SUBPART TEN
Analysis
CHAPTER 35
Accessibility
Dominik Ziemke
35.1 Basic Information
Entry point to documentation:
http://matsim.org/extensions →accessibility
Invoking the module:
http://matsim.org/javadoc →accessibility →RunAccessibilityExample class
Selected publications:
Nicolai and Nagel (2014); Joubert et al. (2015)
In transport science and planning, the term accessibility can refer to at least three different
concepts. First, accessibility may be used to describe how well a certain transport infrastructure
component can be utilized by travelers, particularly those with handicaps (Faura, 2012). In this
sense, accessibility guidelines tell engineers and planners how to design transport infrastructure
elements, such as public transport facilities, to make them accessible, i.e., useable for all travelers.
Second, accessibility may be used to describe how easy/convenient the approach to a given land-use
facility is. There are, for instance, studies (Fujiyama, 2004) to improve the accessibility of shopping
centers by redesigning access roads and their connection to major roads. Finally, the term accessi-
bility can be used in a more global way, to describe availability and spatial distribution of activity
facilities within a given area, e.g., a metropolitan region and the ease with which these facilities can
be reached from other locations in the area. MATSim’s accessibility extension focuses on all these
aspects; the discussion in this chapter draws on Nicolai and Nagel (2014).
How to cite this book chapter:
Ziemke, D. 2016. Accessibility. In: Horni, A, Nagel, K and Axhausen, K W. (eds.) The Multi-Agent
Transport Simulation MATSim, Pp. 237–246. London: Ubiquity Press. DOI: http://dx.doi.org/10.5334/
baw.35. License: CC-BY 4.0
238 The Multi-Agent Transport Simulation MATSim
35.2 Introduction
Improvement in accessibility is often defined as a central goal of proposed transport or infras-
tructure schemes (Geurs et al., 2012b) and accessibility is usually a precisely-defined, quantitative
measure. While Batty (2009) traces the origins of the accessibility concept back to location theory
and regional economic planning in the 1920s (when transport planning began in North Amer-
ica; Geurs et al., 2012b), Hansen, with his widely-cited paper (Hansen, 1959), is generally credited
with the first real definition of accessibility, defining it as the potential of opportunities for interac-
tion. In more detail, Morris et al. (1979) define accessibility as “the ease with which activities may
be reached from a given location using a particular transportation system”. The concept of accessi-
bility is a potential methodology for the assessment of transport systems, as it is a comprehensive
and inclusive way to evaluate how, where and why people move, taking well-known dependencies
between transport and land use into account. Hansen (1959) was probably the first to develop a
procedure for quantitative consideration of accessibility, discussed in more detail in Section 35.3.
In their widely-cited review, Geurs and van Wee (2004) identify four accessibility components
from existing definitions and applied measures:
1. The land-use component reflects the number and spatial distribution of opportunities.
2. The transport component describes the effort to travel from a given origin to a given
destination.
3. The temporal component considers the availability of activities at different times of day,
e.g., during morning peak hours.
4. The individual component addresses various socio-economic groups’ different needs and
opportunities, e.g., different income groups.
In this review, Geurs and van Wee (2004) list and summarize typical approaches applying the
accessibility concept, focusing on the accessibility components discussed above:
1. Infrastructure-based measures focus on the (observed or simulated) performance or service
level of transport infrastructure, e.g., represented as average travel speed. These measures are
typically used in transport planning.
2. Location-based measures describe level of accessibility to spatially distributed activities, such
as number of jobs within 30 minutes travel time from origin locations. These measures are
typically used in urban planning and geographical studies.
3. Person-based measures analyze accessibility at the individual level, such as the activities
in which an individual can participate at a given time. These measures are grounded in
H¨
agerstrand (1970)’s space-time geography.
4. Utility-based measures analyze the economic benefits that people derive from access to
spatially distributed activities. These measures have their origin in economic studies.
