Beyond the Boundary: New Insights from Inside the Space-Time Prism - Space-Time Integration in Geography and GIScience - page 186

Most studies involving the space-time prism only employ the prism boundary to
delimit individual's mobility and accessibility to the environment and the feasible
activities within that environment. In contrast, little attention has been paid to
the properties of prism interior and its implications for measuring accessibility
and its benefits and costs. Although some researchers have developed methods
for estimating the properties of activity locations that intersect with the prism
(Geurs and Van 2004 ;Kwan 1998 ), intrinsic properties of the prism interior have
not been well-explored. Intuitively, we should not expect properties such as the
probabilities of visiting different locations and the distributions of feasible velocities
to be uniform throughout the prism interior. For example, the locations near the
space-time axis linking the two prism anchors are more likely to be visited than
the locations near the prism boundary since there are more possible paths through
the former locations (Winter and Yin 2010a , b ). In addition, different paths with
different velocity profiles may pass through a given location, implying a distribution
of feasible velocities constrained by the prism's maximum velocity.
This chapter analyzes properties of the prism interior and the implications
of these properties for measuring accessibility benefits and costs. We begin by
reviewing the conceptual and analytical framework of time geography defined by
Torsten Hägerstrand and his followers. Based on this, we explore the properties of
prism interior, focusing on the visit probability and the velocity profile for each
location within the prism. To illustrate the potential of estimating the properties
of the prism interior, we provide two examples: (1) a modified utility-based
accessibility benefit measure that considers the visit probabilities; and (2) a new
measure for the potential environmental costs of accessibility based on the visit
probabilities and velocity distributions within the prism.

12.2 Prisms in Classic Time Geography

Time geography (Hägerstrand 1970 ) represents individual activities considering
both spatial and temporal constraints on mobility and activity participation. A
space-time path represents historical (or simulated) movement of an individual
in geographical space with respect to time. Figure 12.1 a illustrates a space-time
path for an individual's typical work-to-home journey. The path goes through three
activity locations that are dispersed in space: a work place, home, and a grocery
store. The former two locations are relatively fixed in an individual's daily routine,
while the third location is flexible because the individual can possibly shop for
groceries at other stores and at other times. In order to travel between activity
locations, the individual needs to trade time for space. The velocities to travel
between locations determine the shape of the space-time path. When an individual
conducts stationary activities, s/he does not move in space but still moves with
respect to time, which results in a path segment parallel to the vertical axis for time.
When an individual travels between two locations, s/he moves along an inclined path