---
category: literaturenote
citekey: vandenbulckemappingaccessibilitybelgiumtool2009
title: "Mapping accessibility in Belgium: a tool for land-use and transport planning?"
authors: "Vandenbulcke, Grégory; Steenberghen, Thérèse; Thomas, Isabelle"
year: 2009
date: "2009-01-01 January 1, 2009"
doi: 10.1016/j.jtrangeo.2008.04.008
publication: Journal of Transport Geography
url: "http://www.sciencedirect.com/science/article/pii/S096669230800032X"
zotero_key: 6M2V43NZ
zotero_storage: H5TGY6E8
collections: doktoritöö
folder: Liiklussageduse kaudne hindamine/05_Artiklid
firstAuthor: "Vandenbulcke, Grégory"
status: converted
---
Contents lists available at [ScienceDirect](http://www.sciencedirect.com/science/journal/09666923)

# Journal of Transport Geography

journal homepage: [www.elsevier.com/locate/jtrangeo](http://www.elsevier.com/locate/jtrangeo)

![](_page_0_Picture_5.jpeg)

# Mapping accessibility in Belgium: a tool for land-use and transport planning?

Grégory Vandenbulcke a,b,\*, Thérèse Steenberghen <sup>b</sup> , Isabelle Thomas a,c

- <sup>a</sup> CORE and Department of Geography, Université catholique de Louvain (UCL), Voie du Roman Pays, 34, Louvain-la-Neuve B-1348, Belgium
- <sup>b</sup> Spatial Applications Division Leuven, Katholieke Universiteit Leuven (KUL), Leuven, Belgium
- <sup>c</sup>National Fund for Scientific Research (FNRS), Rue d'Egmont, 5, Brussels B-1000, Belgium

#### article info

Keywords: Accessibility Congestion Belgium Spatial analysis

#### abstract

This paper compares the spatial structure of car accessibility to towns and to railway stations during peak and off-peak hours in Belgium for the country's 2616 municipalities. A clustering method is applied. It is shown that in a highly urbanised country, the situation is far from being spatially equitable in terms of accessibility, and some areas are more favoured than others. Congestion increases spatial inequalities, differently according to absolute or relative measures of change. By means of examples, this paper shows that even simple accessibility indicators could be useful to support decisions taken by planners and politicians (e.g. as regards the development of residential, industrial and business park areas). Maps indicate the spatial inequalities in terms of accessibility to urban centres and transport nodes, and the impact of congestion on these inequalities. The absolute and relative time losses due to congestion affect different areas in different ways. The location of new developments further increases the congestion problem and the spatial disparities. This paper also insists on the caution that should be adopted when measuring and interpreting ''accessibility", its measurements, its inputs, its temporal changes in absolute and relative terms as well as the need for spatially disaggregated data.

> -2008 Elsevier Ltd. All rights reserved.

## 1. Introduction

During the last few decades, Belgium, like many other countries, underwent a spectacular growth in the total number of vehicles– kilometres travelled: it increased from 29 billion in 1970 to 48 billion in 1980 and 95 billion in 2005 ([FPS Economy, 2007b](#page-13-0)). Belgium has one of the highest rates of car use in the world: 82% of all passenger journeys are made by car, while public transport only accounts for 14% (the other 4% represent travel made by bus companies). The distribution is similar for freight transport (road: 70%; waterway: 14%; rail: 13%; pipeline: 3%). This results in heavy road traffic, congestion, road accidents, social disparities and mobility gaps, and also impacts on the economy and the environment. Moreover, in 2003, an estimated 13 million hours were wasted by drivers in queues due to congestion in Belgium, which represents a cost of € 150 million ([Charlier, 2006; Witlox, 2006\)](#page-13-0).

This massive use of the automobile and the growth of freight transport by road not only have an impact on road traffic but also on the efficiency of public transport when both are sharing the same roads ([Rodrigue et al., 2007](#page-13-0)). One of the major consequences of congestion is a reduction in accessibility, in the sense that trucks and cars hamper the accessibility of towns and public facilities. Places where congestion is high suffer from both social and economic problems (e.g. lack of equality due to the reduced mobility of public transport, and the delocalisation of firms due to the reduced mobility of production units). For instance, in Brussels, accessibility problems due to congestion and the difficulty of finding a parking space for cars and deliveries are among the most significant factors which have encouraged peri-urbanisation ([Mérenne-Schoumaker, 2003; Rodrigue et al., 2007\)](#page-13-0). Congestion problems are predicted to increase in the immediate future: by 2012, traffic jams could extend for 30 km beyond the Brussels ring road, whereas in 2002 they 'only' reached 20 km [\(Charlier, 2006\)](#page-13-0). Consequently, action must be taken not only in transport planning (e.g. improving and increasing the supply of public transport) but also in urban planning (e.g. by giving more importance to the quality of life than to road infrastructure). Indeed, greater accessibility means an increased quality of life for the individual (greater freedom to choose activities and more time to devote to them), and it is even more important for people with limited opportunities (e.g. low incomes) or physical disabilities [\(Makrí, 2001](#page-13-0)). For firms, a high level of accessibility provides a competitive advantage for some locations. With the reduction of trade barriers in Europe and new markets opening up, it may be of prime importance for all countries to have better levels of accessibility ([Banister and Ber](#page-13-0)[echman, 2001; Brans et al., 1981\)](#page-13-0), i.e. reduced travel times to

<sup>\*</sup> Corresponding author. Address: CORE and Department of Geography, Université catholique de Louvain (UCL), Voie du Roman Pays, 34, Louvain-la-Neuve B-1348, Belgium. Tel.: +32 10 47 94 30; fax: +32 10 47 43 01.

E-mail addresses: [gregory.vandenbulcke@uclouvain.be](mailto:gregory.vandenbulcke@uclouvain.be) (G. Vandenbulcke), [therese.steenberghen@sadl.kuleuven.be](mailto:therese.steenberghen@sadl.kuleuven.be) (T. Steenberghen), [isabelle.thomas@uclou](mailto:isabelle.thomas@uclouvain.be)[vain.be](mailto:isabelle.thomas@uclouvain.be) (I. Thomas).

economic activity. Firms that offer services to other firms (i.e. Business to Business) are well advised to minimise the travel time to reach their customers, whereas firms that offer services to people (i.e. Business to Consumer) should be located near the concentrations of population ([Gutiérrez and Gómez, 1999](#page-13-0)).

We suggest the use of accessibility indicators to help Belgian policy makers and planners evaluate and find solutions to mobility problems, and especially to adjust their policies to local conditions. Several indicators are proposed for all Belgian communes (which corresponds to the NUTS 6 level); we limit ourselves to individual transport (mainly to cars) and refer to the full research report for the analysis of the other modes of transportation [\(Vandenbulcke](#page-14-0) [et al., 2007](#page-14-0)). The main objective is to analyse spatial disparity by means of several accessibility indicators and to compare peak and off-peak accessibility. We aim to identify local inequalities and also to pinpoint the places where congestion causes the greatest problems. Based on various typologies of accessibility, measures are proposed to assist the decision-making of spatial planners and policy makers.