Geurs and van Wee (2004) intersects these approaches with the four accessibility components
identified above, creating a matrix. This matrix illustrates how each of the four accessibility com-
ponents is represented in the four different accessibility measures. There, each measure focuses
on certain weaknesses in those accessibility components outside the focus of a specific measure.
Accordingly, Geurs and van Wee (2004) recommend that an accessibility measure include all
four discussed accessibility components. The accessibility extension of MATSim, described in the
following, could be one way to achieve this goal.
In other recent research, as identified by Geurs et al. (2012b), the accessibility concept is also
applied to social exclusion analysis (e.g., by examining the benefit of employment accessibility for
Accessibility 239
disadvantaged populations before and after the implementation of a transport scheme), economic
valuation of accessibility effects (e.g., in cost-benefit analyses and studies assessing the impact of
changes in public transport accessibility on house prices) and behavior analysis vis-a-vis accessibil-
ity measures (e.g., walking behavior dependence on different residential neighborhood accessibility
qualities). It has also been used to explore questions of oil dependence, climate change and other
concerns (Curtis et al., 2013).
35.3 The Measure of Potential Accessibility
Today, methods to assess accessibility quality are often used in superordinate planning procedures,
like regional transport planning, where a central goal is to provide citizens with a certain level
of access to various services. For instance, the approach used by Germany’s agency responsible
for regional planning calculates travel times to major service facilities, like airports or hospitals
(Bundesinstitut f¨
ur Bau-, Stadt- und Raumforschung, accessed March 2015). The results, typically
visualized by multi-colored maps, give useful insights into population access to certain services,
thus aiding transport infrastructure planning. In this approach, travel times are calculated to a
next airport, next hospital and next autobahn access; thus, the implicit assumption is that citizens’
needs are fulfilled by one (i.e., the next, or closest in terms of travel times) type of facility.
An accessibility measure becomes significant, however, if not just the ability to reach the nearest
facility serving a particular need is taken into account, but also a set of multiple reachable facilities
serving the same need; different facilities of the same type may offer varying qualities of a given
service. Services may also expand and improve when combined with complementary services pro-
vided by another facilities of the same type. For instance, a person planning to take a holiday trip
by plane will probably consider several airports in his/her vicinity, instead of just looking at flights
offered from the nearest airport. Thus, accessibility to airports should be made dependent on the
ability to reach all local airports instead of just the nearest one. Facilities offering medical services
may serve as another example. Considering the nearest hospital may be sufficient when looking
at simple services like first aid, presumably available at almost any hospital. In other cases, how-
ever, medical services accessibility should consider several hospitals in the vicinity because they are
likely to offer different specialized medical treatment. Consideration of a set of multiple facilities,
potentially useful from the perspective of a person at a given location, corresponds to taking into
account the land-use component of accessibility defined above.
Hansen (1959) considers the whole scope of potential activity facilities, where an accessibility
measure potential accessibility is defined. Such measures of potential accessibility are specified as the
(weighted) sum over the accessibilities of several specific activity facilities (e.g., shopping, leisure
etc.) and take the mathematical form
A`=gX
j
ajf(c`j),(35.1)
where jare all possible destinations (opportunities), ajdescribes opportunity attractiveness, c`j
denotes the generalized traveling cost between origin `and destination j,f(c)is an impedance
function which (typically) decreases with increasing distance and g(.) denotes an arbitrary, but
usually monotonically increasing function. The weight of each opportunity jis thus the product
of the destination’s attractiveness, aj, and the ease of getting there, f(c`j). As seen in its functional
form, this type of accessibility measure is related to gravity models used in trip generation models,
explaining why this measure is sometimes also referred to as a “gravity type” accessibility indicator
(Morris et al., 1979). The (quantitative) accessibility measure used in the MATSim accessibility
240 The Multi-Agent Transport Simulation MATSim
extension is expressed in this mathematical form and may thus be seen as a potential accessibility
measure.
