Paper prepared for Oral Presentation at the Africa GIS 2005 conference (oct 31 – nov 4) in Tshwane, South
Africa. Reference number 627
TRANSPORT NETWORK EXTENSIONS FOR ACCESSIBILITY
ANALYSIS IN GEOGRAPHIC INFORMATION SYSTEMS
Tom de Jong and Taede Tillema
Department of Human Geography and Planning
Faculty of Geosciences
Utrecht University
Utrecht, NL
Tel: +31302531393
t.dejong@geog.uu.nl
Abstract
In many developed countries high quality digital transport networks are available for GIS
based analysis. Partly this is due to the requirements of route planning software for internet
and car navigation systems. Properties of these networks consist among others of road
quality attributes, directionality and turntables. In contrast in many so-called developing
countries hardly any digital networks of sufficient quality exist for even the most basic GIS
operations. It is not realistic to assume that on a short term high quality digital networks will
become available. In such a case an airline network can be created. However this type of
network assumes homogeneous space and does not take any physical obstacles into
account. The Willowvale case is used to introduce the concept of (modified) Delauney
networks that only creates airline links between physically neighboring locations. The
purpose of this paper is twofold. First it is assessed to what extent ‘Airline’ and ‘Delauney’
based networks can be used as simplified cheap alternatives for the expensive digital road
maps based on reality. The suitability of these alternative networks is examined in a Dutch
case, where a detailed digital road map already exists. Results indicate that origindestination distances computed with Delauney networks, when compared to airline
distances, are much more in line with distances derived from the actual network. This leads
to the conclusion that especially in heterogeneous areas the Delauney method offers an
acceptable way of creating alternative road maps for the sole purpose of estimating the
travel distance between locations. The ‘Dar es Salam’ case is used to illustrate that the
method can also be applied when the road network needs to serve an urban area instead of
linking small villages. The second purpose of the paper goes one step further and aims at
getting insight into the sensitivity of accessibility outcomes when a Delauney network is used
as a network extension to add more detail at the local level to an already existing digital road
map. Results for the ‘Eindhoven’ case indicate that the addition of a more detailed lower
scale network does indeed have a substantial influence on accessibility results.
INTRODUCTION
All over the world service location planning is applied to investigate the need for additional service
centres, the optimal relocation of existing service centres or the effects of a reduction of number of
service centres. Accessibility is a topic that plays an important part in this type of service location
planning and a major requirement for proper accessibility analysis is the measurement of resistance,
most commonly in length or travel time, between clients and service centres. A digital transport
network is commonly used to estimate travel impedance using shortest path analysis. In many
developed countries high quality digital transport networks are available for such GIS based analysis.
Properties of these networks consist among others of road quality attributes, directionality and
turntables. In contrast in many so-called developing countries hardly any digital networks of sufficient
quality for even the most basic GIS operations exist. This lack of suitable networks makes it difficult (if
not impossible) to carry out simulation based service location planning studies in a realistic way.
However, various GIS-techniques can be applied to create hypothesized road maps. The simplest
technique is to use airline distances. In such a situation a road map is created on basis of direct
(airline, as the crow flies) links between all origin and destination points within a study area. This
method is easy, but there are several disadvantages. It assumes spatial homogeneity thus neither
natural nor manmade obstacles are taken into account in the network-building phase, theoretically
leading to a strong underestimation of real travel impedances. Also the effect of intervening
opportunities is totally ignored; airline links unrealistically bypass all other points on the way.
Intervening opportunities are fully taken into account by the second less well-known network building
technique based on so-called Delauney-networks. In case of point data the first step is to construct
Voronoi polygons (also known as Thiessen or Dirichlet polygons) around the origin and destination
points of interest. The second step is to connect topologically adjacent zones via Delauney links,
leading to a connected road map for the total study area. However, also in applying this last
procedure, natural and man made obstacles are still not taken into account. The purpose of this paper
now is twofold. The first purpose is to show how Delauney networks can be modified to take obstacles
into account and to assess to what extent airline distance and modified Delauney networks, can be
used as a simplified and cheap alternative for expensive real world digital road maps. Finally the
analysis will be taken one step further. Suppose, a quite detailed digital road map is available. Does in
such a situation the addition of an extra Delauney network, making the total network more detailed,
have a substantial impact on service location accessibility? Or are the effects only marginal?
