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Smart and Sustainable Built Environment
Modelling walking and cycling accessibility and mobility: The effect of network
configuration and occupancy on spatial dynamics of active mobility
Pirouz Nourian, Samaneh Rezvani, Kotryna Valeckaite, Sevil Sariyildiz,
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Pirouz Nourian, Samaneh Rezvani, Kotryna Valeckaite, Sevil Sariyildiz, (2018) "Modelling walking
and cycling accessibility and mobility: The effect of network configuration and occupancy on spatial
dynamics of active mobility", Smart and Sustainable Built Environment, Vol. 7 Issue: 1, pp.101-116,
https://doi.org/10.1108/SASBE-10-2017-0058
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Modelling walking and cycling
accessibility and mobility
The effect of network configuration and
occupancy on spatial dynamics of active mobility
Pirouz Nourian, Samaneh Rezvani, Kotryna Valeckaite and
Sevil Sariyildiz
Department of Design Informatics,
Delft University of Technology, Delft, The Netherlands
Abstract
Purpose –The most sustainable forms of urban mobility are walking and cycling. These modes of
transportation are the most environmental friendly, the most economically viable and the most socially
inclusive and engaging modes of urban transportation. To measure and compare the effectiveness of
alternative pedestrianization or cycling infrastructure plans, the authors need to measure the potential flows
of pedestrians and cyclists. The paper aims to discuss this issue.
Design/methodology/approach –The authors have developed a computational methodology to predict
walking and cycling flows and local centrality of streets, given a road centerline network and occupancy or
population density data attributed to building plots.
Findings –The authors show the functionality of this model in a hypothetical grid network and a simulated
setting in a real town. In addition, the authors show how this model can be validated using crowd-sensed data
on human mobility trails. This methodology can be used in assessing sustainable urban mobility plans.
Originality/value –The main contribution of this paper is the generalization and adaptation of two network
centrality models and a trip-distribution model for studying walking and cycling mobility.
Keywords Social network analysis, Local betweenness centrality, Local closeness centrality, Radiation model,
Spatial urban dynamics, Sustainable urban mobility
Paper type Research paper
Introduction
The main focus of this paper is to devise methods and models to formulate and calculate the
effect of population density and network configuration on the flow of pedestrian and cyclists.
The contributions of this paper are the generalization of two network centrality models and a
mobility flux prediction model. As such, the geo-data and demographics presented are merely
utilized to illustrate the exemplary use of the proposed methodology and models. In addition,
we formulate a computational procedure for validation and/or calibration of the proposed
models. For studying spatial dynamics of mobility, some scholars use network centrality
indicators as proxies (for both pedestrians and vehicles); examples can be seen in: Blanchard
and Volchenkov, 2009; Cooper, 2017; Jiang and Claramunt, 2004; Penn et al., 1998; Porta et al.,
2006a, b; Serra and Hillier, 2017; Ståhle et al., 2005).
Active mobility
As opposed to other modes of transportation, road congestion is not a problem for walking
and cycling mobility, but often a requirement for pedestrians and cyclists to feel safe to walk
Smart and Sustainable Built
Environment
Vol. 7 No. 1, 2018
pp. 101-116
Emerald Publishing Limited
2046-6099
DOI 10.1108/SASBE-10-2017-0058
Received 30 October 2017
Revised 28 February 2018
Accepted 2 April 2018
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/2046-6099.htm
© Pirouz Nourian, Samaneh Rezvani, Kotryna Valeckaite and Sevil Sariyildiz. Published by Emerald
Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence.
Anyone may reproduce, distribute, translate and create derivative works of this article (for both
commercial & non-commercial purposes), subject to full attribution to the original publication and authors.
The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode
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or cycle through urban roads. This is what is usually referred to as the critical mass of
cyclists required to provide the feeling of traffic/social safety. For this reason, and also to
ensure maximum reach/coverage of an intervention in terms of the number of citizens
served by an intervention (e.g. a pedestrianization plan, a pedestrian bridge, a bike-sharing
network, etc.), we need to be able to predict both the walking/cycling flows and accessibility
of locations. For both purposes, networks are ideal abstractions to use as the basis of models
because the walkable/cycleable space as a two-manifold[1] can be best discretized as a
network in which the costs of traversal can be attributed to the links (Figure 1).
