Hanson, (1995, p. 4) defines accessibility as "the number
of opportunities, also called activity sites, available within a certain distance
or travel time." Ingram (1971) says that accessibility is an inherent
characteristic of place and is operationalized in terms of overcoming some form
of friction. There are three dimensions to these definitions.
First, a distance or spatial interaction among locations (activity sites); second,
a transportation system or network that links these locations; and, third, the
desire and means or ability (financially, physically, and temporally) to visit
these sites and overcome the spatial separation (an impedance function).
The study of the extent and strength of human interaction
with the environment is a central concern within the study of Human Geography.
These measures can be used to address planning and policy decisions (Talen,
1995, 1996) . Accessibility is also a common focus for geographic study
of fields ranging from social equity to urban form, and from transportation
to economic growth. Although central to this research, accessibility
is often a misunderstood and poorly measured construct and it seems that every
sector of this field has its own definitions and methods for discovering this
interrelationship and process. This is true, because finding an operational
concept of accessibility is very difficult and quite complex. Gould (1969,
p. 64) summed up these problems well with his statement that accessibility
"is a slippery notion…one of those common terms that everyone uses until
faced with the problem of defining and measuring it."
Traditional measures treated accessibility as strictly a
physical or spatial construct. They were usually based on distance between
origins and destinations. Later, other surrogates for travel efforts
were used, such as network modeling showing travel times or costs. All
these models of spatial separation and interaction are based on physical networks
or topology and might be considered as revealing a potential accessibility within
that system. They ignored constraints of time or constraints on the activities.
They most certainly ignored other social and individual constraints that
might hinder the ability to connect with different activities.
Relative measures of accessibility (Ingram, 1971) are expressed
by distance or travel time between two points. The further away the points
are, the less accessible they are. The measure is usually symmetric if
the connection between the two places is not unidirectional. Physical
distance, time, or some measure of cost can be used to measure the degree of
spatial separation. Integral measures determine the relationships between
one point and all others in the study area. This is like the attraction
model in store location theory. Unlike the relative measure, it is not
reflexive (the accessibility of a store to all homes is not the same in the
other direction). It can also be used to show which points have the highest
or lowest degree of accessibility to the entire set of opportunities.
This can be used to determine social equity in the case of planning agendas
(Talen, 1995) .
The gravity measure is, so far, the most popular
of accessibility measures. It is based on network distances combined
with a measure of opportunity or attractiveness at the other nodes (Hanson,
1995) . The distance or effort that needs to be overcome reduces the number
of opportunities or attractions at a particular node. This gives a measure
of the relative accessibility of that location. An impedance function
is used to define the effort needed to overcome distance or effort. The
most widely used impedance functions are the inverse power function, a negative
exponential function, or a modified Gaussian function. A major problem
with this seemingly straightforward approach is that, as urban structures, opportunities,
and people's desires and abilities change, the distance decay or impedance function
also changes. To be successful, these functions need to be fine-tuned
for each new study to reflect the true impedance at that point in time and space.
Another problem here is that zonal centroids are used, and so the models
assume that all individuals are gathered at the centroid and enjoy the same
accessibility, although they may perceive the set of alternatives quite differently
(Ben-Akiva & Lerman, 1979) . Also, any change in intra-zonal access,
like local roads or shuttle service, will not be reflected. Pirie (1979)
says that zonal accessibility measures not only neglect the distribution of
activity sites within the zone but also assume that all individuals within the
zone have the same set of opportunities.
If the impedance function from the gravity model can be made to exclude opportunities beyond a set distance, this leads to another type of measure of accessibility, cumulative opportunity measures. These are based on how many opportunities are available within a certain distance, travel time, or cost (Wachs & Kumagai, 1973) . They do not discount measures of opportunity over this restricted distance, because all sites within the distance are rated as equally accessible. For those with a car this is not such a shortcoming as for those who are on foot.
Traditional measures treat attractions, such as zonal employment possibilities, equally for all members in a designated zone. In fact, job skills and job vacancies may mean that no one in the zone can be employed there. Also, with these measures it is incorrectly assumed that all trips originate from the home location. They ignore the many trips that originate from the work location (such as noon errands and child-care), other anchor points, and the abundance of multi-linked trips (Golledge & Stimson, 1997) . These complex linkages of multi-stop trips present major problems for these types of models. Although helpful, these models appear to be more a measure of mobility around a network. They are perhaps best for modeling the transportation network and looking for ways to model traffic flow and future improvements. Although accessibility is central to human activity and movement, standard transportation analysis such as travel demand modeling and methods like Intelligent Transportation Systems (ITS) actually ignore accessibility and, instead, focus on increasing system throughput. Zonal models are highly efficient computationally, and the data are available from many sources, usually already in digital format.
