throughout the HSR.
The implementation of the new rail line to the urban
area is an opportunity to increase the dynamism of an
area that generally is of great value, but which also faces
problems that are a result of the scar caused by rail in
the 19th century. The scenario chosen when analysing the
four cases, with their railway stations located in the centre thereof, allows city halls to execute projects integrating the new transport mode with the other transport systems. That way, efficient use of the new accessibility conditions is guaranteed. The analysis of the systematic studies
of the cases in different European countries shows common patterns related to the recipient of the actions. In the
first place, it can be noted that there is a direct relationship
between those inherent factors of cities and their location
within the network and the potential impact of stations
in them. Although the aforesaid location factors condition
the strategies adopted by the cities, city halls can execute
others enabling them to optimise the implementation of
HSR in their cities.
Regarding the dynamic analysis of those networks
analysed, and in sight of the fact that a favourable accessibility value corresponds to a good location in comparison to the rest of the nodes that make up the network, the
value obtained in the case of the high-speed railway station is important because it can guarantee a good relationship between the same and the rest of the local environment, which will in time assure good links between the
high-speed network and other secondary networks, as it
has commonly been claimed. There is a significant different between the values obtained in the four analyses. In
the German cases, that link is fundamentally important.
Thanks to this fact, the rank is 4th (out of 249) as the best
connected node in the case of Fulda or 1st (out of 177) in the
case of Ulm-Neu Ulm. Nevertheless, regarding the Spanish
cases and particularly the case of Toledo, ranking 8th (out
of 73), the station’s accessibility decreases significantly,
making its necessary relationship with the local secondary
network worse. Finally, Lleida ranking 10th (out of 226)
shows a slightly better result than Toledo regarding the relative accesibility, but worse than the German networks.
It thus seems that, in the near future, an in-depthreview is necessary that guarantees multiple objectives
for new HSR lines or for those already built, in order to
serve a wider range of traffic, which will result in a reasonable level of use. In that case, it would be necessary to
review the existing design criteria to meet new demands as
Unauthenticated
Download Date | 10/27/17 9:11 PM
174 | C. Mota et al.
far as possible, reducing in time the need for investment,
which is especially important in the current scenario of
budgetary constraints.
Acknowledgement: This work has been partially supported by MINECO grant numbers MTM2014-51891-P,
DPI2016-80894-R and TIN2015-72931-EXP, Fundación
Séneca de la Región de Murcia grant number 19219/PI/14
and FEDER OP2014-2020 of Castilla-La Mancha grant number GI20163581.
References
[1]
Shailesh Ch., Sharada V., Evaluating accessibility impacts of
the proposed America 2050 high-speed rail corridor for the Appalachian Region, J. Transp. Geogr., 2010, 37, 28-46.
[2] Hernández A., Jiménez J.L., Does high-speed rail generate
spillovers on local budgets?, Transp. Policy, 2014, 35, 211-219.
[3] Garrison W.L., Towards simulation models of urban growth and
development, Lud studies in Geography, Series B, Hum. Geogr.,
1962, 24, 92-108.
[4] Potrykowsky M.T., Geografía del transporte, Ariel Geografía,
Barcelona, 1984
[5] Shen Y., Silva J.A., Martínez L.M., HSR Station Location Choice
and Its Local Land Use Impacts on Small Cities: A Case Study of
Aveiro, Portugal, Procedia Soc. Behav. Sci., 2014, 111, 470-479.
[6] Gutiérrez J., González R., Gómez G., The European high-speed
train Network. Predicted effects on accessibility patterns, J.
Transp. Geogr., 1996, 4 (4), 227-238.
[7] Plassard F., Le traina a grande vitesse et le reseau des villes,
Transports, 1991, 345, 14-23.
[8] European Community, Development strategies of high-speed
rail, Experiences in medium-sized cities. Interreg IIIA Project,
2006
[9] Adler N., Pels E., Nash C., High-speed rail and air transport
competition: game engineering as tool for cost-benefit analysis,
Transp. Res. B Meth., 2010, 44 (7), 812–833.