Social-spatial network analysis and urban mobility
Social network analytics provide a theoretical basis for understanding the dynamics of
networks by identifying the structural tendencies associated with positions in a network.
The reasons for viewing active mobility as a social-spatial network are manifold, namely:
•Geographical space can be best modeled with networks (as opposed to plane maps)
because the distance between any two points is almost always considerably larger
than the straight-line Euclidean distance due to obstructions; therefore, modal
accessibility for active modes of mobility is greatly influenced by network structure.
•Active mobility flows depend on the social ambience of environments, which is
arguably influenced by the structural position of spaces within the larger
environment. The heterogeneity of structural positions can be very well analyzed by
centrality models adopted from social network analytics.
MEGAJOULES PER PASSENGER KILOMETER TRAVELED
Cycling
Walking
Tram (Light Rail)
Bus
Electric and Diesel Rail
Heavy Rail
Motorcycle
Cars
Boeing 727 Aircraft
Taxis
0.06 0.16
0.91 0.92
1.65 1.69 1.73 2.1 2.42
2.94
Sources: Based on the data of (Banister, 2009) reproduced from an image of www.
treehugger.com, by A.K. Streeter, www.treehugger.com/bikes/trying-travel-city-
bikes-are-most-efficient-way-move.html
4
Bicycle and Rider
Walker
Runner
Moped and Rider
Train and Riders
Car and Riders
Speed (MPH)
Horseback
Swimmer
Car - 1 Rider
kcal consumed/km of travel
0 200 400 600 800 1,000
10
10
20
30
30
40
10
15
30
60
15
4
Figure 1.
Energy-efficiency
in transportation
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•The practicality or impracticality of walking or cycling depends on the cognitive
complexity of paths and the slope of paths, both of which can be best considered on
networks.
Street network and urban population density
There is a scholarly debate on how the structure of networks or the land use (and thus
population density) determine the centrality of locations in cities. The theoretical framework
of space syntax assumes that it is the configuration of the environment that eventually
determines the distribution of land uses and densities (Hillier, 2007). Such a harmony
between network structure and land use distribution patterns can be observed in historical
city centers and vernacular settlements that have organically evolved. However, in new
towns where municipal authorities and planning measures can decide on land-use plans
(quite possibly), regardless of the network structure, this assumption might not be correct.
In transport planning, the so-called land-use transport interaction models (see Carvalho and
Iori, 2008) seek to explain the interrelations between the network and land uses and their
effect on the mobility flows. In this paper, we focus on the particularities of active modes of
transport and the relation between the walking/cycling flows with both the network
structure and the (actual occupants) population density distribution. The assumption
behind this approach is that the degree to which a location within a network is a potential
origin or a destination is related to the number of people present at that location, i.e. the more
the population, the higher the attraction or “radiation.”
Methodology
This paper reports a methodological development, and thus the data presented are for
illustrating the functionality of the proposed methods. We propose a methodology to generalize
the mobility flux radiation model (Simini et al., 2012) to predict the flow of pedestrians/cyclists
on the streets within such neighborhoods. The procedure is as follows (Figure 2):
(1) enhance the resolution of street networks by homogenizing the segment lengths
(shattering street lines into pieces not larger than a certain length) and reducing
unnecessary junction points (i.e. cartographic generalization by making topological
vertices as representatives of the junction points) (see Figures 3 and 4);
(2) construct a bipartite topological model in which vertices represent junctions and
edges represent streets;
(3) construct a dual network model where nodes represent streets and links represent
junctions;
(4) compute the graph traversal costs;
(5) find the easiest paths ( from Nourian, van der Hoeven et al., 2015) (Nourian, 2016)
between any pair of origin and destination for walking or cycling (within range of
acceptable travel-time);
(6) map the given population (occupation) of the plot to the closet street(s); and
(7) compute the transition flows between locations within the given range.
Research objectives and research questions
The goal of this research is to provide a foundation for assessing sustainable urban mobility
plans in terms of their effectiveness for walking and cycling accessibility improvements.
To this end, we propose to utilize a universal mobility flow model generalized for networks.
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Thus, the objective of this research is to generalize the so-called universal model of mobility
(Simini et al., 2012) from the Euclidean space to network spaces, where distances are
calculated through geodesics (optimal paths on network). The matrix of origin–destination
distances in such a setting is generally asymmetrical, and all distances D
i,j
are greater than
or equal to the 3D Euclidean distance, i.e. D
i,j
⩾|L
i,j
|.