Aristotle reminded us to examine problems at the scale of detail that they admit to us; this research problem needs to be examined on the individual or disaggregate level. More than measures of physical mobility or distance are needed—it is also necessary to examine accessibility from a behavioral perspective. These methods (the aggregate, zonal, network distance, time, or cost models), fail to answer the most important question “what about the people?"
The seminal work by Hägerstrand
(1970) , "What about people in regional science," brought human actors
to the forefront of physical measures of accessibility. His work led
to the realization that it was necessary to address accessibility from an individual
and behavioral perspective. One of his major concepts was his theoretical
framework of constraints, which influence “how paths are channeled
or dammed up” (p. 11). This framework is applicable to all
people but is especially pertinent when analyzing the activity space and travel
behavior of different disabled groups. Hägerstrand points out that
the “set of potentially possible actions is severally restricted”
by these constraints that are “imposed by physiological and physical needs”
(p. 11) as well as other types of decisions, both public and private.
Daily, we face societal constraints on our time and travel that restrict
our freedom to interact in the environment, and Hägerstrand identifies
three classes of constraints: capacity, coupling, and
authority . Marston et al. (1997) consider how these constraints
can affect people with limited vision. Capacity constraints limit
human activity because of biological (like sleeping and eating) and physical
conditions (ambulatory problems or restricted vision). The lack of tools
, such as a car or ability to use transit, affect the travel time or distance
which one can travel (based on the total time budgeted or available.).
Lack of access to tools or materials are then also capacity constraints that
limit activities. Coupling constraints are those arrangements
of time and duration where people have to meet up with other people or tools,
(such as rides), to perform activities, or to form bundles of consumption,
social interaction, and production (Pred, 1977)
. These couplings or bundles occur when people have to arrange
their schedule to match that of another. For example, using transit requires
meeting the vehicle and being dependent on its arrival time. A work schedule
might involve having to meet clients or superiors within a small time window
or leaving at a specified hour, regardless of the transportation available.
Authority constraints refer to social and economic barriers and all
the laws and rules of a structured society. These constraints limit freedom
of movement and activity participation, or the freedom to “choose activity
bundles” (Pred, 1977, p. 638) . Indeed, these three types
of constraints form a system of barriers that prevent certain movements or the
ability to move freely (Hägerstrand, 1975)
.
The urban landscape and our interactions within it are rapidly changing due to forces like suburbanization, transportation and telecommunication technologies, economic and global restructuring, and the life stages and cycles of the people within. These interactions are widely studied, and Pirie (1979, p. 299) states “there can scarcely be a book or paper on urban and regional affairs that does not allude to the notion of accessibility.”
Hanson, (1995, p. 4) defines accessibility as "the number of opportunities, also called activity sites, available within a certain distance or travel time." Ingram (1971) says that accessibility is an inherent characteristic of place and is operationalized in terms of overcoming some form of friction. There are three dimensions to these definitions. First, a distance or spatial interaction among locations (activity sites); second, a transportation system or network that links these locations; and, third, the desire and means or ability (financially, physically, and temporally) to visit these sites and overcome the spatial separation (an impedance function).
The study of the extent and strength of human interaction with the environment is a central concern within the study of Human Geography. These measures can be used to address planning and policy decisions (Talen, 1995, 1996) . Accessibility is also a common focus for geographic study of fields ranging from social equity to urban form, and from transportation to economic growth. Although central to this research, accessibility is often a misunderstood and poorly measured construct and it seems that every sector of this field has its own definitions and methods for discovering this interrelationship and process. This is true, because finding an operational concept of accessibility is very difficult and quite complex. Gould (1969, p. 64) summed up these problems well with his statement that accessibility "is a slippery notion…one of those common terms that everyone uses until faced with the problem of defining and measuring it."
Traditional measures treated accessibility as strictly a physical or spatial construct. They were usually based on distance between origins and destinations. Later, other surrogates for travel efforts were used, such as network modeling showing travel times or costs. All these models of spatial separation and interaction are based on physical networks or topology and might be considered as revealing a potential accessibility within that system. They ignored constraints of time or constraints on the activities. They most certainly ignored other social and individual constraints that might hinder the ability to connect with different activities.