It is important to note that the above-defined measure quantifies how accessible a given location
`is to certain services j. This kind of accessibility is outgoing accessibility, while a measure of ingoing
accessibility quantifies how accessible a given destination location jis from other locations. Nicolai
and Nagel (2014) discuss circumstances under which these measures are interchangeable.
35.4 Accessibility Computation Integrated with Transport Simulation
As mentioned above, accessibility computations are often based on travel times (Bundesinstitut
f¨
ur Bau-, Stadt- und Raumforschung, accessed March 2015; B¨
uttner et al., 2010), which serve as
an impedance measure. Ways of calculating these travel times can, however, vary significantly. The
simplest way to calculate a travel time between two locations is to measure the Euclidean distance
(beeline distance) between these two locations and multiply with some average speed. According
to Geurs and van Wee (2004), this is the usual approach in location-, person-, and utility-based
accessibility approaches, where the focus is not specifically on the transport system.
To strengthen the transport component of accessibility (as introduced above) and make acces-
sibility measure sensitive to transport infrastructure changes, a better representation of the travel
impedance between origins and destinations is required. The most common approach is travel time
calculation using shortest-path algorithms on a real-world transport infrastructure network repre-
sentation. Many accessibility computations are embedded into GIS software, offering procedures
for network-based computations (Bundesinstitut f¨
ur Bau-, Stadt- und Raumforschung, accessed
March 2015; Curtis et al., 2013; B¨
uttner et al., 2010).
The accessibility extension in MATSim also offers this type of accessibility computation. To run
it, an accessibility controler listener, e.g., the GridBasedAccessibilityControlerListenerV3 must
be added to the MATSim controler. An example is given in RunAccessibilityExample (see http:
//matsim.org/javadoc →accessibility →RunAccessibilityExample for details). As input, a net-
work file and a facilities file are required (for more information on networks and facilities, refer to
Section 4.1.1 and Section 6.4 of this book). This procedure is more disaggregate than many com-
mon approaches to accessibility computations, where single facilities are seldom considered; there,
structural data like zone sizes, number of jobs, or total sales area are used to represent the potential
of a given zone (B¨
uttner et al., 2010; Gulhan et al., 2014) (also see Section 35.6).
Either way, performing an accessibility computation this way can be regarded as a supply-based
approach, since both supply with transport infrastructure (required to reach a given location) and
supply with activity opportunities at these locations are taken into account. The utilization of these
two supply dimension by users, i.e., the dimension of demand is, however, not considered in this
approach. Therefore, no effects of competition (Geurs and van Wee, 2004), either for transport
infrastructure resources (defined by network capacities), or activity facilities capacities, are taken
into account. It is obvious, however, that supply and demand interaction effects are relevant,
because opportunities may disappear if they can no longer be reached within reasonable travel
times, or when activity facility capacities are exceeded.
By considering demand-supply interaction effects in addition to just the supply side, the scope
of the accessibility calculation can be significantly increased. Gauging these effects on facility
capacities can be addressed by specifying facility capacities in the according value in the facilities
input file. Observation of network capacities and their effects on agents’ behavior is one of the core
features of the MATSim transport simulation. This is also one major argument for the integration
of an accessibility computation with the dynamic transport simulation system MATSim. While
other accessibility tools—the majority based on GIS systems (Bundesinstitut f¨
ur Bau-, Stadt- und
Raumforschung, accessed March 2015; Curtis et al., 2013; B¨
uttner et al., 2010; Liu and Zhu, 2004;
Accessibility 241
Gulhan et al., 2014)—can calculate travel times on a routed network, they do not calculate accessi-
bilities dependent on transport infrastructure usage level. This property, is, however, essential when
making accessibility measures sensitive to transport demand management policies, i.e., transport
system changes that do not alter the transport infrastructure and are thus not captured by models
considering only the supply side.