The main questions that this paper answers are:
RQ1. How to generalize a (mobility flux) radiation model for network spaces?
RQ2. What is the relation between the generalized (mobility flux) radiation model and
social/spatial network centrality models?
RQ3. How to validate and/or calibrate the generalized (mobility flux) radiation model,
given crowd-sensed mobility data?
Street Centerline
Topographic Terrain
Building Occupancy
Populations
Map the given population
(occupation) of the plot to the
closet street(s)
Street Populations
Compute the transition flows
between locations within the given
range
Display on
Easiest Paths and
Building Plots
Compute Local
Closeness
Centrality
Compute Local
Betweenness
Centrality
How Far (R)
Enhance the resolution of
street networks by
homogenizing the segment
lengths and reducing
unnecessary junction points
Construct a bipartite
topological model where
vertices (V) represent
junctions and edges (E)
represent streets
Walking/Cycling
Compute the graph traversal costs
and find the Easiest Path between
any pair of origin and destination
for walking or cycling (within
range of acceptable travel-time
Constructing a dual network
model where nodes represent
streets (E) and links represent
junctions (V)
{E, E2E}
{V2E, E2V, V2V, E2E}
C?B?F?
Figure 2.
The proposed
methodology for
analyzing active
urban accessibility
and mobility in
terms of closeness,
betweenness and
radiation-mobility
flows
Notes: From left to right, respectively, cartographic generalization, forming vertices as junctions,
simplifying junctions as vertices
Figure 3.
Cartographic
generalization and
topological modeling
of the street network
(steps 1 and 2 in the
Methodology)
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Network space and network distance
Walking and cycling do not incur costs for a traveler, therefore a natural measure of
deterrence for a journey would be the travel-time, provided the physical and cognitive
conditions are already considered in computing the minimum travel times. As with any
other measure of distance, the distance between two points must be an indicator of the
spatial/temporal length of an optimal path or a geodesic. In many urban and regional
studies, Euclidean distance is used for measuring the distances and accessibilities.
Arguably, the importance of difference between Euclidean distance and network distance in
large scales fades away. This is shown, for example ,in the study of simplest paths
(Duckham and Kulik, 2003) and a comparison of urban network analysis methods (Sevtsuk
and Mekonnen, 2012). However, for studying the micro-scale dynamics of walking and
cycling mobility, we argue that not only the network space should be the basis of any study,
but also the travel-time distance should be used instead of other metrics. Consider two
buildings located on opposite sides of a river or an arterial road; for a pedestrian, no matter
how close these two locations seem to be in terms of Euclidean distance, the actual walking
travel-time distance might be much more than the Euclidean distance. In fact, in built
environments, the minimum distance between any two points on the streets is almost
always longer than the length of a straight line between those points (Euclidean distance);
let alone the extra time wasted for navigation through a complex path.
Local closeness centrality
By computing geodesics between any pair of origin–destination, we can also obtain a matrix
of mutual temporal distances between any two points in a network space. Note that for a
pedestrian or a cyclist, this distance is not symmetrical, i.e. the distance between A and B
might be shorter or longer than B and A. This is because a downhill road is easier to walk
than an uphill road; therefore, the travel-time for a downhill path is necessarily less than the
travel-time for the same path traversed in the opposite direction. We calculate the local
closeness centrality (after Sabidussi, 1966) of every location using the distances computed
from easiest paths geodesics in a manner similar to the calculation of local integration in
space syntax (Hillier, 2007). Following the fuzzy (Rosyara et al., 2008) definition of closeness
given in Nourian (2016), we can put forward a more straight-forward definition of local
closeness as “the average closeness to all other location”:
CC
iRðÞ¼
PjAACR
i;j
N;catchment area :¼A¼jA0;n
½Þ
9Di;jpRg:
Figure 4.
All junctions modeled
as vertices, all streets
longer than a certain
length shattered into
pieces, therefore
forming new vertices,
later modeled
topologically as edges
of the network (part of
the city of Lisbon in
this case)
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Considering a mode of transportation, we can model the closeness of a location as to
the threshold distance above which a traveler’s tendency to traverse is inconsiderable.