Therefore the second purpose of this paper is to get insight into the sensitivity of accessibility
outcomes when a Delauney network is used as a more detailed network additive to an already (quite
comprehensive) available digital road map.
The paper is organized as follows. Section 2 focuses on Delauney networks, but more specifically at
creating a Delauney network taking obstacles within a study area into account. The Willowvale area in
South Africa is taken as a case study to describe the network creation procedure. Section 3 aims at
the validation of Delauney as well as airline distance networks against an existing digital road map.
This validation is carried out for the Friesland area in the Netherlands, a lake district that contains
many natural obstacles. So far the analyses in section 2 and 3 assume that point data for origins and
destinations is available. However, this is not always the case. Therefore, section 4 shortly elaborates
on the procedure that can be followed if one wants to create a (additional) Delauney network in case
clear origin and destination locations are not digitally available. The city of Dar es Salam is taken as an
example. Finally, section 5 deals with the second purpose and compares job accessibility outcomes
for the Eindhoven study area in the south of the Netherlands, computed with a ‘basic’ digital network
and an updated more detailed road map also containing a Delauney net.
CREATING MODIFIED DELAUNEY NETWORKS
Figure 1 shows the location of all primary schools and villages in the Willowvale area in combination
with the available digital transport network, in this particular area consisting of unpaved roads only.
Although at first glance the network looks to cover the whole area, a closer inspection learns that the
level of detail is not very sophisticated. There may be various causes, for instance the formal network
as maintained of government agencies may indeed be very limited or it may have to do with the
purpose for which the network was created; a network that is complete for one mode of transport like
heavy trucks maybe incomplete for another mode of transport like cycling or walking. In any case
many villages and schools in the study area are not directly situated “on” this network. Calculating a
network distance in those cases then is heavily affected by the way locations are linked to the network
and how “off” road distances are handled. Moreover this network contains some very large loops that
also affect network calculations, especially when locations are linked to opposite ends of such a loop.
A culmination of all these effects is shown in Figure 2. Situated close to the centre of the study area
the airline distance between the village of Cquba and the nearby school at Ziqorana is only some 940
meters. However when locations are snapped or linked somehow to the nearest road, each would find
a different road and a resulting network distance (accentuated in figure 2) that is more than 25 times
larger than the airline distance. Also the combined distance from the two locations to each nearest
road is also almost twice as large as the airline distance between them.
Often in these cases it is fair to assume that there will be an informal road or footpath that connects
the village and the school. It is highly unlikely that anyone who has an alternative will follow the formal
road. So heavy trucks may not have a choice, but people on foot, bicycle or with a four wheel drive
certainly do. If we assume for the moment that there will be an informal network that connects
neighbouring schools and villages over short distances, than such a network can be easily computed
in a three step procedure. The first step is to construct Voronoi polygons (also known as Thiessen or
Dirichlet polygons) focussing on all villages and schools involved (see figure 3). Voronoi diagrams
basically represent delimitations of the map area between the input points (i.e. villages and schools),
based on the proximity of every point in the map area to the input point. This results in convex
polygons, named Voronoi polygons. From these polygons it can be easily deducted which villages and
school are adjacent and than these adjacent villages and schools can be connected with straight lines.