To take these effects into account, the MATSim accessibility extension must be run with a
MATSim transport simulation. To do so, an initial plans file (as described in Chapter 2 of this
book) needs to be specified in the MATSim config file. Furthermore, the value timeOfDay in the
accessibility module of the MATSim config file needs to be specified. If then, as described, an
accessibility controler listener is added to the MATSim controler, the best-path travel times, on
which the accessibility computation will be performed, are taken from travel times observed in the
MATSim transport simulation at the time specified by the value timeOfDay. This is useful when
transport demand level varies significantly during the day; for instance, with morning and after-
noon peaks; it also allows transport policy accessibility changes (and decision makers’ reactions)
to be better analyzed.
35.5 Econometric Interpretation
As pointed out by Morris et al. (1979), accessibility indicators provide a very useful way to summa-
rize a large volume of information on household locations and how they relate to urban activities’
distribution and connecting transport systems. They also take land use, the transport system and
their inter-dependencies into account holistically. Curtis et al. (2013) explain that accessibility
assessment tools overcome policy innovation restrictions associated with traditional transport
planning practice, pointing out that use of such tools enables examination of a broader range of
policy issues.
For effective policy decisions, accessibility assessment tools must be economically interpretable.
To make an accessibility measure clearest in an econometric evaluation (e.g., cost-benefit analyses),
it seems sensible to adapt equation 35.1 as follows: g(.) =ln(.),aj=1, f(c`j)=e−c`j, and −c`j=
V`j. Thus, equation 35.1 becomes
A`:=lnX
k
eV`k,(35.2)
where kdenotes all possible destinations and V`kequals the disutility of traveling from location `to
destination k. Equation (35.2) is the so-called logsum term of exponentials and can be interpreted
as the expected maximum utility (e.g., Ben-Akiva and Lerman, 1985; de Jong et al., 2007). Equation
35.2 can be derived by assuming that the full utility of destination location kas perceived at origin
location `, is U`k=Vbase +V`k+`k, where Vbase is a base utility for performing a given activity
without considering its location, V`kis the systematic or observed disutility of traveling to from
origin `to destination k, and `kis a random term which absorbs the randomness of the disutility
of traveling, as well as fluctuations in utility around Vbase. Under the usual assumption that the `k
are independent and identically (iid) Gumbel-distributed random variables, the expectation value
of U`kbecomes
E(U`)=E(max
kU`k)=lnX
k
eV`k+Const ≡A`+Const .(35.3)
Const does not need to be considered, as it is invariant for all locations. As a consequence of
dropping the positive Const,A`may take negative values.
Geurs et al. (2012a), for instance, use the logsum measure of user benefits as an alternative to
the travel time savings method (i.e., rule-of-half measure) in a case study examining the effects of
spatial planning on accessibility benefits and economic efficiency of public transport projects.
242 The Multi-Agent Transport Simulation MATSim
35.6 Spatial Resolution, Data, and Computational Aspects
In contrast to many other transport simulations, MATSim is based on coordinates (see
Chapter 2 of this book), not zone-based. Therefore, accessibility computation in MATSim
can also be conducted independent from any zoning system and, instead, be based on
a raster with arbitrary granularity, i.e., adjustable grid size. Depending on the calcula-
tion planned (zone-based or grid-based), a ZoneBasedAccessibilityControlerListenerV3, or a
GridBasedAccessibilityControlerListenerV3, respectively, need to be added to the MATSimcon-
troler. Unlike the MATSimaccessibility extension, most other accessibility assessment tools rely on
the zone-based approach (Curtis et al., 2013; Liu and Zhu, 2004; B¨
uttner et al., 2010). More detail
about the interpretation of cell- and zone-based accessibility measures is given by Nicolai and Nagel
(2014).
Running a grid-based calculation, especially if a high spatial resolution is selected, avoids several
issues that could arise (like“self-potential”) if accessibility computations are based on zones (see,
e.g., Nicolai and Nagel, 2014). A zone-based approach also makes the measure dependent on size
and shape of the geographical units (cf. MAUP (Modifiable Areal Unit Problem)). Due to its typi-
cally lower resolution level, a zone-based approach may also not adequately represent local details
(Kwan, 1998). This is especially relevant when lower-speed mode accessibilies (like walking) must
be considered.