The structure of the paper is as follows. A brief review of the literature on the concept and the measurement of accessibility is given in Section 2. The study area is presented in Section [3](#page-3-0). The fourth section describes the methodology, the data and the accessibility indices used in this paper, as well as some preliminary results. The cluster analysis is reported in Section [5](#page-8-0) and the last section concludes with operational guidelines.

## 2. Definition and measurement of accessibility

#### 2.1. Definitions

Accessibility becomes more and more essential in land-use and transport decisions, thus having significant economic, social and environmental implications ([Geurs and Ritsema van Eck,](#page-13-0) [2001\)](#page-13-0). Jointly with positive externalities such as investments or a favourable policy environment, accessibility influences the organisation and the dynamics of regions and, consequently, the location of activities and individuals [\(Bavoux et al., 2005\)](#page-13-0). Its measurement is then a convenient tool to direct decisions taken by the planners and politicians. For instance, the accessibility patterns can help them to analyse the potentials of the development of industrial and business park areas as employment centres by focusing on the accessibility to working population. Moreover, companies and employers usually want to know from which location they can reach a large number of consumers and workers, so helping them to locate their businesses and services ([Zhu and Liu, 2004\)](#page-14-0). Modelling and mapping accessibility is then of great help in order to evaluate the expected market area size and justifies the recent upsurge in the use of geographic information system (GIS)-based accessibility analysis for business and residential planning ([Ritsema van Eck and de Jong, 1999](#page-13-0)). For example, [Geertman and Ritsema van Eck \(1995\)](#page-13-0) used accessibility measures combined with the use of GIS (geographical information system) in order to conduct a major residential programme in the most densely populated part of The Netherlands (i.e. Randstad Holland); on the basis of relevant location criteria (i.e. the location in regard to major employment centres and key supply centres), they produced ''potential surfaces" to determine the location of possible building sites.

Accessibility is a frequently-used concept but there is no consensus about its definition and formulation. It is a common term experienced by diverse individuals (i.e. characterised by different needs, abilities and opportunities) at any place and moment of the day, which results in considerable variation in components included in the measure, and in how it is formulated. Accessibility is commonly defined as the ease with which activities can be reached from a certain place and with a certain system of transport ([Morris](#page-13-0) [et al., 1979; Johnston et al., 2000\)](#page-13-0). The concept generally takes the combination of two elements into account: the location on a surface relative to suitable destinations and the characteristics of the transport network [\(Vickerman, 1974\)](#page-14-0). [Handy and Niemeier](#page-13-0) [\(1997\)](#page-13-0) suggested that accessibility is determined by the spatial distribution of potential destinations, the ease of reaching each destination, as well as the magnitude, quality and character of the activities found there. Each definition includes one or more components which affect accessibility (e.g. the location of activities, or the system of transport). [Geurs and Ritsema van Eck](#page-13-0) [\(2001\)](#page-13-0) formulated a very complete definition of the concept: according to them, accessibility reflects ''the extent to which the land-use transport system enables (groups of) individuals or goods to reach activities or destinations by means of a (combination of) transport mode(s)" (p. 36). This implies that the concept of accessibility is determined by four interdependent components: a transport component (transport system), a land-use component (the magnitude, quality and characteristics of activities found at each destination), a temporal component (availability of activities) and an individual component (needs, abilities and opportunities of individuals).

The concept of ''peripherality" is also used in the literature and is synonymous with inaccessibility to economic activity [\(Keeble](#page-13-0) [et al., 1988\)](#page-13-0). Peripheral regions generally face poor economic performances and negative net-migration rates [\(Spiekermann and](#page-14-0) [Neubauer, 2002\)](#page-14-0). However, it is not always true and some regions can have a high economic performance in spite of low levels of accessibility (e.g. Sweden).

#### 2.2. Measurement of accessibility

Accessibility is not easy to quantify, and there is no best approach to measuring it [\(Gutiérrez, 2001](#page-13-0)). Different situations and purposes require different approaches ([Gutiérrez and Urbano,](#page-13-0) [1996; Handy and Niemeier, 1997; Linneker and Spence, 1996\)](#page-13-0). The choice of an indicator affects the spatial pattern of accessibility ([Talen and Anselin, 1998](#page-14-0)) and is therefore critical for land-use and transport planning. Moreover, the detail and accuracy of the analysis should reflect the needs of a specific situation ([Halden, 2002\)](#page-13-0). In the scientific literature, accessibility measurements have generally been used to evaluate the performance of transport networks as well as access to employment opportunities and other facilities for various socio-economic groups ([Kwan, 1998](#page-13-0)). The measurement of accessibility also plays a key role in evaluating the competitive advantage of some locations due to the quality of their transport infrastructure.

[Handy and Niemeier \(1997\)](#page-13-0) classified the available measures into three categories: isochrones (which indicate the number/proportion of destinations reachable within a given travel time/distance/cost from an origin), gravity-based measures (which assume a gradual decrease in accessibility as the travel time to destinations increases) and utility-based measures (which estimate the accessibility at the individual level). Another classification was established by [Geurs and Ritsema van Eck \(2001\)](#page-13-0) and [Geurs](#page-13-0) [and van Wee \(2004\)](#page-13-0), who suggested four basic perspectives: (1) infrastructure-based measures, (2) activity-based measures, (3) person-based measures and (4) utility-based measures.

Infrastructure-based measures analyse the observed or simulated performance of the transport infrastructure. Typical are the level of congestion or the average speed on the road network. Such measures provide comprehensible information on the service level of transport infrastructure and are easy to operationalise (e.g. the necessary data are often readily available and measures are easy to understand for planners, policy makers or researchers), but they do not include a land-use component (e.g. they are not sensitive to changes in the spatial distribution of activities) and they are not able to treat temporal constraints as well as individual characteris-

tics [\(Geurs and Ritsema van Eck, 2001; Geurs and van Wee, 2004\)](#page-13-0). Activity-based measures analyse accessibility at locations on a macro-level, i.e. the range of available activities with respect to their distribution in space and time. Also more complex measures include capacity restrictions of supplied activity characteristics to include competition effects (e.g. competition for job vacancies or hospital beds; see e.g. [van Wee et al., 2001](#page-14-0)). Common activitybased measures are cumulative-opportunity measures, potential measures (also called gravity-based measures), as well as measures based on competition effects. Derived from the gravity model, potential measures are very often used in planning as well as land-use and transport evaluations [\(van Wee et al., 2001\)](#page-14-0). Originally applied by [Stewart \(1947, 1948\)](#page-14-0) in order to calculate ''population potentials" for different regions in the United States, they were subsequently used in location analysis ([Harris, 1954](#page-13-0)) and to describe accessibility to employment activities ([Hansen, 1959](#page-13-0)). Potential measures are derived by weighting the opportunities located in an area by a measure of attraction (e.g. population, purchasing power, total retail floor space, or the number of households) and discounting each opportunity by a measure of impedance [\(Knox, 1978; Handy, 1993; Geertman and Ritsema van Eck,](#page-13-0) [1995; Wyatt, 1997; Johnston et al., 2000](#page-13-0)). Hence, potential measures present the advantage to account for impedance and attraction of destinations but a potential value is not easily interpreted and the intrazonal potential (i.e. the number of activities within origin zone is weighted by the average travel time or distance within this zone) has a substantial impact on the measurement of potential values ([Geertman and Ritsema van Eck, 1995\)](#page-13-0). The first shortcoming can be overcome by modifying the potential formula in such a way that the measure gives meaningful units, and the second is avoided when the spatial framework approximates a continuous representation of space ([Frost and Spence, 1995; Geert](#page-13-0)[man and Ritsema van Eck, 1995](#page-13-0)).

