# Active-travel modelling: a methodological approach to networks for walking
and cycling commuting analysis.

Ivann Schlosser  Centre for Advanced Spatial Analysis, University College
London, London, W1T 4TJ, UK  Valentina Marín Maureira  Centre for Advanced
Spatial Analysis, University College London, London, W1T 4TJ, UK  Richard
Milton  Centre for Advanced Spatial Analysis, University College London,
London, W1T 4TJ, UK  Elsa Arcaute  Centre for Advanced Spatial Analysis,
University College London, London, W1T 4TJ, UK  Michael Batty  Centre for
Advanced Spatial Analysis, University College London, London, W1T 4TJ, UK

###### Abstract

Walking and cycling, commonly referred to as active travel, have become
integral components of modern transport planning. Recently, there has been
growing recognition of the substantial role that active travel can play in
making cities more liveable, sustainable and healthy, as opposed to
traditional vehicle-centred approaches. This shift in perspective has spurred
interest in developing new data sets of varying resolution levels to
represent, for instance, walking and cycling street networks. This has also
led to the development of tailored computational tools and quantitative
methods to model and analyse active travel flows.

In response to this surge in active travel-related data and methods, our study
develops a methodological framework primarily focused on walking and cycling
as modes of commuting. We explore commonly used data sources and tools for
constructing and analysing walking and cycling networks, with a particular
emphasis on distance as a key factor that influences, describes, and predicts
commuting behaviour. Our ultimate aim is to investigate the role of different
network distances in predicting active commuting flows.

To achieve this, we analyse the flows in the constructed networks by looking
at the detour index of shortest paths. We then use the Greater London Area as
a case study, and construct a spatial interaction model to investigate the
observed commuting patterns through the different networks. Our results
highlight the differences between chosen data sets, the uneven spatial
distribution of their performance throughout the city and its consequent
effect on the spatial interaction model and prediction of walking and cycling
commuting flows.

##  1 Introduction

Urban mobility, a key component of urban dynamics, intersects with various
areas of urban life including economy, environment, and social structures.
This critical aspect involves the movement of people and goods within urban
areas, and its efficiency and sustainability directly influence the overall
functioning of cities. Given its significance, it is crucial to acquire
knowledge and understanding that help plan and develop improved mobility
networks. This represents an ongoing challenge, as both transport methods and
human mobility patterns continue to evolve.

An essential aspect of urban mobility is commuting, which is defined as the
regular travel between residence and work places. Observing trends in
commuting patterns can provide valuable insights into broader shifts in urban
mobility. Nowadays, there is an increased focus on small-scale movement,
primarily through cycling and walking. These modes of transportation are often
grouped under the term "active-travel". Contemporary planning practices
accentuate their importance for reasons of health, sustainability, and safety.

While active travel currently represents a moderate share of commuting methods
in England, with about 10% [35], this figure is projected to increase. The
rise in active travel not only signifies potential reductions in air and noise
pollution due to less reliance on cars, but also implies urban redesign
opportunities. The decrease in space required for parking and driving could
allow for expanded green areas, and increased housing, leisure and commercial
spaces [18]. Given the current context of rising living and transport costs
and global supply chain disruptions, active travel represents a practical and
cost-effective transport alternative. Therefore, gaining a better
understanding of the active travel flow patterns could help us adapt to these
trends and meet the evolving needs of the population.

In this paper, we conduct a methodological analysis to study active travel.
The study compares different walking and cycling networks to investigate how
different models predict real-world flows. The findings of this research have
tangible implications for policymakers and urban developers. By providing a
more accurate understanding of active travel flows, the results can assist in
the formulation of strategies that facilitate and promote walking and cycling.

The paper is structured into three main sections: Networks, Routing, and
Modelling. In the first section, the focus is on constructing and comparing
different walking and cycling networks from open data sources. In the second
section different cost matrices are built based on shortest paths distances
for each specific network using different origin-destination centroids. Upon
examining the resulting detour index of various networks, we observe
substantial disparities between the standard detour values and those that
incorporate the real flows between locations. Even in the absence of ground
knowledge of paths taken, relying on such metrics can prove helpful to
construct efficient links between populations and job distributions. The final
section integrates previous insights into a spatial interaction model,
assessing the predictive capabilities of the different networks and routing
parameters in relation to real walking and cycling flows. Finally, we combine
these flows to model active travel commuting as a single phenomenon. We apply
this method in London at the Middle Layer Super Output Area (MSOA) scale
taking 2011 census data sets as reference for observed commuting flows.

The results show that choosing the appropriate network and distance measure
can impact the accuracy of flow estimations, making it key to carefully
consider network construction and analysis to ensure more accurate
outputs.These findings not only bring attention to the differences between
networks, but also stress how results diverge throughout the city, contingent
upon the distribution and connectivity of networks as well as the uneven
coverage of distinct data sources.

###  1.1 Walking and cycling

Walking and cycling are active modes of transport because they require
physical activity and are recognised for their potential health benefits and
low carbon impact. Research has shown that they are associated with improved
cardiovascular health, reduced risk of chronic disease, and better mental
health outcomes [47, 21, 34]. They are considered sustainable modes of
transportation due to their low carbon footprint and potential to promote
transportation equity. In addition, they are cost-effective alternatives to
traditional modes of transport. On the contrary, an increasing amount of
literature is pointing at the fact that cars inside cities cause a series of
problems that impact our health and well-being, such as noise and air
pollution [13], free space availability [18], congestion and heat island
effects.