These lines form a so-called Delauney network. This procedure very closely resembles (M.Yuan 2002
p 435) the construction of a TIN or triangulated irregular network (see figure 4). The essence of such a
network is that there are no crossing roads, and all neighbouring locations are connected directly. This
latter assumption may not quite resemble the real world as in practise there are often all sorts of
obstacles that hinder direct passage. These obstacles can be both physical (like steep hills or rivers)
and/or man-made like fenced areas such as airfields or military complexes. The Willowvale area is
mostly open range farming void of man made obstacles, but the area is famous for the steep slopes
around impassable rivers. So we need a third step to modify the Delauney network by taking these
rivers into account. There are two ways to do this, one is a post-processing step by simply removing
all Delauney connections that cross a river, the second way involves a change in step 1 in which
obstacles are already taken into account when creating the Voronoi polygons around neighbouring
locations. This second method will be dealt with in detail in the next example, for the moment we
simply remove all connections that cross a river (figure 5). At this stage also additional reductions
could be realised, for instance based on length, local knowledge or effectiveness, before finally a
modified Delauney network is merged with the formal road network (figure 6). If we now assume that
on the formal roads travellers can achieve a higher travel speed than on the estimated connections,
we can estimate overall travel times that are realistic in the sense that on the longer distance the
formal roads will form a substantial part of the shortest path and a must to cross a river, but that very
lengthy detours at short distance will be avoided. The resulting network was also used to analyse the
effect of a new coast road on market areas (see also Naudé et al., 1999).
COMPARING MODIFIED DELAUNEY AND AIRLINE NETWORKS
Apart from a plausible look and feel there is no way that results using the modified Delauney network
in the Willowvale context can be validated without extensive field research. However in the
Netherlands a higher quality digital road network is available. So in order to check the modified
Delauney approach travel times on actual roads can be compared with estimated ones. To do so an
area was selected in the North of the country that is void of major high ways (so all roads are more or
less of the same order) and where there are many obstacles; the area is famous for its many lakes.
There are no major towns in the area, but some 70 of villages with the number of inhabitants varying
from forty to four thousand. When we apply the similar procedure as used above, a Delauney network
is produced that has some flaws (figure 8); direct connections between the villages ‘Koudum’ and
‘Nieuw Buren’ and ‘Heeg’ and ‘Gaastmeer’ are missing and ‘Sandfirden’ is not connected at all. The
basic assumption of Delauney network is that centroids of adjacent polygons are connected, post-
processing may lead to the situation that a direct connection between two adjacent polygons is partly
overlapping an obstacle and hence removed without proper justification as the obstacle does not have
to be crossed, but could easily be bypassed. So the thing to do is not to remove Delauney connections
afterwards, but to update the polygon map with obstacles before the Delauney links between adjacent
polygons are created. Figure 9 shows a merge between obstacles (lakes) and Voronoi polygons
centred on villages. Obviously polygons centred on villages on opposite sides of the larger lakes are
no longer in any way adjacent because the full common boundary literally falls in the water. Sandfirden
is now still adjacent with several other villages and there is a common border between the villages
‘Koudum’ and ‘Nieuw Buren’. But there are some new complications. Several of the original Voronoi
polygons have been split into two of more physically separate sections. In such a case only the
sections that contain the original village should be taken into account when generating a Delauney
network. The other sections (hatched sections in figures 9 and 10) must be ignored as there is no
direct access from the central village. For Sandfirden this leads to no direct connections to villages to
the west and to the north, although the original Voronoi polygon indicates several neighbours in those
directions. Off course the hatched areas should be redistributed among the remaining physically
neighbouring villages, but in the South West Friesland example the effect seems to be limited to the
‘Gaastmeer-Heeg’ stretch, where a blocking detached section now prohibits a direct connection.