Also called ''space–time accessibility measures" (see e.g. [Kwan,](#page-13-0) [1998; Miller, 1999; Miller and Wu, 2000; Kwan and Weber, 2003\)](#page-13-0), person-based measures analyse accessibility at the individual level (i.e. on a micro-level) and assume that ''accessibility applies to a particular individual at a particular time and place" ([Helling,](#page-13-0) [1998\)](#page-13-0). Unlike conventional measures (i.e. infrastructure-based and activity-based measures), person-based measures consider accessibility as an attribute of individuals [\(Kwan and Weber,](#page-13-0) [2003](#page-13-0)); they evaluate accessibility in terms of an individual's ability to reach opportunities given the person's daily activity programme and spatio-temporal constraints [\(Landau et al., 1982; Kwan, 1998\)](#page-13-0). Hence, a disaggregation is performed by person-based measures and the accessibility is evaluated separately for different trip purposes, transport modes, income, gender, age, occupational groups and activity types [\(Wachs and Kumagai, 1973; Ben-Akiva and Ler](#page-14-0)[man, 1979; Handy and Niemeier, 1997; Kwan, 1998](#page-14-0)). For example, [Kwan \(1998\)](#page-13-0) showed that the male and female adults of the same household experience different levels of individual accessibility. [Church and Marston \(2003\)](#page-13-0) also analysed the differences in accessibility between individuals with physical disabilities and individuals without disabilities. Originated from the space–time geography of [Hägerstrand \(1970\)](#page-13-0), person-based measures often use space–time prisms to describe the travel patterns in space and time. These prisms can be interpreted as accessibility measures, i.e. they can give the potential area which can be reached given predefined time constraints. [Miller \(1999\)](#page-13-0) defined a potential path space (PPS) delimiting all locations in the space and time that can be reached by an individual (given certain constraints). The projection of this PPS on the x–y space produces the corresponding two-dimensional potential path area (PPA) in which all feasible locations k are included, given a number of space–time constraints ([Kwan,](#page-13-0) 1998). Modified space–time prisms also have been developed to measure the individual accessibility, given changes in activity schedules, multistop trip chaining and various travel speeds [\(Hall, 1983; Arentze et al., 1994\)](#page-13-0). Generally, it is not so easy to operationalise the space–time framework as an accessibility measure. However, the increasing availability of georeferenced individual data and the drastic increase in computer power as well as the recent development of methods using network-based GIS procedures allow to overcome such operational difficulties (see e.g. [Miller, 1991; Kwan and Weber, 2003; Kwan, 2004](#page-13-0)).

Utility-based measures analyse the economic benefits (e.g. consumer surplus) that individuals derive from access to spatially distributed activities. This approach estimates the accessibility at the individual level and accounts not only for users' characteristics (e.g. income) but also for modal characteristics (e.g. travel costs; [Banister and Berechman, 2001; Geurs and Ritsema van Eck,](#page-13-0) [2001](#page-13-0)). The main assumptions on which the utility approach is based are defined by [Koenig \(1980\)](#page-13-0). Firstly, people associate a cardinal utility with each alternative they are facing and choose the alternative associated with the maximum utility. Secondly, the utility function can be represented as the sum of a non-random (deterministic) component and a random (stochastic) component. Specifying such a function requires the incorporation of variables representing the attributes of each choice, reflecting the attractiveness of the destination and the travel impedance, the socio-economic characteristics of the individual (or household), and individual tastes and preferences [\(Handy and Niemeier, 1997\)](#page-13-0). Commonly used in economic studies, utility-based measures are therefore difficult to interpret and make severe demands on data.

Given that each accessibility measure requires different data and differs in its operationalisation, interpretability and communicability, a major methodological challenge is to find the right balance between a measurement which is theoretically and empirically sound and one which is sufficiently plain to be useful in land-use and transport planning. Although infrastructure measures (e.g. travel speed) are easy to interpret and communicate to planners and decision makers, such measures are not very useful for evaluating the accessibility impacts because the spatial, temporal and individual components are not incorporated in the measure. On the other hand, more complex measures such as utilitybased or person-based measures use a better theoretical basis and have the advantage to incorporate individuals' characteristics. Nevertheless, this theoretical superiority of both utility-based and person-based measures makes them more difficult to operationalise and more demanding on data. After evaluating the availability of data, models and techniques, as well as time and budget, activity-based measures seemed to us to be the best way of analysing accessibility at a national level. Such measures describe the level of accessibility of a range of spatially distributed activities. Common measures are distance measures (which analyse the relative position of each location in the transportation network), isochrones and gravity-based measures. During the research project, type of activity-based measure was applied to different modes of transportation (car, train, underground, bus) and different types of location (towns, airports, railway stations, underground stations, bus stops). This paper is limited to distance measurements. We refer to the full report ([Vandenbulcke et al., 2007\)](#page-14-0) for other transportation modes, terminals, infrastructures or scales.

Regardless of the approach, four interrelated issues must be considered before measuring accessibility ([Handy and Niemeier,](#page-13-0) [1997\)](#page-13-0). First, the degree and type of disaggregation is quite important. Disaggregation can be considered not only in spatial and socio-economic terms but also according to the purpose of the trip or the type of activity. In this paper, we only consider communes and the time of day (see Section [4.1](#page-3-0)). Second, origins and destinations must be defined. For all the distance measurements used <span id="page-3-0"></span>here, the origins are taken to be the centroid of the commune. On the other hand, the destinations can be towns (large cities, regional cities, or small towns with a large number of facilities), or railway stations. Thirdly, the travel impedance has to be specified: time units are used because they are more relevant for the transport of passengers than either Euclidian or Manhattan distances, expressed in kilometres. Travel time varies according to the type of roads used between two locations (e.g. motorways allow high speeds, which reduce the travelling time). Moreover, time units can incorporate more time components (e.g. waiting time) than the simple journey time. Finally, the attractiveness of a destination is often estimated by factors such as the number of activities or jobs. In this study, attractiveness is considered for railway stations as well as for towns. We assumed that the frequency of stopping trains determines the attractiveness of stations. Belgian towns were simply rated as attractive (1) or not attractive (0). Large cities, regional towns and small towns with numerous facilities [\(Van](#page-14-0) [Hecke, 1998](#page-14-0)) were considered as destinations. It is worthy of note that this strong rating has the disadvantage of disregarding the influence of potential public facilities (located in smallest villages) on the accessibility of nearby communes. Hence, accessibility to towns could be probably underestimated in some cases. The use of potential measures could be of great help to overcome this shortcoming.