All those problems can be tackled with efficient public transport, active
travel and policies. Thus, it is necessary to rethink and adapt infrastructure
to better integrate them in the urban layout. Many of the worlds biggest
cities are turning towards cycling as a sustainable and efficient mode of
transport, incorporating new policies that facilitate the development of
cycling infrastructure, and discouraging car driving. New York
111https://onenyc.cityofnewyork.us/wp-
content/uploads/2019/05/OneNYC-2050-Efficient-Mobility.pdf ,
Chicago222https://www.chicago.gov/content/dam/city/depts/cdot/CDOT%20Projects/Strategic_Plan/Strategic_Plan_for_Transportation21.pdf
, San Francisco
333https://sfgov.org/sfplanningarchive/ftp/General_Plan/I4_Transportation.htm
, Boston 444https://www.boston.gov/sites/default/files/document-
file-06-2018/ib2030_book_spreads-transportation.pdf , Singapore
555https://www.ura.gov.sg/Corporate/Planning/Master-Plan/Themes/Convenient-
and-Sustainable-Mobility and others mention cycling and walking as central
elements of their current and future public transport policies in their latest
master plans.

Walking and cycling share many similarities as active travel modes yet also
exhibit some distinctions. While cycling is typically characterised as faster
and more suitable for longer journeys, it necessitates specialised equipment
and could present more safety risks due to the increased vulnerability of
cyclists on the road. Walking is more accessible, exempt from equipment
requirements, and generally considered safer. These modes differ substantially
in terms of their typical movement speeds. For walking, speeds of around
$V_{w}=1.3\unit{m.s^{-1}}(4.6\unit{km.h^{-1}})$ [57, 17] are usually assumed,
while for cycling the value are usually of about
$V_{c}=4.2\unit{m.s^{-1}}(14\unit{km.h^{-1}})$ [46]. This results in
significant differences in the area that can be covered within a given time,
with cycling being a more efficient way to cover longer distances while
walking may be better suited for short journeys.

###  1.2 Commuting and recreational trips

As with other modes of transport, it is common to distinguish trips by
purpose, commuting on one hand, and leisure on the other. The two types of
travel have varying influencing factors, and require different approaches for
analysis and specific planning and policy interventions [22].

Factors such as a high-quality built environment, urban amenities,
infrastructure, land use mix, and street scenery can impact the decision to
walk or cycle for both recreational and commuting trips [48, 8], but also
factors like safe and diverse route options and the availability of
destinations within a reasonable walking or cycling distance. Specifically for
cycling, there is consistent evidence that the quality, extent, and
connectivity of a road or cycle network have a positive correlation with
cycling uptake [8, 12]. Under the context of walking and cycling for
commuting, time and distance are crucial factors. Recreational trips are
typically less frequent, more flexible, and do not prioritise travel
time/distance efficiency. Conversely, commuting trips are done regularly, with
time constraints being a significant factor in route choice. As a result,
commuting trips tend to prioritise distance and be less responsive to other
variables [7].

With distance being identified as a major barrier to active travel, it is
essential for predicting and explaining travel behaviour. As such, analysing
shortest paths within cycling and walking routes provide a useful benchmark
for identifying optimal commuting routes. While shortest paths may not always
align with observed route choices, empirical evidence suggests that people
generally do not deviate significantly from the shortest distance route, with
most trips being less than 10$\%$ longer than the optimal path [56, 28].

##  2 Networks

This section considers the aspects directly related to downloading and
manipulating open data to construct road networks, modelled as graphs with
positive edge lengths. Using different types of networks can further on allow
us to build varying distance matrices to examine the potential active travel
between locations.

When it comes to calculating the shortest paths between origins and
destinations, there are different distance metrics that can be used. On top of
considering euclidean distance between locations, it is important to account
for the actual distance travelled on the road network between two points.
Doing so allows to build a more accurate understanding of the spatial
distribution of trip lengths originating from or reaching a place, thus
uncovering some connectivity aspects, local network properties and their
impact on the magnitude of active travel flows.

###  2.1 Road networks

Networks representing physical roads have already received a fair amount of
attention in the literature and their properties have been observed across
geography and even time [50, 30, 2], to study economic indicators [44, 43, 23,
41], to perform comparative analysis between cities [19, 51], to examine
social and demographic indicators [54, 32], and asses accessibility to land-
uses [14, 33], to name a few. In the context of network science, street
networks are commonly represented using a directed or undirected primal and
planar graph. In primal graphs, a road network is modelled using links to
represent the street segments and nodes to represent street junctions [42,
29]. While planar means that the network is constrained to a two-dimensional
space.

The level of detail required to construct street networks for graph analysis
can vary depending on the specific analysis objectives, which may have
different effects on the outcomes [29, 2, 20]. For analyses at a very local
scale, a more intricate street network is typically used, which is constructed
by taking into account pedestrian-specific infrastructure like crosswalks and
sidewalks [38, 45, 52]. In studies focused on spatial configuration and human
behaviour, such as those using the Space Syntax theory, street networks are
constructed using centre lines that represent angular changes [40]. In this
paper, we aim to use open data sources and construct an undirected primal and
planar graph with an optimal level of resolution for active travel routing and
modelling. To do so, we use the two most detailed available representations of
the road network currently available for the UK.

First, England’s official provider of digitised infrastructure data, Ordnance
Survey 666https://www.ordnancesurvey.co.uk/business-government/products/open-
map-roads covering England, Wales and Scotland, is used. Second, OpenStreetMap
(OSM) , an open source platform aiming at digitising as much of the physical
world as possible. It does so through user contributed map features that have
a detailed tagging system associated to them. The high quality of the road
networks data makes it highly used in modern research on the built
environment. Among the advantages of using OSM are transferability between
areas of observation and scalability, making any analysis scalable to the
whole planet. It allows large scale road network analysis [15, 26, 1, 27],
going beyond the borders of a single country [6, 25], while maintaining
confidence in the quality of the data.