[10] Monzón A., Ortega E., López E., Eflciency and spatial equity impacts of high-speed rail extensions in urban areas, Cities, 2013,
30, 18–30.
[11] Maćkiewicz A., Ratajczak W., Towards a new definition of topological accessibility, Transp. Res. B Meth., 1996, 30 (1), 47–79.
[12] Ureña J.M., Menerault P., Garmendia M., The high-speed rail
challenge for big intermediate cities: a national, regional and
local perspective, Cities, 2009, 26 (5), 266–279.
[13] Chang Y.H., Yeh C.H., Shen C.C., A multiobjective model for passenger train services planning: application to Taiwan’s highspeed rail line, Transp. Res. B Meth., 2000, 34 (2), 91–106.
[14] Martínez Sánchez-Mateos H.S., Givoni M., The accessibility impacts of a new high-speed rail line in the UK – a preliminary analysis of winners and losers, J. Transp.Geogr., 2012, 25, 105–114.
[15] Willigers J., Floor H., Accessibility indicators for location choices
of oflces: an application to the intraregional distributive effects
of high-speed rail in the Netherlands, Environ. Plann. A, 2007,
39 (9), 2086–2098.
[16] Gutiérrez J., Location, economic potential and daily accessibility: an analysis of the accessibility impact of the high-speed line
Madrid-Barcelona-French border, J. Transp. Geogr., 2001, 9(4),
229-242.
[17] Pol P.M.J., The economic impact of the high-speed train on urban
regions. Department of regional economics and transport and
port economics, Erasmus University Rotterdam, 2003
[18] Mota C., Planning of the implementation of high-speed rail. A
comparative study on the planning policies from the analysis
of the territorial implications thereof, PhD thesis, University of
Castilla-La Mancha, Cuenca, Spain, 2013, (in Spanish)
[19] Sallis J.F., Frank L.D., Saelens B.E., Kraft M.K., Active transport
and physical activity: Opportunities for collaboration on transport and public health research, Transport. Res. A - Pol., 2004,
38(4), 249-268.
[20] Litman T., Integrating public health objectives in transport
decision-making, AM. J. Health Promot., 2003, 18 (1), 103-108.
[21] Vickerman R.W., Accessibility, attraction, and potential: a review of some concepts and their use in determining mobility,
Environ. Plann. A, 1974, 6 (6), 675-691.
[22] Burns C.M., Inglis A.D., Measuring food accessing Melbourne:
access to healthy and fast foods by car, bus and foot in an urban
municipality in Melbourne, Health Place, 2007, 13(4), 877-885.
[23] Yigitcanlar T., Sipe N., Evans R., Pitot M., A GIS-based land use
and public transport accessibility indexing model, Aust. Planner, 2008, 44(3), 30-37.
[24] Silva C., Pinho P., The Structural Accessibility Layer (SAL): revealing how urban structure constrains travel choice, Environ.
Plann. A, 2010, 42(11), 2735-2752.
[25] Kansky K.J., Structure of transport networks: relationships between network geometry and regional characteristics, University of Chicago, Department of Geography, Research Papers 84,
1963
[26] Mohammad R.F., Muhammad K.J., Muhammad I., Vertex PIv
Topological Index of Titania Carbon Nanotubes TiO2 (m,n), Appl.
Math. Nonlinear Sci., 2016, 1(1), 175-182.
[27] Gamir A., Ruiz M., Seguí J.M., Prácticas de análisis espacial,
Oikos-Tau, Barcelona, 1995
[28] Garmendia M., Ribalaygua C., Ureña J.M., High-speed rail: implication for cities, Cities, 2012, 29 (2), S26-S31.
Unauthenticated
Download Date | 10/27/17 9:11 PM
Документ
Категория
Без категории
Просмотров
3
Размер файла
1 995 Кб
Теги
0017, 2017, phys
1/--страниц
Пожаловаться на содержимое документа