Figure 11: Scattergram Airline vs Network distance
Figure 12: Scattergram Delauney vs Network distance
40000,00
Modified_Delauney_Distance
Modified_Airline_Distance
40000,00
30000,00
20000,00
10000,00
30000,00
20000,00
10000,00
0,00
0,00
0
10000
20000
30000
40000
0
10000
Network_distance
20000
30000
40000
Network_distance
To measure the quality of the new network, shortest paths can be calculated between all possible
combinations of villages resulting in 4830 (69*70) estimated distances. This can be done for both the
40,00
Delauney_Distance_in_km
Airline_Distance_in_km
40,00
30,00
3.702
20,00
3.827
2.168
2.100
10,00
4.804
829
4.096
3.346
3.215
4.793
4.672
4.165
1.7551.687
4.687
4.105 4.172
4.755 4.671 4.519
280
4.821
0,00
30,00
3.635
4.141
20,00
4.145
4.076
4.766
4.743
3.883
10,00
4.6614.119
3.215
4.809
4.407
4.683
4.755
4.521 1.189
2802.765
0,00
36,00
40,00
34,00
32,00
30,00
28,00
26,00
24,00
22,00
18,00
20,00
16,00
14,00
12,00
10,00
8,00
6,00
4,00
,00
Figure 13: Boxplot Airline versus Network Distance
2,00
36,00
40,00
34,00
32,00
30,00
28,00
26,00
24,00
22,00
18,00
20,00
16,00
14,00
12,00
10,00
8,00
6,00
4,00
,00
2,00
Network_Distance_in_km
3.695
Network_Distance_in_km
Figure 14: Boxplot Delauney versus Network Distance
actual network and the revised Delauney network. Also simple direct airline distances can be
calculated for all combinations. The correlation between airlines distances and actual network
distances amounts to 0.865, the same comparison for the revised Delauney network results in a much
improved correlation of 0.968. On average in this area the airline distance underestimates the actual
network distance by a factor of 1.7 whereas the Delauney net is of by 1.2. This latter statistic closely
matches the usual statistic (known as the crow flight conversion statistic) for rural areas. The reason
for the higher correlation of the modified Delauney network is revealed by the scatter grams (figures
11 & 12) and box plots (figure 13 & 14). Specifically on the middle and longer distances the quality, in
terms of reduced variation, is much better. So even without creating perfect Voronoi polygons taking
the effect of obstacles fully into account, the revised Delauney method already produces much more
reliable distance estimations than simple airline distances. In the next sections we will explore some
more uses of revised Delauney networks.
CREATING DELAUNEY NETWORKS IN AREAS WITHOUT CLEAR FOCAL POINTS
The city of Dar es Salam in Tanzania has been
growing considerably over the last decades in a
largely uncontrolled fashion and the accessibility of
health care provision is a constant concern. In order
to study the accessibility of governmental health
facilities Amer & de Jong (2002) developed a digital
transport network on the basis of aerial photographs
and the analogue topographic map. Neither data
source was fully up to date and clearly the result
was incomplete in most of the informally developed
sections of the city. Also in this study it was found
that visitors to health facilities mainly make use of
only two modes of transport; they walk on the short
distance and use public transport on the longer
distance. Figure 15 shows the south western part of
Kinondoni municipality that is close to the actual city
centre. There is a clear contrast between the road
networks in the different sections of the town. On the
one hand there is the modern looking well
connected network in the sections of town where planned development took place and on the other
hand there is the more rural looking network in the informal sections where connections are not so
good. Network distances calculated based on this section of the network might result in long detours
on the short distance. In reality these areas are filled with only small dwellings standing alone without
any private gardens or fences, so accessibility for pedestrians is effectively unhindered in virtually all
directions. Hence supplementing the existing network with a Delauney net for pedestrians seems a
must to make acceptable estimations of travel time. In this case however we don’t have clear villages
to connect but rather a continuous urban field only disturbed by a few major rivers that cannot be
crossed without a formal bridge. So instead of creating Voronoi polygons around a set of given point
locations, we must generate these points ourselves by tessellating the informal area. Figure 16 shows
a tessellation of the informal areas in hexagons making sure the area directly bordering on the rivers is
not included. A Delauney net can then be created that connects all centroids of adjacent tiles and that
net can be merged with the existing network (Figure 17), thereby ensuring the same effects as in the
Willowvale application
SENSITIVITY OF ACCESSIBILITY FOR LEVEL OF DETAIL IN A DIGITAL ROAD MAP
The Eindhoven study area is part of the Dutch province called Noord-Brabant (situated in southern
part of the Netherlands close to the Belgian border). The east-west length amounts to approximately
50 kilometres. In the north-south direction the size of the study area is somewhat smaller
(approximately 30 kilometres). Two major cities are located within the boundaries of the area. The
biggest city is Eindhoven with about 208.000 inhabitants. The other one is Helmond. This city, roughly
having 86.000 inhabitants, is substantially smaller. For this study area an already quite detailed digital
road network is available (see figure 18), which is used for several modelling purposes (see also
Tillema et al., 2005). The total area is divided into 2378 residential zones. For each zone the number
of available jobs is known, making it possible to compute the job accessibility per zone. As residential
zones and the road network originate from a different source, virtually no zone is directly situated ‘on’
the network. A common practise in such a case is to extend the network with a limited number of (441)
feed points. These points are used as points where the traffic can enter (‘feed’) the digital road
network. The advantage of the feed link approach is that the network needs no further adjustments,
irrespective of the zoning system used. All zones tap to the network via the feed point. This kind of
simplification is also decreases the computational complexity, but in effect this will generate identical
distances for all zones that tap on the same feed point. Also the distance between all zones that tap
on the same feed point is by definition zero. What are the consequences of this simplification? In this
section we will try to answer the specific question whether or not the simplification has a substantial
impact on job accessibility by car.