Figure 1: OS and OSM road network coverage in London, UK. a) Percentage of OS
over OSM road coverage, based on road linear metres per MSOA level. b) and c)
Overlapping of OS and OSM networks showing differences in coverage depending
on the urban structure of London areas, Marylebone and Stratford respectively.
Table in d) shows the percentage of linear metres from roads on OSM that are
not covered by the OS network. Percentages are organised by road types.

The two sources used present some differences that need to be put in context,
as evidenced by the comparison in figure 1. Although both data sets could
differ in terms of geographical extent, geometrical shape and attribute
accuracy of segments, this comparative study focuses mainly on the
completeness of the data sets. We examine to what extend their coverage is
suited for the analysis of pedestrian and cycling networks. OS Open Roads
considers exclusively roads that are used by cars, while OSM represents a
wider range. On figure 1 one can see the two data sets overlayed on two areas:
in Fitzrovia (b) and Stratford (c). The blue network being OSM and red being
OS. In b), most of the roads can be taken by car, the only differences can be
seen in pedestrian paths crossing squares and parks. But when looking at the
area of Stratford, the differences become more striking. In this case, the OSM
network presents a much greater set of roads, which are primarily dedicated to
pedestrians and cyclists, including those around and inside the mall and the
Olympic park. Further inspection shows that the difference of road linear
metres coverage for both networks is unevenly distributed across MSOAs (Figure
1a). Knowing in advance that OS is a more high-level representation of roads,
the higher coverage percentage of OSM is not a surprise. However, the high
difference between MSOAs is a fact to consider when analysing the results in
areas with different urban structures. We then examined whether the difference
was consistent across street types, so we measured the percentage that are not
covered by the OS dataset. Results show that streets classified as footways,
service, paths and cycleways in OSM are under covered by OS (Figure 1d).

###  2.2 Network setup

This section introduces some of the commonly used open source tools to
download and construct a road network. OSM data can be downloaded from a
number of sources, including the OpenStreetMap website and dedicated download
servers like Geofabrik 777https://www.geofabrik.de, which help download raw
OSM data in different formats as files with multiple layers of features.
Optimal access to this data can be achieved by using many software packages
across different programming languages. We mainly consider R and python
packages as they are widely used in the community. With each being designed
for different purposes, the format and attributes within the data can vary. We
considered a non exhaustive list of packages and the main criteria used to
select the appropriate one are shown in table 1.
OSMnx888https://OSMnx.readthedocs.io/en/stable/ [4] is a python
package,osmdata 999https://docs.ropensci.org/osmdata/ [37] and osmextract
101010https://ropensci.github.io/osmextract/index.html [16] are R packages. We
examine and compare different sources for downloading and working with OSM
road networks to evaluate which is the most suitable considering the
requirements of our analysis (Table 1). Therefore, we will be using OSMnx as
the source of OSM data.

| osmdata | osmextract | Geofabrik | OSMnx
---|---|---|---|---
Big data | no | yes | yes | yes
Optimal for building graphs | no | no | no | yes
High details | yes | yes | yes | no

Table 1: Overview of packages for working with OSM road networks. This list is
non exhaustive and contains the options considered [28, 5, 9] as well as the
main criteria for selection. The first category, Big data implies that it is
possible to download region and country scale data sets. Optimal for building
graphs means that the downloaded data is structured in a way that allows to
build graphs without further engineering. Usually, it would be divided into
two data sets, one containing nodes with their id, coordinates and additional
optional attributes. The other data set contains edge ids, origin node id,
destination node id and extra optional arguments such as length. Finally, High
details means that several columns of OSM key$\sim$tag values are present
additionally to the main classification corresponding to the highway key.
Additionally, some even more powerful command line tools are available, and
would be useful for a bigger scale of analysis, but are omitted from this
work.

As streets have varying attributes and serve distinct purposes, network
modelling for specific modes of transportation, such as buses or private cars,
only incorporates streets suitable for those modes. However, when it comes to
walking and cycling networks, the definition is less precise as pedestrians
and cyclists can move more freely throughout the city. This has promoted the
interest for creating alternative network profiles using the OSM network as a
base. Therefore, additionally to downloading the desired networks, some
packages offer the functionality to filter the roads based on a specific mode
of transport, like walking, cycling or driving. The OSMnx package in python
provides profiles for different transport modes by filtering out streets based
on the tag keys. The dodgr 111111https://atfutures.github.io/dodgr/ [36]
package in R creates alternative profiles by weighting the segments according
to different attributes such as speed, preferences and restrictions. Moreover,
since both profiles rely on the accuracy of the attribute tags given to each
street when it is mapped on the OSM network, we first examined whether some of
the streets were miss-classified resulting in the inappropriate exclusion or
inclusion of street segments (Figure 2).

Figure 2: OSMnx walk and cycle profiles overlapping the OSM full network. The
OSM full network in different colours showing the class types that are
filtered out in the walk and cycle network. a) In grey the OSMnx walk profile
on top of the full network. In cian The Greenway footpath running from
Victoria park to the southeast, and classified as cycleway. Other footpaths
within parks are also classified as cycle ways only. b) In grey the OSMnx
cycle profile, in green, the Woolwich and Greenwich foot tunnels highlighted.
Given that these tunnels are classified as footways in the OSM network, they
are filtered and not considered within the cycle profile.

By looking at figure 2, the streets that were filtered out (in colors) from
each profile (in gray) can be identified. For instance, in the case of walking
(a), some routes along parks and The Greenway footpath, which runs from
Victoria Park to the southeast are excluded from the network as are classified
as cycleways in the OSM dataset. A similar case is that of (b), where the
tunnels that cross the Thames are excluded from the cycling network as they
are classified as footways. As a result, connectivity costs are increased,
which may affect global and local patterns, such as the connectivity within
East London or between the north and south areas of the river.