### 3. The study area

The analysis was conducted on Belgium, a small and highly urbanised European country with more than 10 million inhabitants spread over approximately 30,000 km2 . The population density varies from 30 inhabitants/km<sup>2</sup> in rural regions to over 20,000 inhabitants/km2 in highly urbanised areas. The country varies in terms of topography and urbanisation, as well as economic, social, political and environmental contexts (see e.g. [Mérenne](#page-13-0) [et al., 1997](#page-13-0)). Urban sprawl is one of the major characteristics of the geography of Belgium. New urban areas are spreading in rural and low density areas, along the main transportation links (e.g. motorways). Obviously this has consequences. Impacts related with the sprawling nature of Belgian towns are adverse to the natural and rural environments, as well as to the quality of life for people living in towns; in Belgium, the extension of towns in rural and poorly served areas favours the use of the car and then causes congestion, pollution (air and noise) and physical inactivity. Other impacts are the creation of barriers for the ecosystems (e.g. construction of residential developments, new roads, etc.) and an increased consumption of energy and soils [\(EEA, 2006\)](#page-13-0).

The Belgian town network is dominated by Brussels (see Appendix A), with more than 1.5 million inhabitants in its extended urban agglomeration. It is centrally located and sprawls out into neighbouring regions, across its administrative borders (see e.g. [Dujardin et al., 2007](#page-13-0)). Approximately 57% of the Belgian population lives in towns, which cover 26% of the national surface ([Van der](#page-14-0) [Haegen et al., 1996](#page-14-0)). These numbers indicate the importance of urban sprawl, sub- and peri-urbanisation in Belgium. The country is subdivided into three regions (Flemish Region, Walloon Region and Brussels-Capital Region), three communities, 10 provinces, 44 districts, 589 communes and 2616 old communes. The three regions are, respectively, the Flemish Region (13,522 km2 and 6,117,440 inhabitants on 1st January 2007), the Walloon Region (16,844 km2 and 3,435,879 inhabitants on 1st January 2007) and the Brussels-Capital Region (162 km2 and 1,031,215 inhabitants on 1st January 2007; [Mérenne et al., 1997; FPS Economy, 2007a\)](#page-13-0). At the smallest scale, the communes stem from the fusion of old communes and are classified into the NUTS 5 and NUTS 6 level, respectively. In this study, only old communes are used.

At the EU level, Belgium is quite accessible (see e.g. [Gutiérrez](#page-13-0) [and Urbano, 1996; Schürmann et al., 1997; Spiekermann and](#page-13-0) [Wegener, 1996; Spiekermann et al., 2002](#page-13-0)). The Belgian road network is dense and intensely used, especially in the Brussels–Antwerp–Ghent triangle. However, the southern part of the country is less accessible (see e.g. [Thomas and Verhetsel, 1999; Thomas](#page-14-0) [et al., 2003\)](#page-14-0). The rail network is also dense and centred on Brussels ([Thomas et al., 2003](#page-14-0)).

## 4. Data and methods

## 4.1. Construction of the OD matrix

We here limit ourselves to accessibility by car along the road network from any Belgian commune to two different types of destinations: the major cities (and their facilities) and the railway stations. In order to compute accessibility indices, the origins and destinations are represented by nodes, e.g. communes and railway stations are simplified into points. The basic data needed are: (1) network data (road network and geographical coordinates of railway stations), (2) origins and destinations, i.e. the administrative boundaries of all Belgian communes, the location of their centroids as well as their hierarchical rank in terms of urbanisation [\(Van](#page-14-0) [Hecke, 1998](#page-14-0)). In this paper, a centroid corresponds to the geometric centre of the administrative statistical ward of the commune. It is assumed to represent the highest concentration of population in the commune.

Network data include line coverages representing the road network and were obtained from the three regional Ministries in charge of transport. These data allowed us to construct a topological graph which consists of a non-empty set of nodes connected by a possibly empty set of arcs (roads). The graph is undirected, weighted, non-planar and connected. It has 510,469 nodes and 627,856 arcs. It is noteworthy that the road network was taken on its whole, which means that not only motorways but also arterial, collector and local roads were considered. Each arc is characterised by a length and a maximum allowed speed (which is attributed according to the type of road, e.g. the allowed speed limit is 120 km/h on Belgian motorways, 90 km/h on major arterial roads, 70 km/h on feeder/collector roads and 50 or 30 km/h on local roads). Both length and speed are used to calculate the travel time on the road network.

At the scale of the country, the 589 current Belgian communes are too coarse for accessibility computation, especially as their shapes and sizes vary a lot. When destinations are railway stations, using the 20,464 statistical wards would have led to a giant origin/ destination matrix (more than 11 million solutions) and consequently unmanageable computation times. Therefore, an earlier definition of 2616 communes was adopted as the basic spatial unit (BSU). The average area of the BSU was thus 12 km2 . The centroid of each BSU (after it was snapped to the road network, with a tolerance of less than 100 m) was used for distance computation. Such centroids summarise the information about the BSUs. The urban hierarchy of Belgian communes was used for selecting destinations [\(Van Hecke, 1998\)](#page-14-0). Hence, the 2616 BSUs correspond to the origins in the origin–destination (OD) matrix, while there are two types of destinations: the main towns (53 nodes) and the railway stations (545 nodes). It is a choice of the Belgian Ministries not to include any node from neighbouring countries (e.g. Luxembourg and Lille), although considering this would certainly reduce the inaccessibility of some areas.