We can model such a closeness value using a sigmoid function:
Cx;RðÞ¼ 1
1þelxR
2
ðÞ
;
where xdenotes travel-time distance, λdenotes a limitation coefficient and Rdenotes
the radius above which the perceived convenience or feasibility of traveling with a certain
mode of transportation is practically zero; i.e. Cx;RðÞoe9xXR
. To ensure this feature,
we put (Figure 5):
l¼2
Rln 1
e1
:
Therefore, we reformulate local (cognitive/fuzzy) closeness centrality as below:
Intuitively, the closeness of any location at nearly zero distance is 1 (100 percent),
and the closeness of any location located beyond the acceptable range of travel is nearly 0
(Figure 6).
Local betweenness centrality
Considering a radius of search, we can generalize betweenness centrality (Freeman, 1977)
for a network of nodes and links (usually referred to as vertices and edges) G(V,E) as below,
where Gðs;tÞdenotes the geodesic path between two nodes {s,t} (Figure 7):
ℙRðÞ¼ Gs;tðÞ9s;tAVðÞLsaiatðÞLDs;t
½
oRðÞ
;
1.00
0.75
0.50
0.25
0.00
0123
Walkin
g
travel-time distance in minutes
Closeness
Fuzzy closeness function
45
Figure 5.
Fuzzy (cognitive)
closeness vs distance
(Nourian, 2016), for
an exemplary
pedestrian who is not
willing to walk more
than 5 minutes for
daily commutes,
i.e. when R¼5
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The network radiation model of mobility fluxes
The fundamental equation of the radiation model (Simini et al., 2012) is an alternative to
the conventional gravity models, often used for “Trip Distribution”in transport modeling
(de Dios Ortúzar and Willumsen, 2011). Gravity models are also used for modeling
migration/mobility patterns and studying spatial interactions:
Ti;j¼Ti
minj
miþsi;j
miþnjþsi;j
;
where m
i
is the total population of the ith location, n
j
is the total population of the jth
location, S
i,j
is the total population in the circle of radius R
i,j
¼D
i,j
centered at i(excluding
the source and destination population), T
i
is the total number of commuters that start their
journey from the ith location, i.e. Ti¼PiajTi;j, which is proportional to the population of
the source location; hence T
i¼
m
i
(N
c
)/(N), where N
c
is the total number of commuters and N
is the total population in the country.
R=5minR=3min R=10min R=15min
Note: The images on the top show the computed results visualized only on the streets, and the
images below show those results projected to the attributed building polygons
Figure 7.
Local betweenness;
mode of
transport: walking
R=2min R=3min R=4min R=5min
Note: The images on the top show the computed results visualized only on the streets, and the
images below show those results projected to the attributed building polygons
Figure 6.
Local fuzzy closeness
centrality; mode of
transport: cycling
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This means we can rewrite the equation of the radiation model as follows:
Without knowing the actual number of commuters (the N
c
), we can safely assume that the
portion N
c
/Nis equal to 1. The reason is that we are after the statistical distribution of flows
and not the actual number of individual commuters. In other words, the statistical
distribution pattern will be the same regardless of this scalar coefficient. Therefore,
effectively, we consider this proportionality as an equality. In order to generalize this model
of transition flows, we take the following steps:
(1) generalize the notion of search radius from Euclidean distance to network geodesic
distance;
(2) change the nature and the unit of distance from spatial (meters) to temporal
(minutes);
(3) generalize the search circle centered at the origin to a “catchment area”from that
origin;
(4) prove that the transition flux to locations beyond the specified reach of a location
can be safely ignored and assumed to be zero;
(5) specify a minimum buffer for a model to avoid the so-called “network edge effects”;
(6) map the (occupancy) population of locations onto network locations; and
(7) develop a procedure to compute transition flows in an urban street network.
Using a street-to-street network model (similar to those of Batty, 2004; Hillier and Hanson,
1984; Jiang and Liu, 2009; Porta et al., 2006a; Turner, 2007; Turner and Dalton, 2005), we
model the distance from every street segment to all other street segments, by means of
easiest paths (Nourian, van der Hoeven et al., 2015), considering the cognitive impedance
of path complexity, the physical impedance of slopes for pedestrians or cyclist and the
length of the paths. Using this methodology, we compute an asymmetrical matrix of
distances [D
i,j
] containing temporal walking/cycling distances between any possible pair
of origins and destinations within the network. This model provides for the first three
steps of the generalization.