Based on these initial observations, different network profiles are used to
create distinct OD cost matrices between MSOAs, including those provided by
popular packages, and one where minimal filtering was done (motorways removed
as forbidden to cycle or walk on) to serve as a base model for our tests. The
Ordnance Survey (OS) data is also used as it is the official and open source
reference for the road network in the UK.

##  3 Routing

The next step in developing our analysis consists in using the networks for
routing origins and destinations. In the scope of this work, we will only look
at the distances that separate OD pairs in the network by using shortest paths
algorithms. To accomplish this, we compared a set of commonly used packages
for computing shortest paths. We then examined various approaches to determine
origin-destination points for commuting, particularly when data is aggregated
at geographical units, such as the MSOA level in this case. As a result of
this procedure, different cost matrices are created, one for each network,
which will serve as inputs for the following section to obtain the prediction
of pedestrian and cycling commuting flows.

###  3.1 Shortest paths

We consider the distance between an origin and destination in a specified
network to be the length of the shortest path that connects them. An
alternative approach that can be used and is already implemented with certain
packages is to consider time. An extra layer of sophistication can also be
added by attributing additional weight factors to each link of the network
based on its classification and the willingness of cyclists or pedestrians to
use it. For example, a commuter might have a tendency to use a smaller,
quieter route of greater length rather than a shorter, but busy and risky one.
For the purposes of our work, we prioritise distance as the most critical
factor for commuting decision-making, which also provides an approach that is
easy to implement for a large scale analysis and can be further developed with
more variables in future works. The other methods could be useful to learn
more about path choice of commuters, who on the one hand think about their
safety and comfort, but on the other aim to minimise their trip distance or
duration. The significance of other factors may be challenging to validate and
is left out of the scope of this work.

Table 2: Mean and median times in seconds to compute a distance matrix between 50 and 100 randomly chosen locations. Different types of heaps are tested for dodgr and two different algorithms for cppRouting, as well as multiple core run when this functionality is provided. sf_networks [53] is a package that, together with tidy_graph [39] relies on igraph [10] for routing. Tests are done with the microbenchmark [31] package in R. The hardware used is a 2022 M2 MacBookPro with 16 GB RAM.  |  | 1 thread, 50x50 OD | 4 threads 100x100 OD
---|---|---|---
package | option | mean | median | mean | median
tidygraph | - | 5.13 | 5.13 | - | -
sf_networks | - | 4.10 | 4.06 | - | -
dodgr | fheap | 24.12 | 22.92 | 18.66 | 17.81
dodgr | bheap | 16.87 | 16.89 | 13.91 | 13.90
dodgr | triheap | 26.96 | 26.61 | 20.54 | 19.79
cppRouting | phast | 2.40 | 2.41 | 1.37 | 1.37
cppRouting | mch | 0.35 | 0.34 | 0.37 | 0.37

Based on the outputs from the benchmark shown in table 2, we use the
cppRouting package in R to perform the one-to-one and many-to-many
calculations and to build distance matrices. This package implements fast,
multi-threaded processes, relying on the Dijkstra [49], A-star and PHAST
algorithms as well as a contraction hierarchy optimisation which greatly
reduces computational times on big graphs.

Figure 3: Origin-destination centroids (Beddington MSOA illustrated here).
a)The geometric centroids from every MSOA polygon. b) The network centroid
based on the distribution of the street network within the MSOA boundary by
taking the centre of mass of a sample of road intersections between “living
street", “primary", “secondary", “tertiary", “trunk" and “residential" OSM
road types (in blue). c) The "commute" centroids, based on the population
distribution (origin) in pink and job location (destination) in yellow.

###  3.2 Selecting origins and destinations

The next aspect of routing consists in solving the what to what problem,
namely determining the actual locations to use as the origin and destination.
This step is particularly important when the data is aggregated by relatively
big units of space (MSOA). For smaller units, like output areas (OA), this
question might not be as relevant, because they cover only the area of a few
houses, and thus a regular centroid will not bear significant difference from
any other node within an area. However, for larger areas that span about
$1\unit{km}$ and include multiple streets, overlap parks, rivers and rails,
this can become significant, as is demonstrated later on. Although it seems
appropriate to choose the smallest available resolution, breaking down the
system into small sub units comes at a great cost when running any model.
Aiming to develop a methodology that could further on be scaled up to the
country level, the MSOAs were used, with 983 in London.

We further consider 3 types of MSOA centroids that are illustrated in figure
3. The first one is the geometric centroid, that is quite commonly used in
research [3, 59]. The second one is referred to as network centroid and is the
centroid of a sample of nodes that lie within residential roads, this allows
to exclude parks, industrial or shopping areas. The third one is a tuple of
nodes. The first being the population weighted centroid
121212https://geoportal.statistics.gov.uk/datasets/ons::msoa-
dec-2011-population-weighted-centroids-in-england-and-wales/about that
accounts for the distribution of residents in space, and the other being the
workplace weighted centroid, that is obtained using the definition of
workplace
zones131313https://geoportal.statistics.gov.uk/datasets/ons::workplace-zones-
december-2011-population-weighted-centroids-in-england-and-wales/about in the
UK statistics office. We refer to this pair as the commute centroids. For each
centroid point, the nearest network node is assigned and the distance between
them is added to the final matrices.

###  3.3 Flows data

In the following, the methods and data described earlier will combined with
flows data to develop a metric that helps understand the commuting patterns of
active travellers.

The commuting data in this work comes from the 2011 UK census and is accessed
through the governmental data portal (See details in the appendix). It is
available in its raw format for research purposes to individuals linked to a
university. The flows contain information on the origin area, destination
area, and method of travel, for more details on the variables refer to the
online material141414https://github.com/ischlo/QUANT_at. Different levels of
spatial units are used in the UK census, and this study relies on MSOAs, which
are constructed to contain around 8000 individuals each. In this work, only
the data for cycling and walking is used for the flows. Additionally, the
flows on distances beyond 15km are considered as outliers or collection errors
and are excluded.