Weights are associated with the arcs and nodes. Railway stations are weighted according to the frequency of services ([SNCB/](#page-14-0) [NMBS, 2005](#page-14-0)). Integrating this variable into a so-called ''generalised time" allows us to account for the attractiveness of each station. Arcs (i.e. roads) are weighted using a density-based model. Travel times are computed along the road network between all 2616 nodes and for two periods of time: peak (i.e. from 7 to 9 a.m. and from 3 to 6 p.m.) and off-peak hours (i.e. from 9 p.m. to 5 a.m.). Using speed limitations as well as population and job densities (obtained from the 2001 census of population), we were able to include an ''impedance function", reflecting the time taken to cross urban areas, cities as well as smaller towns. Measurements carried out without impedance produce results that underestimate travel time. Assuming that population and jobs generate the same quantity of traffic, the corrected travel time can be expressed as:

$$T_{ij} = t_{ij} + t_{ij}.[(1 - e^{-\alpha J_i}) + (1 - e^{-\alpha P_i})]$$
 (1)

where Tij is the corrected travel time from i to j (including impedance), tij is the travel time from i to j (without impedance), a is a coefficient to calibrate, J<sup>i</sup> is the density of jobs in commune i and P<sup>i</sup> is the population density. In Eq. (1), population and job densities are used to compute the impedance function and correct travel time. Using densities is more representative than absolute measures (e.g. the number of inhabitants), especially for large communes where population is highly concentrated on only a part of the surface. In this case, using the total number of inhabitants or jobs might not be representative of the road traffic in communes characterised by sharp changes of land-use (e.g. between rural and urban areas). Based on Eq. (1), we also observe that the level of impedance (which can be calibrated through a) makes it possible to consider the different saturation levels of roads; in other words, a can be used to represent a period of time (e.g. rush hours), characterised by a particular level of road congestion. The Pearson's product moment correlation coefficient between the computed off-peak travel times and those obtained from a route planner (Viamichelin) was very high (0.97) and highly significant. The lack of reliable empirical data for travel movements in peak periods makes it impossible to calibrate the model for congested times. Using a fixed value of a, a hypothetical state of road saturation was generated on the basis of the location of regular traffic jams. These results were further validated by experts.

Renowned for its ability to visualise, analyse and model geographical data ([Wu and Hine, 2003\)](#page-14-0), GIS technology was used to combine the different layers of information (i.e. integrate origins and destinations within the road network) and spatially assess the different levels of accessibility. The road network was then used to construct an OD matrix in Network Analyst (an extension of ArcGIS 9.1). The results are presented in the form of a table of travel times between each origin (i) and destination (j) in Belgium.

#### 4.2. Description of the accessibility variables

The variables are here restricted to: (1) travel time to the closest large Belgian town and (2) travel time to the closest railway station. Assumption is made that individuals take the shortest path (in terms of time units). We measure fairness in the distribution of goods and services (e.g. hospitals, shops, schools and jobs), spatial equity between the communes. This measure of fairness here refers to the differences in accessibility derived from the spatially distributed activities (located in the towns) and the transport system, and a major issue related to this is to maximize accessibility to key nodes of transport, housing, employment, leisure and other social activities. Indeed, it reduces the global time spent on trips to work and for other purposes [\(Gutiérrez and Gómez, 1999](#page-13-0)). Thus the spatial equity here connotes to the fact that all individuals should be equally treated, wherever they live in Belgium, i.e. they should benefit from an equal spatial separation from facilities ([Tsou et al., 2005](#page-14-0)).

4.2.1. Travel time to the closest large Belgian town

In a first step, we assume that the largest Belgian towns correspond to the three groups of urban communes defined by [Van](#page-14-0) [Hecke \(1998\)](#page-14-0). These are the five largest cities (Brussels, Antwerp, Ghent, Liège and Charleroi), 17 regional cities (such as Bruges, Leuven or Namur) and 31 small towns (e.g. Wavre and Vilvoorde). The choice of these urban communes as destinations is justified by their centrality: towns generally concentrate population and activities (offices, administrations, tourism, transport and so on). As a result, most traffic flows converge on towns.

[Fig. 1](#page-5-0) shows that the present structure of the urban network generates spatial disparities and has the effect that the southern part of the country is quite remote: off-peak travel time to the closest town often exceeds 30 min. In the northern part of the country, the accessibility is on the average better, with some less accessible areas mainly located at the border of the country. This is mainly an edge effect, since urban centres across the Belgian border were not included in the calculations. It is also worthy of note that remote areas (i.e. whose travel time exceeds 30 min) are characterised by low densities of population and activities. Furthermore, some of these remote areas correspond to the most deprived sections of the Belgian population. The situation is then far from being equitable when accessibility to the closest town is considered.

During peak hours [\(Fig. 2\)](#page-5-0), the remote areas (i.e. more than 30 min) are more extensive: a larger number of communes are located more than 30 min travel time from any urban centre. This is especially true in the southern part of the country, in the peripheral areas and between towns as the time needed to get to the nearest town increases because of the time spent in traffic jams. Hence, by additive effects, rural areas suffer from an increase in congestion in urban areas. Congestion is certainly a problem within towns but it also weighs heavily on the transportation bill of other areas. Compared to the spatial pattern obtained for off-peak hours, high local differences can also be observed. Indeed the way the road network is laid out results in the apparition of sorts of ''enclaves", i.e. areas that are characterised by smaller values of travel time than their surrounding environment. It is also observed that not only deprived and low-density areas are disadvantaged but also some suburbs (generally characterised by moderate densities and relatively high incomes). Enclaves are observed in municipalities which, although located near urban centres and thus, apparently very accessible, need very long travel times to reach these cities during peak hours. This means that, in term of accessibility to typical urban facilities such as secondary schools, hospitals, etc. they need as much time as many peripheral municipalities.

[Figs. 1 and 2](#page-5-0) can easily be accompanied by tables using the GIS function. The percentage of communes, population and surface area in each travel time band in peak and off-peak hours are reported in [Appendix B.](#page-12-0) It clearly shows that different spatial structures are generated in peak and off-peak hours. At peak times, a large part of the population living in and around towns (in the agglomeration or in the suburbs) has to spend a considerable time travelling, and hence the gap in terms of accessibility decreases: for example, more than 46% of the population has to spend more than 15 min travelling to a town in peak hours, while in off-peak hours this only applies to 13% of the population.

The calculation did not take travel preferences into consideration. The real travel behaviour is likely to result in even longer travel times, as people may prefer to go to more distant urban centres due to, for example, language and/or cultural factors. Congestion and other factors may also affect the time of day people choose to travel. Such factors were not further researched in this case.

## 4.2.2. Travel time to the closest railway station

It is assumed that commuters use the car as a feeder mode for access trips; they leave their vehicles in a car park and take the

<span id="page-5-0"></span>![](_page_5_Figure_2.jpeg)

Fig. 1. Travel time (minutes) by car to the closest town during off-peak hours.

![](_page_5_Figure_4.jpeg)

Fig. 2. Travel time (minutes) by car to the closest town during peak hours.

train afterwards. This combined use of car and train refers to the concept of 'Park and Ride'. Travel time to the closest railway station is computed in such a way that trips are carried out by car only.