Here we explain and prove that the transition fluxes to destinations beyond the accepted
range of travel can be safely ignored as being equal to zero. First, observe that for a traveler,
there are infinitely many locations beyond reach, but only a countable number of locations
within reach, i.e. within a catchment area.
We can verify this by considering the inverse of the closeness function (Nourian, 2016):
x¼logit C xðÞðÞ0:5lRðÞ=l:
Therefore, when the perceived closeness of a location approaches zero, it can be any location
farther than the reach range, even infinitely far away, that is:
lim
CxðÞ-0
ln 1CxðÞ
CxðÞ
lR
2
l¼lim
CxðÞ-0
1
lln 1
Cx
ðÞ
¼1:
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Now, considering the distance x¼D
i,j
we formally define S
i,j
in terms of the population
within a catchment area, in which P
k
denotes the (projected) population of a location:
Si;j¼X
kA0;n
½Þ
Pk9Di;kpDi;j
kaiðÞ
kajðÞ
()
:
Therefore, if D
i,j
approaches infinity, the number of kth destinations fitting to the above
conditions will be infinitely many, going beyond the boundaries of the network; and
so, the sum of populations will be virtually unbounded and thus approach infinity,
i.e. limDi;j-1Si;j¼1. Hence:
lim
Di;j-1Ti;j¼lim
Di;j-1
m2
inj
miþSi;j
miþnjþSi;j
¼lim
Di;j-1
m2
inj
s2
i;j
¼0:
Therefore, we conclude that we can safely assume T
i,j
¼0 when D
i,j
WR, this is because
for a traveler (pedestrian/cyclists) any destination beyond reach is considered infinitely
far away.
If we consider a metric buffer large enough to ensure that its equivalent travel-time is
larger than R, then the model shall not suffer from the so-called network “edge effects”
(Gil, 2017). To convert Euclidean distance to travel-time distance for walking/cycling,
we adopt the equations ( from Tobler, 1970; Nourian, 2016):
In which, δdenotes metric distance (displacement), αdenotes slope and D
m
(δ,α) denotes
(modal: walking or cycling) travel-time distance. This means, to ensure a large-enough
buffer, we can rely on the inverse of these functions:
These two functions can be interpreted as:
•the typical pace of walking on a flat terrain is nearly 84 meters per minute;
•the typical pace of cycling on a flat terrain is nearly 269 meters per minute; and
•a typical reach range for a cyclist is nearly 3.2 times more than that of a pedestrian
for the same travel-time.
Using appropriate multiples of these values to enlarge the extents of a map, we can ensure
that the model shall not suffer from the so-called edge effects because in presence of any
terrain, the actual walking/cycling distances will be larger than those assumed.
In order to visualize, understand and analyze the results of the radiation model, we need
to attribute the transition flows to some kind of arcs, lines or in general geodesics in between
every two points. At the same time, we need to compute the catchment populations in order
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to compute the flows in between two points. We compute the flows and attribute them to the
network geodesics between all pairs of origin–destination. However, before proceeding with
the flow computations, we must find out how the populations values can be attributed to
locations outside of the network space (typically building polygons) are attributed to and
indexed as to the locations on the network (nodes). For such an attribution, we follow two
procedures to find, respectively:
(1) which street segments (L) are closest to which building polygons (P); and
(2) which building polygons (P) are closest to which street segments (L).
Exemplary results
In this section, we show exemplary results of the algorithms in order to illustrate their
functionality (Figure 8).
We have verified that the network radiation model works in a network space.
To illustrate the steps taken in verification, we show how the network radiation model
works on a on a symmetrical regular grid. These results clearly verify the proper
functionality of the model.
Interpreting the results of the network radiation model on Lisbon requires a statistical
analysis. It is even visually clear that in the case of the hypothetical homogenous grid
network, the radiation flows correspond directly to the distribution of population; however,
in the case of the heterogeneous network (Lisbon), it appears that the distribution of flows
does not significantly change in spite of the change in the distribution of population.
By statistically inspecting the four numerical distributions of flows in the four hypothetical
population distributions, we can see that indeed the distributions are nearly the same
and that they are all in the form of power-law distributions. This is indeed an interesting
phenomenon that can be interpreted as the high influence of network configuration on
mobility fluxes; however, to draw such conclusions, further studies are needed to
validate the model.