###  3.4 Detour index

When measuring the performance of networks in terms of distance, as in the
context of transport studies, it is useful to look at a measure called the
detour index, also referred to as circuity [2], which can take different forms
if we consider a whole network or a node, or a specific route:

$\delta_{ij,k}=\frac{l_{ij,k}}{d_{ij}}$ (1)

where $l_{ij,k}$ is the distance in the network $k$ between location $i$ and
$j$, and $d_{ij}$ is the Euclidean distance between them. If aggregating on an
origin node and considering a set of destination nodes, which is not
necessarily all the nodes in the network:

$\delta_{i,k}=\frac{1}{N_{S}-1}\sum_{j\in S,i\neq j}\delta_{ij,k}$ (2)

which gives the average detour index of the routes from node $i$ to all other
nodes of interest in set $S$ for a specified network $k$. And, for the whole
network other the set of nodes $S$:

$\delta_{k}=\frac{1}{N_{S}(N_{S}-1)}\sum_{ij\in S,,i\neq j}\delta_{ij,k}$ (3)

where $N_{S}$ is the number of nodes in set $S$. The detour index is greater
or equal to 1, and the more efficient, or straight, a network path is the
closer the value will be to 1. Typical values are between $1.1$ and $1.5$ and
values over 2 show a poor performance [24, 58]. This index has been linked to
important aspects of the network such as accessibility and efficiency. In [9],
the detour index was found to decrease with time in cycling networks. This
indicates a tendency of the network to ameliorate it’s connectivity, by
growing new links or changing the routing possibilities. In [24] it was
observed that users of the network tend to locate in places that minimise
detour for their commuting trip compared to a random selection of origin-
destination pairs. The authors observe different values of average detour for
random selections of OD nodes compared to observed OD flows, indicating that
the efficiency of the network is better understood through the mobility
patterns occurring in it. Hence, the consideration of a subset $S$ of the
nodes involved in observed OD flows, in our case the MSOA with flows between
them, is relevant to better understand commuting trip distributions in the
network.

In this section we took the different street networks and consider the
geometric centroids as origin-destination points for a straightforward
comparison.

Figure 4: Detour given walking and cycling times when comparing shortest paths
from the OSM and dodgr networks with the euclidian distances between MSOAs. We
converted distance into time cost using 1.3 m/s and 4.2 m/s as the walking and
cycling speeds, respectively. We excluded trips wich would take longer than 1
hour as a maximum threshold for commuting by these modes. We visualised
differences in time longer than 15 minutes as a way to highlight detours that
would have a greater impact on the decision to use active travel

We plot the detour distance values in Figure 4, translated into walking and
cycling times, to make the comparison of both modes easier. Differences in the
cost of the shortest paths between MSOAs are considerable across space.
Results are highly determined by the uneven distribution of the street network
provision and network impedance. Due to the lack of crossings in the east, for
example, MSOAs at each side of the Thames present the higher detour values
with commuting times reaching a difference of up to 3 hours. Higher
differences can be found in MSOAs with large green areas, large block sizes
and other barriers like train lines. Based on the results, when comparing the
different commuting times it is important to consider that the differences
between the network distances are not evenly distributed in space, and that
the selection of one or the other may affect the results of future analyses in
specific areas of the city.

(a)

(b)

(c)

(d)

Figure 5: The detour index is the ratio of the distance between two points in the network chosen and the shortest, Euclidean distance, $\delta^{k}_{ij}=\frac{l_{ij,k}}{d_{ij}}$, where $l_{ij,k}$ is the distance in the network $k$, and $d_{ij}$ is the Euclidean distance between those points. Clearly, $\delta\in[1,\infty[$. One can see that the kind of routing (fig 5(b)) proposed by the $\boldsymbol{dodgr}$ package results in longer shortest paths due to the weighting that favours smaller roads to bigger, busier ones for cyclists and pedestrians. The network that approaches the most the theoretical case of $\frac{\sum_{i,j=1}^{N}\delta^{k}_{ij}}{N(N-1)}=\bar{\delta^{k}}$ = 1, is the OSM full network, which contains short cuts and links not included elsewhere. The Ordnance Survey network (dashed purple line) is the least efficient of the networks without custom weighting profiles. On 5(a), one can observe the decreasing average detour and shrinking standard deviation as the Euclidean distance between locations increases. On figures 5(c) and 5(d), the detour distribution, weighted (solid line) and non weighted (dashed line) by commuter flow for different distance intervals of Euclidean distance of trips. The table in the appendix, presents the same observation for finer distance intervals, removing the effects of the growing number of destinations with distance. d (km) | OS | OSM
---|---|---
min | max | $\delta_{c}$ | $\delta_{n}$ | t-test | $\delta_{c}$ | $\delta_{n}$ | t-test
0.0 | 0.6 | 2.113 | 2.108 | 0.1 | 1.498 | 1.518 | -0.8
0.6 | 0.9 | 1.931 | 1.914 | 0.9 | 1.454 | 1.471 | -1.6
0.9 | 1.2 | 1.780 | 1.791 | -0.7 | 1.384 | 1.423 | -4.9
1.2 | 1.5 | 1.666 | 1.700 | -3.0 | 1.357 | 1.388 | -4.7
1.5 | 1.8 | 1.610 | 1.623 | -1.4 | 1.307 | 1.347 | -8.5
1.8 | 2.1 | 1.538 | 1.535 | 0.5 | 1.266 | 1.313 | -14.0
2.1 | 2.4 | 1.464 | 1.514 | -7.4 | 1.253 | 1.303 | -15.2
2.4 | 2.7 | 1.454 | 1.473 | -3.5 | 1.237 | 1.284 | -16.6
2.7 | 3.0 | 1.402 | 1.457 | -9.5 | 1.232 | 1.274 | -14.8
Table 3: This table summarises the detour for commuting trips and for typical
network values by distance ranges between origin and destination. It shows how
they significantly differentiate, especially as crow fly distance grows
(column $d$). In this table, we look at granular intervals, within the
distance band 0-3km (darkred distributions from figures 5(c) and 5(d)), the
full table for up to 15km is given in the appendix.