Relative measures of accessibility (Ingram, 1971) are expressed by distance or travel time between two points. The further away the points are, the less accessible they are. The measure is usually symmetric if the connection between the two places is not unidirectional. Physical distance, time, or some measure of cost can be used to measure the degree of spatial separation. Integral measures determine the relationships between one point and all others in the study area. This is like the attraction model in store location theory. Unlike the relative measure, it is not reflexive (the accessibility of a store to all homes is not the same in the other direction). It can also be used to show which points have the highest or lowest degree of accessibility to the entire set of opportunities. This can be used to determine social equity in the case of planning agendas (Talen, 1995) .
The gravity measure is, so far, the most popular of accessibility measures. It is based on network distances combined with a measure of opportunity or attractiveness at the other nodes (Hanson, 1995) . The distance or effort that needs to be overcome reduces the number of opportunities or attractions at a particular node. This gives a measure of the relative accessibility of that location. An impedance function is used to define the effort needed to overcome distance or effort. The most widely used impedance functions are the inverse power function, a negative exponential function, or a modified Gaussian function. A major problem with this seemingly straightforward approach is that, as urban structures, opportunities, and people's desires and abilities change, the distance decay or impedance function also changes. To be successful, these functions need to be fine-tuned for each new study to reflect the true impedance at that point in time and space. Another problem here is that zonal centroids are used, and so the models assume that all individuals are gathered at the centroid and enjoy the same accessibility, although they may perceive the set of alternatives quite differently (Ben-Akiva & Lerman, 1979) . Also, any change in intra-zonal access, like local roads or shuttle service, will not be reflected. Pirie (1979) says that zonal accessibility measures not only neglect the distribution of activity sites within the zone but also assume that all individuals within the zone have the same set of opportunities.
If the impedance function from the gravity model can be made to exclude opportunities beyond a set distance, this leads to another type of measure of accessibility, cumulative opportunity measures. These are based on how many opportunities are available within a certain distance, travel time, or cost (Wachs & Kumagai, 1973) . They do not discount measures of opportunity over this restricted distance, because all sites within the distance are rated as equally accessible. For those with a car this is not such a shortcoming as for those who are on foot.
Traditional measures treat attractions, such as zonal employment possibilities, equally for all members in a designated zone. In fact, job skills and job vacancies may mean that no one in the zone can be employed there. Also, with these measures it is incorrectly assumed that all trips originate from the home location. They ignore the many trips that originate from the work location (such as noon errands and child-care), other anchor points, and the abundance of multi-linked trips (Golledge & Stimson, 1997) . These complex linkages of multi-stop trips present major problems for these types of models. Although helpful, these models appear to be more a measure of mobility around a network. They are perhaps best for modeling the transportation network and looking for ways to model traffic flow and future improvements. Although accessibility is central to human activity and movement, standard transportation analysis such as travel demand modeling and methods like Intelligent Transportation Systems (ITS) actually ignore accessibility and, instead, focus on increasing system throughput. Zonal models are highly efficient computationally, and the data are available from many sources, usually already in digital format.
Aristotle reminded us to examine problems at the scale of detail that they admit to us; this research problem needs to be examined on the individual or disaggregate level. More than measures of physical mobility or distance are needed—it is also necessary to examine accessibility from a behavioral perspective. These methods (the aggregate, zonal, network distance, time, or cost models), fail to answer the most important question “what about the people?"
The seminal work by Hägerstrand (1970) , "What about people in regional science," brought human actors to the forefront of physical measures of accessibility. His work led to the realization that it was necessary to address accessibility from an individual and behavioral perspective. One of his major concepts was his theoretical framework of constraints, which influence “how paths are channeled or dammed up” (p. 11). This framework is applicable to all people but is especially pertinent when analyzing the activity space and travel behavior of different disabled groups. Hägerstrand points out that the “set of potentially possible actions is severally restricted” by these constraints that are “imposed by physiological and physical needs” (p. 11) as well as other types of decisions, both public and private. Daily, we face societal constraints on our time and travel that restrict our freedom to interact in the environment, and Hägerstrand identifies three classes of constraints: capacity, coupling, and authority . Marston et al. (1997) consider how these constraints can affect people with limited vision. Capacity constraints limit human activity because of biological (like sleeping and eating) and physical conditions (ambulatory problems or restricted vision). The lack of tools , such as a car or ability to use transit, affect the travel time or distance which one can travel (based on the total time budgeted or available.). Lack of access to tools or materials are then also capacity constraints that limit activities. Coupling constraints are those arrangements of time and duration where people have to meet up with other people or tools, (such as rides), to perform activities, or to form bundles of consumption, social interaction, and production (Pred, 1977) . These couplings or bundles occur when people have to arrange their schedule to match that of another. For example, using transit requires meeting the vehicle and being dependent on its arrival time. A work schedule might involve having to meet clients or superiors within a small time window or leaving at a specified hour, regardless of the transportation available. Authority constraints refer to social and economic barriers and all the laws and rules of a structured society. These constraints limit freedom of movement and activity participation, or the freedom to “choose activity bundles” (Pred, 1977, p. 638) . Indeed, these three types of constraints form a system of barriers that prevent certain movements or the ability to move freely (Hägerstrand, 1975) .