The time taken to access rail transport consists not only of the travel time by car from a commune i to a railway station j but also includes a measure of the waiting time for the next train. Inhabitants of commune i could choose a more distant station with a higher train frequency rather than the closest station with a lower level of service. Hence, time to rail transport is computed as the sum of the travel time tij by car from municipality i to railway station j, and the average waiting time w<sup>j</sup> for a train at j. This ''generalised time" Tij is given by:

$$T_{ij} = t_{ij} + w_j \tag{2}$$

The average waiting time w<sup>j</sup> is based on the inverse of the number of trains serving station j on a weekday. Note that w<sup>j</sup> does not make the distinction between the number of trains during peak hours and those during off-peak hours; such a distinction should require additional data, describing the supply level for each station and for both periods of time (peak and off-peak hours). Following this, w<sup>j</sup> was just computed on a daily basis. Given that on the average a traveller would arrive by chance midway between trains, a correcting factor K (2) is introduced to reduce w<sup>j</sup> to a realistic value:

$$w_{\rm j} = \frac{1}{K} \cdot \frac{H}{f_{\rm j}} \tag{3}$$

where H is the time during which trains run on the network (20 hours a day) and f<sup>j</sup> is the frequency of weekday trains at railway station j. The travel time to the closest railway station is thus the minimum generalised time Tij separating the commune i from a station j. Inhabitants of commune i will generally choose to use the railway station whose generalised time Tij is least. Using train frequency data [\(SNCB/NMBS, 2005](#page-14-0)), the generalised time was computed for each Belgian station (Figs. 3 and 4). Once again, the southern part of the country is characterised by low values of accessibility to rail transport during off-peak hours (Fig. 3). With the exception of communes located close to the Namur–Luxembourg line, the travel time to the closest station from communes in the south is generally more than 20 or even 25 min. When communes are located close to a station (in terms of network distance) but have high generalised travel time values, the poor accessibility can be explained by low train frequency at the closest station. Such communes are often rural, generally characterised by a small population and low job density. They are often deprived areas in terms of transportation and economic activities.

During peak hours [\(Fig. 4](#page-7-0)), there are more communes where people need more than 25 min to reach the nearest train station. Interestingly, the increase in peripherality is especially evident in the northern part of the country (near The Netherlands) and affects a large number of suburban communes. More enclaves are observed on the map, due to combined effects of the rail network and the location of jobs and population. The high peri-urbanisation increases road traffic and hence travel time to reach a railway station. Better land-use and transport planning (e.g. using indicators measuring the accessibility of population to the public transport facilities) could help to improve the mobility and reduce the social inequalities due to the increasing congestion. For instance, new residential developments should be preferably concentrated near public transport facilities. This could lead to a higher modal share for public transport and, at the same time, to a traffic reduction on the road network (or at the very least to a traffic mitigation for the future). Within the same framework, [Lau and Chiu \(2004\)](#page-13-0) showed that a compact land-use combined with an efficient integration and performance of public transport provide higher levels of equality in terms of accessibility to employment activities than those obtained for cities (or small countries) with dispersed land-use. Belgium obviously belongs to the latter category.

![](_page_6_Figure_10.jpeg)

Fig. 3. Generalised time (minutes) to the closest railway station during off-peak hours.

<span id="page-7-0"></span>![](_page_7_Figure_2.jpeg)

Fig. 4. Generalised time (minutes) to the closest railway station during peak hours.

Once again, the cartographic results were quantified using GIS; the same values (for communes, population and surface areas) were computed for each period of travel time as for access to towns. [Appendix C](#page-12-0) shows that the railway network is less accessible in peak hours than in off-peak hours; for example, the population located more than 15 min from the railway network increases from 17.2% during off-peak hours to 37.4% during peak hours. This situation is not compatible with the overall purposes of sustainable mobility and it confirms that planning measures should be urgently implemented in order to reach a more sustainable mobility. Residential locations should be privileged near stations with suitable train frequencies.

#### 4.3. Congestion and peripherality

Interesting spatial differences are observed not only in terms of accessibility but also in terms of time of travel (peak and off-peak hours). It is well known that congestion affects large cities and makes travel more difficult but our analysis also shows that congestion in and around destination areas increases the peripherality of some rural areas. Table 1 demonstrates that the correlations between the different aspects of accessibility are lower in peak hours than in off-peak hours (e.g. the correlation between the travel time to the closest town and the travel time to the closest railway station is reduced from 0.74 during off-peak hours to 0.60 during peak hours). This means that congestion increases spatial inequalities. Such a result can be explained by: (1) an increase in the spatial divergence of travel times during peak hours and (2) the existence of local isolation due to road congestion (i.e. enclaves, or ''peripheral islands"). Consequently, the choice of a particular mode of transport could be more important during peak hours than during off-peak hours. As expected, train could be a better alternative during peak hours.

Comparing correlation coefficients between peak and off-peak hours, it is observed that the resemblance between the distributions is generally high (Table 1). This does not mean that there is no change in travel time between the two periods; it simply shows that the spatial structure of accessibility is the same, i.e. deprived and accessible areas remain the same. Scatterplots were also made (see Appendices D and E) and show that in some communes the travel time increases very markedly – by up to 100% – during peak hours. Most of these communes are urban and suffer from congestion. For some remote communes, the scatterplots also show a divergence in travel times between the two time periods (whichever measure of accessibility is considered). In a country like Belgium, larger distances increase the probability of having

Table 1 Pearson product–moment correlation coefficients between the accessibility measures (all coefficients are significant at or beyond the 99.9% level)

|            |                                | Off-peak hours        |                                | Peak hours            |                                |  |
|------------|--------------------------------|-----------------------|--------------------------------|-----------------------|--------------------------------|--|
|            |                                | Minimum time to towns | Minimum time to rail transport | Minimum time to towns | Minimum time to rail transport |  |
| Off-peak   | Minimum time to towns          | 1                     | –                              | –                     | –                              |  |
| hours      | Minimum time to rail transport | 0.742                 | 1                              | –                     | –                              |  |
| Peak hours | Minimum time to towns          | 0.963                 | 0.685                          | 1                     | –                              |  |
|            | Minimum time to rail transport | 0.611                 | 0.941                          | 0.600                 | 1                              |  |

<span id="page-8-0"></span>![](_page_8_Figure_2.jpeg)

Fig. 5. Absolute time lost (%) due to congestion going to a town (computed from travel times during off-peak hours).

alternative routes but the time losses are also larger due to congestion (which varies according to the area being crossed, i.e. whether it is rural or urban). In other words, congestion particularly affects urban areas in terms of relative variation and rural areas in terms of absolute values. The latter become less accessible at peak hours but, in relative terms, urban areas are more affected by the waste of travel time due to congestion. Fig. 5 illustrates the first part of this statement. With some exceptions (e.g. Antwerp or Ghent), it is observed that the absolute time lost due to congestion going to the closest town is higher in rural and low-density communes than in urban areas. On average, approximately 6 min are lost on the road while travelling to the closest town during peak hours (Table 2). When trips are carried out to railway stations, this loss of time is limited to 4 min. Concerning the second part of the statement, the relative time lost due to congestion can be computed from the travel times during peak and off-peak hours as:

$$\Delta T_{\%} = \left(\frac{T_{\text{peak hours}} - T_{\text{off-peak hours}}}{T_{\text{off-peak hours}}}\right).100 \tag{4}$$

where DT% is the relative time lost due to congestion, Tpeak hours is the travel time during peak hours and Toff-peak hours is the travel time during off-peak hours. Eq. (4) yields the additional travel time needed in peak hours (expressed as a percentage of the time taken in off-peak hours). [Fig. 6](#page-9-0) presents the results for stations; at first