The distribution of all $\delta_{ij,k}$ is shown in figure 5(b). It is not
surprising to see that the resulting $\boldsymbol{dodgr}$ networks with a
custom weighting profile, which tends to increase the actual distances, show
greater values. The results for the remaining networks are more similar, with
slightly increasing mean and variance from the whole OSM network, followed by
the OSMnx walk and cycle profiles and finally OS. To our knowledge, there is
no research linking typical detour values to the density of the nodes and
edges of the network, however, it seems intuitively natural for a detour to
increase as a consequence of removing edges from a network. Hence, sparser
networks are expected to have greater typical detour values.

We further develop the detour index to account for the flows observed across a
set of origin-destination pairs. Let $w_{ij}$ be a flow observed between
origin $i$ and destination $j$, by weighting the detour values with the flow,
we obtain a more accurate representation of the detours that commuters take on
average during their commute:

$\delta_{c}=\frac{1}{W}\sum_{i,j\in S,i\neq j}w_{ij}\delta_{ij,k}$ (4)

where $W=\sum_{i,j\in S,i\neq j}w_{ij}$ is the total flow between different
origins and destinations.

One of the main characteristics of flows is that their magnitude decreases as
we get further from an origin. They also show a wider range of values for
shorter distances, spanning several orders of magnitude. At the same time, we
observe a decreasing average detour index as the Euclidean distance increases
(fig. 5(a)) between origin and destination, while the potential number of
reachable destinations from an origin grows approximately as the square of the
distance. These different trends introduce some non trivial relations between
flows, their magnitude, the distances on which they occur and their detour
values. To further uncover some patterns relating these, we look at the
distribution of the mean weighted detour (equation 4) of a trip and the mean
detour of the network in 300 metres intervals of Euclidean distance between 0
and 15 km. In this way we minimise the effects of a varying Euclidean
distance, and focus only on the typical values of the detour weighted and non
weighted by flow. Within each resulting interval we test for the significance
in the difference between the means, and find that it becomes strong (p-value
$\approx 0$) inside the interval 900-1200 metres (see table 3) and remains
statistically significant for all the distances beyond that. Moreover, the
t-statistic gets stronger as the Euclidean distance increases. This indicates
that for shorter trips, detour has a less significant or no impact on the
trip, but as the distance increases, we observe a significant shift of the
average weighted detour towards smaller values. This observation can be useful
when designing road infrastructure, where aiming to minimise a weighted detour
index of a population can potentially have a positive effect on the number of
trips done between locations, especially as the Euclidean distance separating
points gets greater. Figure 5(a) shows an example distribution of detours with
wider intervals for better visualisation purposes. We observe that as the
Euclidean distances increase, the distribution of detours narrows down and
shifts towards a smaller mean. This behaviour seems to be a fundamental
property of the detour index and has been observed for other real world road
networks. The full results for granular distance intervals and statistical
significance is included in the appendix table 4.

##  4 Modelling

This section considers the previous results and integrates the distance
matrices produced from the different network profiles and origin-destination
centroids into a spatial interaction model. With the available flows data, a
doubly constrained gravity model is built and tested.

###  4.1 Spatial interaction models

This family of models, also referred to as gravity models, has been around for
a while and was formalised in the late 1960s by [55]. It allows to build good
predictions of flows based on input variables that are relatively easy to
find. The name originates from the similarity with the gravity law derived by
Isaac Newton. This problem has been reformulated and formalised with
statistical considerations of the optimal assignment from a set of origins in
a grid to a set of available destinations under a cost value that depends on
the distance. Intuitively, we consider that there are factors contributing to
a greater flow of people between 2 given places and others reducing it. Some
parameters will thus be directly proportional to the flow of people while
others will be inversely so. The factors contributing to the flow positively
are usually taken to be the population at the origin location and the job
availability at the destination, while the distance between the two locations
has a inverse effect on the flow. Formally, this means that $T_{ij}\sim
O_{i}D_{j}f(d_{ij})$ where $O_{i}$ is the origin population in location $i$,
$D_{j}$ is the employment at the destination location $j$, $f(d_{ij})$ is a
decreasing function of the distance, usually referred to as generalised cost.
The known constraints of the system impose that all the flows originating at a
location $i$ must be equal to the local working population, while all the
flows arriving to a destination $j$ be equal to the local number of jobs,
thus:

$\begin{split}O_{i}=\sum_{j}T_{ij},\\\ D_{j}=\sum_{i}T_{ij}\end{split}$ (5)

The travel cost function can be derived [55] and has the form
$f(d_{ij})=e^{-\beta d_{ij}}$, where $\beta$ is an exponent that depends on
the system and is usually calculated for different modes of transport and
geographies. Additionally, the origin and destination weighting parameters are
obtained through the Lagrange multipliers method, resulting in a equation of
the form:

$T_{ij}=A_{i}O_{i}B_{j}D_{j}e^{-\beta d_{ij}}$ (6)

which is referred to as the doubly constrained one since the available
information about the system allows to set constraints on both the origin and
destination locations. Alternatively, if some information is missing, it is
possible to use only one constraint.