To take distances between zones and feed points into account a Delauney network has been created
following the same procedure as was applied in the Friesland case (section 2). First of all the polygon
map was updated with obstacles within the study area, such as lakes, wed lands, impassable
highways and an airport. In the second place a Delauney network was generated between the 2378
centre points avoiding all impassable areas. Finally, the Delauney network was merged with the
already available digital road map leading to a ‘full’ network. Note: as apart from the zone centre points
also all feed points were included in the Delauney network, ensuring automatic connectivity with the
original network. Figure 19 shows an enlarged part of the study area (squared part in figure 18) with
the addition of the extra network links. Using this new network in stead of the simple network has two
implications. First of all, in most cases the impedance between two zones will increase (and thus
accessibility will decrease) in the new network case as distances between zones and the feed point to
which they belong are no longer equal to zero. Secondly, in some situations the impedance between
two zones tapping onto different feed points may be smaller in case of using the new network. This
occurs when the distance following the Delauney network is shorter than the corresponding distance
via the basic network. However, the exact accessibility effects can be assessed in a better way by
conducting a simulation.
The effects of the two network types on job accessibility have been assessed by using two types of
geographical accessibility measures: the proximity count and the potential measure. Contour and
potential measures are quite well known and often used measures in transport geography. A proximity
count, counts the number of opportunities which can be reached within a given travel time, distance or
cost (fixed cost), or is a measure of the (average or total) time or cost required to access a fixed
number of opportunities (fixed opportunities). The potential measures (also called gravity-based
measures), estimate the accessibility of zones to all other zones (n) in which smaller and/or more
distant opportunities provide diminishing influences (Geurs & Van Wee, 2004). Geographical
accessibility measures, such as the proximity count and potential measures consist of a location
component and a resistance component. The location component indicates which or which type of
activity location(s) is central within the analysis; in this case jobs. The resistance component is
different for both measures. The proximity count works with discrete impedance steps; for example
reachable jobs within 10, 15 or 30 minutes. The potential measure on the other hand uses a
continuous impedance function, in which the strength of the distance decay is determined by a cost
sensitivity factor.
Figure 20: job accessibility difference (basic –
full network) for proximity count 15 minutes
Figure 21: job accessibility difference (basic –
full network) for proximity count with different
impedance steps
Figure 20 shows the differences in job accessibility computed with the basic and the full network (i.e.
including the Delauney network). The accessibility measure used is the proximity count with an
impedance boundary of 15 minutes. Absolute
differences are presented on the x-axis and the
percentage of all zones (i.e. 2378) having such a
difference is indicated on the y-axis. The figure
shows that the differences in accessibility are
substantial. Virtually for all zones the number of jobs
in reach has changed. By using the basic network,
roughly 60 percent of the zones have a 0 to 25000
higher job reach within 15 minutes. But higher
difference classes are substantial too. On the other
hand, only a small percentage of zones have a
higher accessibility in case of using the full network
(i.e. –25000 to 0 jobs). Furthermore, figure 21 shows
the results for different applied impedance steps and
indicates that accessibility differences between the
two network types first increase by applying a higher
impedance step. This can be explained by the
Figure 22: job accessibility ratios (full/basic
higher number of jobs reachable within a wider time
network) for potential measure with decay
interval, seemingly resulting in higher absolute
parameters 0.5, 1 and 2
accessibility differences. However, for 30 and 45
minutes differences decrease again, because a large share of jobs in the study area can be reached
within the time limit, leading to smaller absolute differences. Next to the absolute differences, relative
ratios for the contour measure (impedance step 15 minutes) are assessed. These ratios enforce the
conclusion that differences in accessibility, due to the level of detail of the network used, are
substantial.