In Figures 9 and 10, we have shown four hypothetical distributions of a fictitious
population of 10,000 people for the depicted area in Lisbon and simulated flows of pedestrians
and cyclists, respectively. In Figure 11, we show the statistical distributions of pedestrian
flows. As also evident from Table I and Figure 11, the distributions are very similar.
Data analytics
In this section, we suggest some generic methods for testing, validating and calibrating the
proposed models and methods. We have chosen to illustrate exemplary results on a 1 square
Notes: From left to right, with a uniform distribution of population on building plots, with a
u
niform distribution of populations from southeast to northwest, with a bell-like distribution, with
a random distribution (the warmer the colors, the higher the populations). The street flows are
depicted by shades of gray; the darker the color, the higher the flow
Figure 8.
The exemplary
results of the radiation
model on a
hypothetical
grid network
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km-sized map of Lisbon, especially because of the considerably hilly landscape of the city.
However, if the topographic terrain is negligible, the methods can be applied in an analogous
way. In the absence of a topographic terrain, the matrix of distances between origins and
destinations will be a symmetric matrix. Note that our method ignores the directional
limitations imposed on cycling movements as well as traffic lights, climatic conditions,
pavement quality, presence of stairs, etc.
Geo-data: street lines and building polygons
The main geo-data inputs required for the proposed models include street centerlines,
building polygons and (optionally) topographic terrain models as digital terrain models
(DTM) or digital elevation model. Street centerline and building polygon data can be
acquired from OpenStreetMap (OSM) or governmental geo-data sets. The topographic
terrain model needed for the models must be provided as a triangulated irregular network or
a polygon mesh; however, the DTM models are often available as raster models. The raster
models can be used to generate 3D points, from which, using Delaunay triangulation, a
terrain model can be generated.
Demographics: estimating population density or occupancy
The census data are almost always too coarse (spatially) to be of use in any model for
walking/cycling mobility. Due to privacy considerations, the population census statistics are
not provided per building, but they are aggregated per larger area units (e.g. postcode
zones). However, as for pedestrians and cyclists, the distances that might be short for car
riders might be quite long; therefore, fine resolution occupancy data are needed for making
walking/cycling models. Besides, the typical population data from census only consider the
dwellers as the population, but in prediction of pedestrian/cyclist fluxes, we need to work
with the occupants. For this reason, working with some indicator of the actual occupancy
rate is suggested for obtaining population counts for the network radiation model.
For instance, the actual energy consumption values or usage data from a cellular
communication network might give a better indication of occupancy than the population
data alone from the census.
Note: The warmer the color, the more the population
Figure 9.
Local pedestrian
flows, given different
hypothetical
(occupancy)
populations
Note: The warmer the color, the more the population
Figure 10.
Local cyclist flows,
given different
hypothetical
(occupancy)
populations
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As an example, we can refer to the public open data of annual average electricity
and gas consumption data for polygons (separately for residences (woningen) and
businesses (bedrijven)) identified by postcodes in the Netherlands provided as open data
by the Dutch Government (on PDOK) and the coarse resolution population data provided
Simulated
Mobility Flux
Simulated
Mobility Flux
Simulated
Mobility Flux
Simulated
Mobility Flux
1,000
800
600
400
200
0
919
118 42 50 33 34 29 11 12
12
21
28
25
45
41
43
132
902
15 16 17 11 610 2
2
2
2
0000 0
0
0
000070