The parameters $A_{i},B_{j}$ are derived from the expression:

$\begin{split}A_{i}=[\sum_{j}B_{j}D_{j}e^{-\beta d_{ij}}]^{-1}\\\
B_{j}=[\sum_{i}A_{i}O_{i}e^{-\beta d_{ij}}]^{-1}\end{split}$ (7)

with values obtained through an iterative process [11].

The flows data is obtained via the census table with origin destination pairs
and number of commuters by mode of transport. The distance measures can be
obtained in different manners as discussed in section 3. The distance matrices
obtained are used in the gravity model further on.

###  4.2 Case Study: active travel commuters in London.

The methods described in the first two sections will now be combined with the
formalism of spatial interaction models to have a predictive model of active
travel commuter flows in London based on the different networks and centroid
types that were introduced.

(a)

(b)

(c)

Figure 6: Quality of fit calibration for different networks, mode, centroids.
The most significant impact on the quality of fit occurs when changing
centroids on the pedestrian model. Each legend element has first mentioned the
network from which the cost matrix (os,osm,dodgr,norm2), with norm2 indicating
the crow-fly distances matrix. And as second the type of centroids used.

The methods and data described earlier allows for a generalised approach to
modelling flows, and when applied to active travel commuters, provide some
high quality of fit results in the case study of London. Figure 6(a) shows the
results of the calibration of the model to maximise the $r^{2}$ value. The
quality of fit of the models using Euclidean distance between locations as
cost is also computed and, despite being lower than network distance, provides
a good estimate of the flow with values reaching $r^{2}=0.75$. One can see
that depending on the network, the maximum is reached for differing values,
and certain types of networks provide a better stability of the quality of fit
under a varying $\beta$ exponent than others. While all the networks reach a
high and very similar value of around $r^{2}=0.85$, they do it for different
values and the best quality of fit is reached with the OSM and OS networks
using commute centroids, indicating the importance of the discussion in
section 3.2 on the knowledge of where the routing is being done. The network
and geometric centroids appear less adapted for routing based on the quality
of fit obtained for all types of network considered.

##  5 Discussion and conclusion

In this work, we first conducted a methodological analysis covering network,
routing and modelling steps. By comparing different walking and cycling
networks and prioritising distance as a critical factor in commuting route
choice for active travel, we explored their capacity to estimate real-world
flows using a spatial interaction model. We use London as case study, using
the 2011 census flows at MSOA level. Throughout the process, we observe that
the use of different data sources, network construction, and routing
approaches can lead to diverse outcomes in the analysis, both at a broad city-
wide scale and at a more local level in different areas of the city. We
illustrate the limitations of the OSM data when attempting to select network
profiles for specific modes of transport. To counter these limitations, we
keep a network that is filtered only to exclude the types of roads that are
illegal to use as an active traveller, those are motorway and motorway links
and propose a combined active-travel framework allowing to model cycling and
walking trips. The results of the spatial interaction model show that this
type of network performs best when associated to what we defined as commute
centroids, accounting for the spatial distribution of residents and jobs
inside the census areas. The spatial interaction model that we calibrated on
this combination of network and centroid was the best fitting and most stable
across the cost function exponent values, highlighting the importance not only
of the parameters related to the network itself, but also to the routing
process. The quality of fit values for all networks were relatively high, and
the best predictions were obtained using the unfiltered OSM and OS networks
with commute centroids.

We further investigate the commuting trip patterns by using the detour index.
It shows to be a useful measure for assessing the performance of different
networks at minimising the trip length for a given Euclidean distance. We
introduce the weighted detour index and show the tendency of London’s active
travellers to commute in a way that minimises the detour of their trip when
the Euclidean distance to their job is beyond 900-1200 metres. Minimising the
detour on the way to work seems to be important to active travel commuting,
especially as the Euclidean distance between origin and destination increases.
We also observe considerable spatial variation in the potential walking and
commuting time between MSOAs, which is determined by the uneven distribution
and connectivity of the network, as well as the inconsistencies in data
sources, which can impact the models that are built on top of them. These
findings emphasise the importance of careful consideration and validation of
the input data coming from any kind of sources, whether official or crowd
sourced. The network with the lowest average detour index also showed the best
fitting in the spatial interaction model. This indicates the possibility to
use this index as a guide when designing new infrastructure that aims to
connect a population to an employment distribution in a way that minimises the
weighted detour of the trips. The main focus of this work is done on active
travel as a mean to commute, but the applications and possibilities of the
models and methods go beyond that and provide a general framework on open
source data for active-travel modelling. Our research has implications for
urban planning and policy-making, as it highlights the need for accurate
network data and appropriate modelling techniques to inform the development of
sustainable transport infrastructure and promote active travel in cities.

##  6 Acknowledgements

This paper has received funding from the QUANT and RUBICON projects from the
Alan Turing Institute under grant TU/ASG/R-SPEU-102.

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##  7 Appendix

###  7.1 Online material and reproducibility

The main code and process to access the data are described here. Limitations
due to the accessibility of the census flow forbid us to provide it here, but
an institutional account allows to connect and download the detailed msoa
level flows data from the WICID 151515https://wicid.ukdataservice.ac.uk portal
via an account created on UKDataServices 161616https://ukdataservice.ac.uk.