Table 2 Comparison of the mean travel time during off-peak and peak hours

|                | Statistics for travel time | Towns | Railway stations |
|----------------|----------------------------|-------|------------------|
| Off-peak hours | Mean (a)                   | 13.4  | 14.4             |
|                | Standard deviation         | 8.5   | 6.5              |
| Peak hours     | Mean (b)                   | 19.8  | 18.2             |
|                | Standard deviation         | 10.1  | 7.2              |

glance, it shows clearly that densely populated communes are characterised by higher values, which confirms the fact that congestion particularly affects urban areas. Conversely, the more rural communes (especially these located in the southern part of the country) appear less affected by congestion and ''benefit" from a comparative advantage reflected in lower relative values. There seems to be no significant differences between the population densities and the areas affected by congestion. This is confirmed by a correlation of 0.68 between the two measures. This coefficient also shows that the relationship between population densities and congestion is far from perfect, which is partly due to a strong peri-urbanisation around the main Belgian cities. Conceptually, each commune is therefore characterised by an ''immobility index" which is higher when congestion is high. Urban communes generally have a high ''immobility index", while communes in the southern part of the country do not really suffer from important time losses due to congestion.

#### 5. Accessibility in Belgium: a synthesis

The 2616 communes have been classified separately for peak and off-peak hours on the basis of the two accessibility variables (travel time to the closest town and to the closest railway station). Various clustering methods were employed to test the sensitivity of the spatial structure to the method used. The ascending hierarchical method using Ward's criterion proved to be most successful [\(Ward, 1963\)](#page-14-0). This method minimises the sum of squares of any pair of clusters to be merged at each step. In other words, it seeks to minimise the information loss associated with each grouping. It is generally regarded as an efficient method but it presents the disadvantage to be sensitive to outliers and strongly biased towards generating clusters with the same number of observations. Finally, a consensus between the

<span id="page-9-0"></span>![](_page_9_Figure_2.jpeg)

Fig. 6. Relative time lost (%) due to congestion going to a railway station (computed from travel times during off-peak hours).

![](_page_9_Figure_4.jpeg)

Fig. 7. Cluster analysis of accessibility to a town and a railway station during off-peak hours.

![](_page_10_Figure_2.jpeg)

Fig. 8. Cluster analysis of accessibility to a town and a railway station during peak hours.

CCC (cubic clustering criterion), pseudo-F statistic and pseudo-t statistic suggests that four clusters should be used (whichever period of time). These four clusters were summarised graphically in [Figs. 7 and 8.](#page-9-0)

During off-peak hours ([Fig. 7\)](#page-9-0), communes in cluster 1 have the highest level of accessibility to towns and rail transport. This cluster characterises the network of towns and their associated transport network. The map clearly reveals the population and job densities as well as the transportation network. Communes in cluster 2 also have high levels of accessibility, only slightly below those in cluster 1. This cluster mainly covers peri-urban and industrial areas. Cluster 3 is characterised by relatively high scores on both variables – in other words, communes in this cluster have low accessibility levels. They are mainly rural and industrial communes, generally remote from rail transport and towns. Cluster 4 is made up of peripheral communes, mainly located in the southern part of the country and near the border with The Netherlands, which are quite remote from any Belgian town and have poor access to rail transport.

During peak hours (Fig. 8), road congestion is particularly acute in urban communes and causes a large decrease in accessibility; it also reduces the number of communes included in cluster 1. The reduction in accessibility is all the more important since these communes are highly congested. During peak hours, these communes are faced with mobility problems and suffer from a greater reduction in accessibility than less congested areas. For instance, the southern part of the country (e.g. Arlon) is not highly congested and does not suffer from a drop in accessibility. The general picture in Fig. 8 shows that congestion is important everywhere, with the exception of some peripheral areas characterised by low economic and demographic dynamics.

Through these examples, we show how transport accessibility confirms urban geography processes: it is well known that urban sprawl is one of the major characteristics of the geography of Belgium [\(EEA, 2006\)](#page-13-0). Originated from the need to have more space combined with an increase in mobility (particularly facilitated by the car ownership) during the second half of the 20th century, this sprawl of the city and its facilities in the surrounding countryside leads to higher car shares and longer distances travelled by means of motorised modes (i.e. car and public transport). Indeed, the increasing number of new residential developments constructed in peripheral areas (i.e. remote from any public transport facility) favours the use of the car, which causes longer travel time and a reduction of accessibility due to the resulting congestion. As illustrated, [Fig. 9](#page-11-0) shows that some peripheral communes located in the outskirts of large urban places (such as Brussels, Antwerp or Liège) were characterised by a high demographic growth between 1990 and 2005 (more than 20% in some cases). In particular, [Fig. 9](#page-11-0) shows that the south-eastern part of Brussels (along the Brussels–Namur axis) faces an increasing number of households attracted by green amenities and lower land prices than in the north. Strong increases are also observed in the southern part of Belgium and are the result of lower housing prices in Belgium than in Luxembourg. For some of these peripheral communes, the quality of public transport (i.e. frequency, density of stops, etc.) is generally low and therefore more flexible modes (e.g. car) are preferred for activity-related trips. This is confirmed by results obtained by [Hubert and Toint](#page-13-0) [\(2002\)](#page-13-0), who show that households established in outskirts have more vehicles than those living in agglomerations. Also most of people living in the surrounding countryside use their car to reach an agglomeration. Another study performed on population census data (2001) gives similar results, showing that the car use for activity-related trips reaches more than 70% in some rural communes ([Verhetsel et al., 2007\)](#page-14-0).

As a result of this periurban movement, the increasing congestion on roads threatens the competitivity of the main urban places

<span id="page-11-0"></span>![](_page_11_Figure_2.jpeg)

Fig. 9. Population growth (%) in Belgium between 1990 and 2005 (source: [FPS Economy, 2007a\)](#page-13-0).

and urgent solutions are needed, such as intermodality or adapted pricing policies. Further, a better management of activity and transport systems could be of great help to solve the mobility problems. Among others, accessibility indicators coupled with the use of GIS could be useful to direct decisions taken by planners and politicians as regards the land-use and transport systems. For instance, accessibility patterns such as those analysed in [Figs. 7](#page-9-0) [and 8](#page-9-0) are useful tools to conduct development of residential developments or industrial and business park areas, especially if the study is projected at the smallest scale and includes more transportation modes.

## 6. Conclusion

This paper focuses on the measurement of accessibility and limits the application to car accessibility and its spatial variation within Belgium. Two types of destinations are considered (cities and railway stations) as well as two types of time periods (peak and off-peak).