00000
12
6
1118161712
29
31
32
44
46
114
0
13
7
9
1818
111 1 1
1
1
1111118
16
16 12
13
3533
24
52
116 42 19
1111
1111
1,000
800
600
400
200
0
1,000 926
800
600
400
200
1,000 920
800
600
400
200
0
0
[0, 200] [0, 210]
(200, 400] (210, 420]
(420, 630]
(630, 840]
(400, 600]
(600, 800]
(840, 1,050]
(800, 1,000]
(1,000, 1,200]
(1,200, 1,400]
(1,400, 1,600]
(1,600, 1,800]
(1,800, 2,000]
(2,000, 2,200]
(2,200, 2,400]
(2,400, 2,600]
(2,600, 2,800]
(2,800, 3,000]
(3,000, 3,200]
(3,200, 3,400]
(3,400, 3,600]
(3,600, 3,800]
(3,800, 4,000]
(4,000, 4,200]
(4,200, 4,400]
(1,050, 1,260]
(1,260, 1,470]
(1,470, 1,680]
(1,680, 1,890]
(1,890, 2,100]
(2,100, 2,310]
(2,310, 2,520]
(2,520, 2,730]
(2,730, 2,940]
(2,940, 3,150]
(3,150, 3,360]
(3,360, 3,570]
(3,570, 3,780]
(3,780, 3,990]
(3,990, 4,200]
(4,200, 4,410]
(4,410, 4,620]
(4,620, 4,830]
(4,830, 5,040]
(5,040, 5,250]
(5,250, 5,460]
(5,460, 5,670]
[0, 210]
(210, 420]
(420, 630]
(630, 840]
(840, 1,050]
(1,050, 1,260]
(1,260, 1,470]
(1,470, 1,680]
(1,680, 1,890]
(1,890, 2,100]
(2,100, 2,310]
(2,310, 2,520]
(2,520, 2,730]
(2,730, 2,940]
(2,940, 3,150]
(3,150, 3,360]
(3,360, 3,570]
(3,570, 3,780]
(3,780, 3,990]
(3,990, 4,200]
(4,200, 4,410]
(4,410, 4,620]
(4,620, 4,830]
(4,830, 5,040]
(5,040, 5,250]
(5,250, 5,460]
[0, 210]
(210, 420]
(420, 630]
(630, 840]
(840, 1,050]
(1,050, 1,260]
(1,260, 1,470]
(1,470, 1,680]
(1,680, 1,890]
(1,890, 2,100]
(2,100, 2,310]
(2,310, 2,520]
(2,520, 2,730]
(2,730, 2,940]
(2,940, 3,150]
(3,150, 3,360]
(3,360, 3,570]
(3,570, 3,780]
(3,780, 3,990]
(3,990, 4,200]
(4,200, 4,410]
(4,410, 4,620]
(4,620, 4,830]
(4,830, 5,040]
(5,040, 5,250]
(5,250, 5,460]
Number of Streets per Flux Range
Notes: From the top, for hypothetical population distributions, Uniform, West-Center,
South Center and Random, respectively (shown previously)
Figure 11.
Histograms of
simulated
mobility fluxes
(number of
pedestrians)
for 1,321 streets in
the Lisbon network
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for the chosen district (“Buurt”in Dutch). It can be assumed that the number of people
living/working in an address on an average annual basis is correlated with the
consumption of gas and electricity. The consumption of gas is measured in terms of cubic
meters and the consumption of electricity is measured in terms of kilo watt hours.
These values are incommensurate, and so, they cannot be added together, but we can
multiply the two values to get an indication of the intensity of use of space. Knowing the
average electricity and gas consumption values per person for residents and employees,
we can possibly estimate the occupancy population of the building polygons.
Such estimates can be adjusted and checked against the resident population of the
district polygons (Buurten).
Data collection and validation of mobility models
We suggest a procedure such as the one proposed in (Sileryte et al., 2016) for collecting the
annual average of walking or cycling GPS trails for validating our mobility models. This
procedure, briefly, can be explained as extracting the GPS trails every eight days within a
year so that different days, seasons, weather conditions and other factors possibly
influencing mobility are sampled without bias. Then the number of times a trail falls
through a “street segment”is counted. It must be noted that the spatial structure of GPS
tracks is so that they refer to Euclidean space, i.e. a GPS trail consists of position
coordinates. However, in validating or calibrating a spatial model whose space is a network
space, any such trail must be first projected to the relevant nodes on the network (streets).
For this very reason, a dual network model (street–street interconnections) such as the one
proposed here can work better than a primal network model (junction–junction
interconnections). This way, the number of times a certain street segment is used on an
annual average basis is counted. The distribution of these counts can be statistically
compared against the distribution of flows from our models (e.g. local betweenness
centrality or network radiation). Such statistical comparisons provide for validation or
calibration of network mobility models.