The MATSim accessibility calculation does not require typical zone-based statistical data. In-
stead, the calculation can be conducted on the basis of so-called VGI (Voluntary Geographic
Information) like OSM, which contains activity facilities data on a coordinate-based level. Hence,
no reference to any zoning system is necessary when using these data. Furthermore, data from
OSM is publicly and freely available; the amount of these data are steadily increasing and quality is
improving. In particular, OSMseems to have established itself as a uniform and globally-accessible
standard for crowd-sourced and other geo-data, which makes the MATSimaccessibility assessment
highly portable.
If the coordinate-based (=grid-based =raster-based =cell-based) version of the MATSim
accessibility computation is selected, its results can be interpreted as an accessibility field, i.e., as a
measure that varies continuously in space. This accessibility field, can be visualized by calculating
the values on regular grid points. Figure 35.1 gives an example of such a visualization and depicts
the accessibility of work places in Nelson Mandela Bay Municipality in South Africa, as calculated
by the grid-based MATSim accessibility computation with a grid size of 1 000 meters.
To calculate the accessibility A`of a given origin location `to opportunity locations k, both the
origin location `, and opportunity locations k, are assigned to a road network. If the option to in-
tegrate the accessibility computation with the transport simulation, as described in Section 35.4,
is chosen, a congested network with time-dependent travel times (as they have been simulated in
MATSim) is used. For every `, a so-called least cost path tree computation (Lefebvre and Balmer,
2007) is carried out. Accessibility of the same location at a different time of day will usually be
different, since congestion patterns vary. The least cost path tree computation determines the best
route and the least negative travel utility V`kfrom the origin location `to each opportunity loca-
tion k, based on Dijkstra’s shortest path algorithm (Dijkstra, 1959). Once the least cost path tree
has explored all nodes, the resulting disutilities V`kfor all opportunities kare queried and the
accessibility is calculated, as stated in Equation (35.2) (Nicolai and Nagel, 2014). A crucial question
is how to choose the point, i.e., the coordinate, where the accessibility computation is anchored.
Most quantitative accessibility tools use geographical centroids of given zones. This is also true
when the zone-based MATSim accessibility computation is selected. Alternative ways to select a
centroid (e.g., land-use-based centroids; B¨
uttner et al., 2010) are discussed as well. If the grid-based
MATSim accessibility computation is selected, the question of choosing a representative point for
a spatial zone becomes less relevant, as cells are usually not selected to be as large.
Accessibility 243
Figure 35.1: Accessibility of work places in Nelson Mandela Bay Municipality calculated by the
grid-based MATSim accessibility computation
If the granularity of the grid-based MATSim accessibility computation is increased, origin
locations `and opportunity locations k, possibly located off the network, become increasingly im-
portant. To keep the approach consistent, the V`kcalculation has to include disutility of travel to
overcome the gap between locations and the road network. Therefore, the disutility of travel cal-
culated by running the least cost path tree computation on the network has to be supplemented by
the disutility to access the network from the origin `(network access) and the disutility to access
the destination kfrom the network (network egress). For origin locations `, shortest distance to the
network is given either by the Euclidean distance to the nearest node, or the orthogonal distance to
the nearest link on the network. For destination locations k, the Euclidean distance to the nearest
node is used to determine the shortest distance to the network.
This assumption (i.e., that opportunity locations are attached to the nearest network node rather
than the nearest network element) is, in fact, the only approximation that the MATSim accessibil-
ity extension makes for the spatial resolution of opportunities (Nicolai and Nagel, 2014). While
this assumption is unlikely to significantly alter accessibility results, it offers great potential for
the optimization of computational performance, which has often been a major obstacle to higher-
resolved accessibility computations (Kwan, 1998; B¨
uttner et al., 2010). In the concrete case of the
MATSim accessibility computation, exploration of the entire network by the least cost path tree is
a computationally expensive task.