Accessibility differences occurring from using the potential measure are presented in Figure 22. Ratios
are used because absolute values are not quite communicable due to the nature (i.e. quotient of
number of jobs and impedance between zones) of potential measures. Results are shown for three
different impedance sensitivity factors. A higher factor resembles a larger influence of the resistance
between two zones (i.e. higher distance decay). Figure 22 shows that higher parameter values lead to
larger job accessibility differences between the applications of the basic or full network. This effect is
due to the nature of potential measures. With a higher distance/travel time decay parameter, the
influence of the impedance between zones increases. Especially local differences become more
important. Because the Delauney links in case of the full network are always used at (least at) the
beginning of a trip, the relative influence of the resistance on these links in a trip will increase, leading
to higher accessibility differences between both network types.
Overall, it can be concluded that adding a Delauney network to an already quite detailed network still
has a substantial impact on the impedance and thus on accessibility of zones. Therefore, even with
already quite detailed networks, the addition of a Delauney network should be considered. Especially
because Delauney networks are easy to generate and, in case of established feed points can be
added without changing the original network in any way.
CONCLUSION
In this paper we have examined a way to enhance existing digital road networks to make travel time
estimation more realistic on the one hand and to make sure on the other that the effect of speed
differentiation is not lost. The problem was identified in the Willowvale application and a suggestion
was made to enhance the existing network with a modified Delauney network thereby reducing the
number of unrealistically long detours on relative short distances. Then, in the South West Friesland
area that is famous for its many lake a test showed that the Delauney network leads to a better
estimation of travel impedance than the airline network; when both airline and Delaney distances were
compared to the actual network distance it was clear that the variation in estimation is much smaller in
case of Delauney networks. The Dar es Salam case showed that after tessellation a Delauney network
can also be applied to an area in stead of to a set of points. Finally, in the Eindhoven application it was
shown that a mix of point locations and network feed point can be used to generate a Delauney net
that automatically is attached to the existing network. Moreover it was shown that even at this level of
detail the use of an additional Delauney net has a substantial effect on the outcome of the accessibility
analysis. Therefore it was concluded that Delauney networks are an easily generated enhancement to
a digital transport network that should be considered with every application where correct estimation of
short distance travel is important.
LITERATURE
Jong, T. de, S. Amer (2002), Using GIS to analyse the influence of public transport availability on the
choice of health service: a case study of Dar es Salaam, Tanzania . In: (X. Godard and I. Fatonzoun.
Eds.) Urban mobility for all. ISBN 90 5809 399 9 Balkema Publishers, Lisse, 2002, pp 145-152
Geurs, K. T., B. van Wee (2004). Accessibility evaluation of land-use and transport strategies: review
and research directions. Journal of Transport Geography 12: 127-140.
May Yuan (2002), Geographic Data Structures. In: J.D. Bossler (Ed.), Manual of Geospatial Science
and Technology, Chapter 26, Taylor &* Francis, London, pp 431-449.
Naudé, A. , T. de Jong & P. van Teeffelen (1999), Measuring accessibility with GIS-Tools: A case
study of the Wild Coast of South Africa. In: Transactions in GIS, vol 3, no. 4, pp 381-395.
Tillema, T., T. de Jong, B. Van Wee (2005). Modelling geographical accessibility under road pricing
conditions (a theoretical review of needed adjustments to the impedance function of
accessibility measures and an illustrative sensitivity analysis regarding the cost component of
measures). 8th NECTAR Conference, Las Palmas G.C. June 2-4, 2005.