Uniform West-Center South-Center Random
Mean 369.1617 Mean 355.8446 Mean 366.1829 Mean 369.894
SE 18.28717 SE 16.87647 SE 18.23119 SE 18.2337
Median 91.24477 Median 95.4273 Median 87.82151 Median 90.505
Mode 0 Mode 0 Mode 0 Mode 0
SD 664.6575 SD 613.3848 SD 662.6228 SD 662.713
Sample
variance
441,769.6 Sample
variance
376,241 Sample
variance
439,069 Sample
variance
439,189
Kurtosis 11.66015 Kurtosis 7.673449 Kurtosis 10.67179 Kurtosis 11.3239
Skewness 3.026711 Skewness 2.655037 Skewness 2.950699 Skewness 2.99135
Range 5,511.152 Range 4,304.772 Range 5,330.66 Range 5,431.61
Minimum 0 Minimum 0 Minimum 0 Minimum 0
Maximum 5,511.152 Maximum 4,304.772 Maximum 5,330.66 Maximum 5,431.61
Sum 487,662.6 Sum 470,070.7 Sum 483,727.6 Sum 488,631
Count 1,321 Count 1,321 Count 1,321 Count 1,321
Largest(1) 5,511.152 Largest(1) 4,304.772 Largest(1) 5,330.66 Largest(1) 5,431.61
Smallest(1) 0 Smallest(1) 0 Smallest(1) 0 Smallest(1) 0
Uniform West-Cent South-Cent Random
Uniform 1
West-Cent 0.988247 1
South-Cent 0.997574 0.987464 1
Random 0.996846 0.985114 0.995889 1
Table I.
Descriptive statistics
of simulated mobility
flows for pedestrians,
using the network
radiation model
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Implementation
The algorithms are implemented in Microsoft .NET framework, using the C# language.
Geometric algorithms are based on Rhinocommon.dll that is the kernel of Rhino3D
(McNeel, 2017); visualization and tests have been done on Grasshopper3D (Rutten, 2007);
the easiest paths are found using the toolkit Configurbanist (Nourian, Rezvani, et al. 2015).
The geo-data from OSM are harvested using the toolkit Elk (Logan, 2012). Numerical
calculations have been performed using Accord.NET (de Souza, 2014).
Conclusion
The proposed analytic models can be used in assessing sustainable urban mobility
planning scenarios such as pedestrianization and cycling infrastructure design, primarily
to measure the effectiveness of proposed interventions in terms of accessibility and
mobility potentials. For instance, such methods can be used in order to find out whether a
new plan for a set of bike-sharing stations is well laid out in terms of accessibility of
stations, as in, for example, how many people will be served in the 3-minute walking
catchment area of these stations, especially incomparisonwithanalternative,ortofind
out how effective it could be to add a pedestrian bridge over a river/valley and where
would be best to place that bridge to ensure highest achievable effect. The complexity of
accessibility and mobility for walking and cycling is twofold: on one hand, the physical
complexity of the urban networks affects the distances and the physical ease of walking
and cycling, and on the other hand, the cognitive complexity of the environment affects
both the perception of accessibility and the choice of walking and cycling as the preferred
mode of transportation. We have used a model of easiest paths to encompass the cognitive
complexity of way-finding in our models. However, the entirety of accessibility and
mobility is in reality much more intricate that can be possibly modeled mathematically;
this is because in reality, many factors play a role in shaping actual flows of people,
namely, climatic conditions, pavement quality, particular/contextual attraction or
repulsion of destinations, scenic quality of places, etc. (some of which might be
possibly taken into account in modeling mobility). Nevertheless, in urban planning, it is
desirable to have models that can explain and thus predict the long-term effect of potential
interventions (not on an individual but on a typical citizen), models that can explain the
spatial dynamics of a city. These models will be, by definition, abstract simplified versions
of reality, whose purpose is not only to predict the spatial dynamics, but also to explain
their underlying mechanisms.
We have generalized the radiation flow model of trip distribution for walking
and cycling on networks. The network radiation model needs to be validated and
calibrated using actual mobility data. Such data can be harvested from crowd-sourced
mobility trails collections. The model is verified in terms of providing plausible results
(as apparent from its application on a regular grid). A preliminary conclusion from the
exemplary results of the network radiation model could be that the flow of pedestrians
and cyclists (at least as simulated with this model) is to a large extent determined merely
by the configuration of the network itself, rather than the distribution of population.
However, for interpreting the implications of the model predictions in real-world urban
contexts, such as the ones shown on Lisbon, a larger statistical analysis is needed and
suggested for future research.
Note
1. A topological space that is everywhere locally similar to a Euclidean space of dimension 2;
definition adopted from: http://mathworld.wolfram.com/Manifold.html
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Corresponding author
Pirouz Nourian can be contacted at: p.nourian@tudelft.nl
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