Thanks to the assumption, it is enough to sum over all opportunities kattached to a node jonly
once. The travel disutility V`kcan be deconstructed as
V`k=V`j+Vjk ∀k∈j,(35.4)
244 The Multi-Agent Transport Simulation MATSim
where k∈jdenotes all opportunities kattached to node j,
X
k∈j
eV`k=X
k∈j
e(V`j+Vjk)=X
k∈j
eV`jeVjk =eV`jX
k∈j
eVjk =:eV`j·Oppj.(35.5)
It is thus sufficient to compute Oppjonce for every network node j, and compute accessibilities as
A`=lnX
k
eV`k=ln
X
j
eVij ·Oppj
.(35.6)
Therefore, the loop performing the calculation does not have to run over all opportunities k, just
over all network nodes j.
Similarly, for each origin location `, the nearest road network node is identified. Locations `
that share the same nearest node have different travel disutilities to reach that node, but from then
on have the same travel disutility to any other network node j. Exactly like the destinations, the
least cost path tree is executed only once and calculated disutilities on the network are reused for
all origins `that are mapped on the same nearest network node. Therefore, only the calculation
of the network access disutility needs to be performed individually for each origin `. Nicolai and
Nagel (2014) show that, due to this run time optimization, computation time increases sub-linearly
with resolution. At the same time, they find that no significant further insights can be gained by
increasing the resolution beyond a grid resolution of 100 meters.
The application example RunAccessibilityExample (see http://matsim.org/javadoc →
accessibility) performs multiple accessibility computations for different types of activity facilities
(e.g., accessibility of workplaces or accessibility of leisure facilities) by adding multiple instances of
GridBasedAccessibilityControlerListenerV3 to the MATSim controler. Other ways of perform-
ing distinct accessibility assessments for parts of the land-use system are just as feasible. Figure 35.1
is an example of work place accessibilities.
35.7 Conclusion
There are many different approaches to calculating accessibilities; most focus on a particular com-
ponent of accessibility, while other components influencing accessibility are represented only in a
limited way. Accessibility computations used in transport planning, for instance, represent trans-
port networks, and thus the transport component of accessibility very well, while they usually
do not represent facility properties or temporal effects. As pointed out by Geurs and van Wee
(2004), it would be optimal if an accessibility computation considered all accessibility components
(i.e., transport, land-use, temporal, and the individual component) well. The accessibility extension
of MATSim could be an approach to achieve this.
First, transport system dynamics are represented by the accessibility computation integration
with the MATSimdynamic traffic simulation. Second, land use is represented in a very disaggregate
way; single facilities’ locations and attributes are taken into account. Third, the temporal dimension
can be observed by representing facilities’ opening times and time-dependent travel times on the
network; these are given as a MATSim dynamic traffic simulation output. Finally, individual char-
acteristics can be taken into account; in the MATSim simulation, each individual is represented by
its own software object, i.e., an agent, whose properties could be considered in the accessibilities
calculation.
Actual accessibility values calculated by the MATSim accessibility extension take the form of
potential accessibility measure, as originally defined by Hansen (1959). The specific selection of
the measure’s mathematical form allows results to be interpreted as logsum values, making them
Accessibility 245
suitable for utilization in economic evaluations like benefit-cost analyses. Because the MATSim
accessibility extension can rely solely on publicly and freely available data, e.g., data from OSM,
it is highly portable. By distinguishing activity facilities along various potential dimensions, many
different analyses can be conducted. In the code example given (see http://matsim.org/javadoc
→accessibility →RunAccessibilityExample), for instance, accessibilities for different land uses,
i.e., different types of activity opportunities, are calculated. Being grid- instead of zone-based
(which most other accessibility tools are), avoids certain problems associated with zones. At the
same time, computations are still within reasonable ranges, partly due to a runtime optimization
that reuses computational steps for locations sharing the nearest network node.