Scheduling of activities is spatially constrained but also highly dependent on available time, desire, means, and individual preferences and abilities. By increasing the resolution to this level of observation and analysis one can find not only the potential accessibility of a system or network, but also a revealed and realized accessibility of individuals, households, and groups. Space-time constraints and individual time budgets determine an individual’s accessibility. It does not matter how many opportunities are located at some distance to an individual, but how many of these are within reach of the individual's capacity and situation (Dyck, 1989) . The zone or census tract models give one only averages to work with. With the use of space-time prisms (Lenntorp, 1976) , one can use potential path space to determine individual accessibility to the environment. No longer tied to zonal averages, one can better understand accessibility for different groups like the elderly, children, non-drivers, families, empty-nesters, single people, and disadvantaged or disabled people.
Behavioral research finally freed us from the tyranny of the rational "economic man" who had perfect knowledge and worked to maximize opportunities. From the work of Golledge and others (e.g., Golledge, 1967; Wolpert, 1965; Amedeo & Golledge, 1975), it is known that people "satisfice" rather than optimize and do not possess perfect knowledge of all available opportunities (opportunity sets) (Golledge, Kwan, & Gärling, 1994) . As work with the vision-impaired has shown, lack of information about the environment is the most limiting factor in independent travel and access to urban opportunities (Marston et al., 1997) . Add to this the anxieties, difficulties, and stress, along with slower walking and search times, and it is no wonder that blind people make fewer trips. For example, it is quite probable that a blind person and a sighted person who lived next door to each other would have completely different access to urban opportunities, but these differences would never be measurable with any of the traditional, physical, and network based systems.
Time Geography was not considered a network accessibility measure at first, probably due to the problems of scaling the concepts into workable aggregate units. Advances in GIS and spatial modeling now allow researchers like Kwan (1998a, 1998b, 1999) and Miller (1991, 1999) to use Hägerstrand's concepts to better understand the individual nature of accessibility. Their research has shown that the problems of efficient computation and geo-coding of individual origins and destinations no longer pose a constraint on the examination of accessibility at its necessary scale of study—that of the individual. These time-space approaches will bring research much closer to Weibull’s definition of accessibility as a measure of an individual’s freedom to participate in activities in the environment (Weibull, 1980) .
This new use of Time Geography allows one to look at both structures and functions of the environment. Instead of a measure of potential accessibility, it is now possible to determine revealed or realized accessibility for different groups of people. Because scheduling of activities is not only spatially constrained but also time dependent, research in human geography demands that people should be the scale of interest for the understanding of spatial interactions.
With time-space prisms, one can also examine gender issues of equality, as researched by Kwan (1999) . She examines issues of space-time constraints such as those imposed by work schedules, child-care obligations, and coupling one’s schedule to friends, children, and those in authority, such as stores or services that are only open certain hours. This author would have liked to use this kind of research to analyze the accessibility of blind people; but simply comparing blind travel patterns to a group of sighted people would have revealed little more than what is already known—i.e., that the majority of people who are blind have a very restricted activity space and hence less accessibility than people who are sighted. There was also no way to test blind people’s actual travel behavior through diaries, with and without new technical travel aids, as no urban area is so equipped.
In this experiment, both objective field data (such as travel times and errors) as well as subjective data (including estimates, opinions, and affective states) were collected and analyzed. The accessibility measurements used traditional models with a behavioral approach. It is easy to see how the lack of a driver’s license, having to rely on transit or other people for travel, along with the lack of vision to inform people about the environment and the lack of information needed to perceive it quickly and correctly add many constraints to life, travel, and accessibility for a blind person.
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