Code: https://github.com/ischlo/quant_cycle_walk

Additionally, a mini package called cppSim was developed to perform fast and
memory efficient spatial interaction models, it is made available in the
following github repository: https://github.com/ischlo/cppSim

d (km) | OS | OSM
---|---|---
min | max | $\delta_{c}$ | $\delta_{n}$ | t-test | $\delta_{c}$ | $\delta_{n}$ | t-test
0.0 | 0.6 | 2.113 | 2.108 | 0.1 | 1.498 | 1.518 | -0.8
0.6 | 0.9 | 1.931 | 1.914 | 0.9 | 1.454 | 1.471 | -1.6
0.9 | 1.2 | 1.780 | 1.791 | -0.7 | 1.384 | 1.423 | -4.9
1.2 | 1.5 | 1.666 | 1.700 | -3.0 | 1.357 | 1.388 | -4.7
1.5 | 1.8 | 1.610 | 1.623 | -1.4 | 1.307 | 1.347 | -8.5
1.8 | 2.1 | 1.538 | 1.535 | 0.5 | 1.266 | 1.313 | -14.0
2.1 | 2.4 | 1.464 | 1.514 | -7.4 | 1.253 | 1.303 | -15.2
2.4 | 2.7 | 1.454 | 1.473 | -3.5 | 1.237 | 1.284 | -16.6
2.7 | 3.0 | 1.402 | 1.457 | -9.5 | 1.232 | 1.274 | -14.8
3.0 | 3.3 | 1.377 | 1.430 | -10.8 | 1.226 | 1.265 | -11.6
3.3 | 3.6 | 1.368 | 1.409 | -9.3 | 1.213 | 1.250 | -17.3
3.6 | 3.9 | 1.343 | 1.393 | -12.0 | 1.204 | 1.248 | -19.2
3.9 | 4.2 | 1.329 | 1.384 | -12.6 | 1.195 | 1.242 | -18.5
4.2 | 4.5 | 1.319 | 1.372 | -13.4 | 1.191 | 1.237 | -19.7
4.5 | 4.8 | 1.301 | 1.361 | -15.1 | 1.184 | 1.229 | -21.0
4.8 | 5.1 | 1.293 | 1.356 | -16.7 | 1.182 | 1.228 | -19.8
5.1 | 5.4 | 1.285 | 1.344 | -16.7 | 1.177 | 1.222 | -24.2
5.4 | 5.7 | 1.279 | 1.334 | -17.3 | 1.171 | 1.218 | -24.2
5.7 | 6.0 | 1.267 | 1.327 | -19.2 | 1.168 | 1.212 | -26.4
6.0 | 6.3 | 1.259 | 1.323 | -21.4 | 1.164 | 1.211 | -28.8
6.3 | 6.6 | 1.254 | 1.317 | -21.7 | 1.160 | 1.208 | -28.9
6.6 | 6.9 | 1.251 | 1.307 | -21.5 | 1.155 | 1.201 | -33.2
6.9 | 7.2 | 1.240 | 1.301 | -24.5 | 1.154 | 1.201 | -32.5
7.2 | 7.5 | 1.233 | 1.298 | -26.8 | 1.147 | 1.198 | -38.0
7.5 | 7.8 | 1.236 | 1.293 | -23.1 | 1.155 | 1.195 | -29.2
7.8 | 8.1 | 1.232 | 1.285 | -24.3 | 1.149 | 1.192 | -36.9
8.1 | 8.4 | 1.223 | 1.280 | -27.2 | 1.142 | 1.189 | -37.2
8.4 | 8.7 | 1.225 | 1.278 | -24.6 | 1.145 | 1.187 | -36.8
8.7 | 9.0 | 1.221 | 1.273 | -25.7 | 1.143 | 1.184 | -36.8
9.0 | 9.3 | 1.216 | 1.268 | -26.3 | 1.145 | 1.182 | -33.3
9.3 | 9.6 | 1.211 | 1.264 | -29.8 | 1.135 | 1.179 | -47.3
9.6 | 9.9 | 1.206 | 1.261 | -30.0 | 1.137 | 1.179 | -40.4
9.9 | 10.2 | 1.209 | 1.255 | -26.7 | 1.141 | 1.177 | -36.2
10.2 | 10.5 | 1.206 | 1.254 | -29.1 | 1.139 | 1.175 | -38.4
10.5 | 10.8 | 1.201 | 1.249 | -30.7 | 1.134 | 1.173 | -40.6
10.8 | 11.1 | 1.201 | 1.244 | -29.0 | 1.135 | 1.171 | -40.0
11.1 | 11.4 | 1.195 | 1.242 | -31.8 | 1.134 | 1.169 | -39.7
11.4 | 11.7 | 1.199 | 1.240 | -28.9 | 1.139 | 1.168 | -31.4
11.7 | 12.0 | 1.197 | 1.239 | -29.3 | 1.137 | 1.168 | -35.9
12.0 | 12.3 | 1.189 | 1.232 | -28.9 | 1.132 | 1.164 | -35.3
12.3 | 12.6 | 1.187 | 1.230 | -34.7 | 1.130 | 1.163 | -43.0
12.6 | 12.9 | 1.192 | 1.228 | -28.1 | 1.133 | 1.162 | -37.7
12.9 | 13.2 | 1.185 | 1.226 | -32.1 | 1.133 | 1.161 | -35.4
13.2 | 13.5 | 1.184 | 1.224 | -34.3 | 1.127 | 1.160 | -48.8
13.5 | 13.8 | 1.183 | 1.220 | -32.7 | 1.132 | 1.158 | -38.5
13.8 | 14.1 | 1.185 | 1.217 | -28.6 | 1.133 | 1.157 | -34.6
14.1 | 14.4 | 1.179 | 1.216 | -35.4 | 1.123 | 1.156 | -52.8
14.4 | 14.7 | 1.181 | 1.213 | -31.1 | 1.127 | 1.154 | -43.5
14.7 | 15.0 | 1.180 | 1.210 | -31.4 | 1.130 | 1.153 | -39.2
Table 4: This table summarises the detour for commuting trips ($\delta_{c}$)
and for typical network values ($\delta_{n}$) within distance ranges of crow-
fly distance. It shows how they significantly differentiate, especially as
crow fly distance grows (column $d$). We test the significance in the
difference of the observed means for the weighted detour compared with regular
network values. The results show that the observed difference are strongly
significant, especially as the crow fly distance between locations increases.