The situation in Belgium is far from being spatially equitable and some areas are more favoured than others. Some findings are not surprising as they have often been observed: large cities are more accessible than smaller ones. Through the mapping of the travel time from each municipality to the closest centre with certain levels of facilities, it becomes apparent that congestion increases spatial divergence and creates enclaves which are far less accessible during peak hours. In less urbanised areas, total travel times to cities often become very large during peak hours, due to additive effects. This is quite interesting in a country like Belgium where households – in accordance with urban economics – appreciate green amenities and locate in places where housing prices are lower, i.e. increasingly further away from city centres. Recent urbanisation developments (see e.g. [Anas et al.,](#page-13-0) [1998](#page-13-0) or [Caruso, 2002\)](#page-13-0) represented here by population growth, occur in locations where accessibility is smaller. The developments seem to ignore congestion effects on accessibility: strong growth is encountered in locations suffering from dramatic increase in travel time due to congestion. The developments also show that urban sprawl is still going on and further increases congestion problems and travel times to the urban centres. These results also confirm how the recent increase in mobility has not reduced accessibility differentials (see e.g. [Bretagnolle et al.,](#page-13-0) [2002\)](#page-13-0).

The empirical results reveal a spatial repercussion of the relationship between transportation, residential and economic developments. Continuous peri-urbanisation of dwellings (and jobs) creates a large proportion of the burden of congestion for firms and for households (in Belgium almost all regions are affected by congestion) and spreads the problems associated with congestion and pollution in the suburbs. Conclusions underscored here are not only valid at a national but also at the local level (see [Vandenbulcke et al., 2007](#page-14-0)). This paper shows the congestion effects on the local accessibility of stations. These are calculated using the same method: travel time to the nearest station.

Besides the mobility problems (mainly caused by commuters living in the surrounding suburbs), the increasing traffic associated with urban sprawl is the root of several environmental and health problems. Thus, the location problems associated with economic activities as well as with personal mobility are questions that require joint treatment by policy makers and that need to be addressed in order to achieve a more sustainable development of land-use and transport infrastructures. Within this framework, accessibility indicators are easy to compute, can be based on readily available data, and provide useful insight in the consequences of spatial developments. Indeed, they could play a key role by avoiding locations of new developments in <span id="page-12-0"></span>poorly served areas and, consequently, strong dependency on the car. Supported by accessibility measurements, planners could then encourage land-use planning that promotes the shift to other transportation modes than car, e.g. 'zero-carbon' modes (i.e. walking and cycling) or public transport [\(Chapman, 2007\)](#page-13-0). Here again, accessibility indicators are useful to examine the potential impacts of developments on the travel times to transport nodes such as railway stations.

The choice of ''the" accessibility indicator is not straightforward and a great challenge is hence to find the right balance between several criteria such as interpretability, communicability and operationalisation, selection of destination, hierarchy of destinations, travel behaviour (oversimplified in our case), spatial data aggregation, etc. A major problem is that all destinations are equally desirable, regardless of the type of activity. As a result, it does not fully reflect human behaviour because a more remote destination could be preferred to the closest destination (e.g. an individual could prefer to travel to a town which is not the closest, simply because of the number of facilities it offers). For future applications aiming at synthesising accessibility at a national scale, the use of potential measures – and particularly the ''modified potential formula" recommended by [Geertman](#page-13-0) [and Ritsema van Eck \(1995\)](#page-13-0) – could be of great help. Such measures are still relatively easy to interpret by non-specialists and require a modest amount of data. Furthermore, the distance decay functions used in potential measures have the advantage of incorporating assumptions on individual's perceptions of transport ([Geurs and van Wee, 2004\)](#page-13-0). The fact that potential measures account for the attractiveness of destinations (e.g. considering the population that lives in each city) is also more relevant than assuming that individuals travel to the closest facility.

## Acknowledgements

This research was made possible by the Belgian Federal Scientific Policy (Contracts AP/10/02A and AP/01/02B) and the Federal Public Service ''Mobility and Transport" (Contract ''Accessibility Indicators"). We are grateful for their support as well as to the users committee. We also thank the anonymous referees for their useful comments and their guidance.

### Appendix A

Network of Belgian cities, railways and motorways.

![](_page_12_Figure_8.jpeg)

## Appendix B

Travel time to the closest large Belgian town: percentage of communes, population and surface area in each travel time band.

| Time<br>(min) | Off-peak hours |                   |                | Peak hours  |                   |                |
|---------------|----------------|-------------------|----------------|-------------|-------------------|----------------|
|               | BSUs<br>(%)    | Population<br>(%) | Surface<br>(%) | BSUs<br>(%) | Population<br>(%) | Surface<br>(%) |
| 0–5           | 10.0           | 28.3              | 10.8           | 3.5         | 17.4              | 5.3            |
| 6–10          | 30.0           | 35.7              | 25.9           | 11.2        | 15.5              | 9.6            |
| 11–15         | 28.6           | 23.4              | 25.0           | 19.7        | 20.7              | 17.0           |
| 16–20         | 14.3           | 7.0               | 14.0           | 23.5        | 21.8              | 20.9           |
| 21–25         | 6.4            | 3.2               | 8.7            | 16.9        | 12.9              | 16.4           |
| 26–30         | 4.4            | 1.1               | 5.9            | 10.8        | 6.3               | 11.0           |
| >30           | 6.2            | 1.3               | 9.8            | 14.4        | 5.4               | 19.8           |
| Total         | 100.0          | 100.0             | 100.0          | 100.0       | 100.0             | 100.0          |

## Appendix C

Travel time to the closest Belgian railway station: percentage of communes, population and surface area in each travel time band.

| Time<br>(min) | Off-peak hours |                   |                | Peak hours  |                   |                |
|---------------|----------------|-------------------|----------------|-------------|-------------------|----------------|
|               | BSUs<br>(%)    | Population<br>(%) | Surface<br>(%) | BSUs<br>(%) | Population<br>(%) | Surface<br>(%) |
| 0–5           | 3.2            | 16.5              | 3.2            | 1.2         | 6.1               | 1.2            |
| 6–10          | 21.8           | 37.6              | 18.9           | 9.6         | 27.9              | 9.3            |
| 11–15         | 37.0           | 28.6              | 32.2           | 23.9        | 28.5              | 21.6           |
| 16–20         | 21.6           | 11.0              | 21.6           | 30.7        | 20.4              | 27.3           |
| 21–25         | 9.1            | 3.6               | 11.7           | 19.6        | 9.6               | 18.7           |
| >25           | 7.3            | 2.6               | 12.4           | 14.9        | 7.4               | 21.8           |
| Total         | 100.0          | 100.0             | 100.0          | 100.0       | 100.0             | 100.0          |

## Appendix D

Comparison of the travel time to the closest large Belgian town during peak and off-peak hours.

![](_page_12_Figure_17.jpeg)

#### <span id="page-13-0"></span>Appendix E

Comparison of the travel time to the closest railway station during peak and off-peak hours.

![](_page_13_Figure_4.jpeg)

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