GIS Tools for Measuring Individual
Accessibility in Real and Virtual
Spaces
Harvey J. Miller
Department of Geography
University of Utah
Salt Lake City, Utah USA
harvey.miller@geog.utah.edu
eSI Visitor Seminar, National e-Science Centre, Edinburgh,
Scotland - 06 September, 2007
1
Introduction
• What is accessibility?
– A multi-faceted concept
– Individual’s ability to conduct activities
• Shopping, education, health care, employment,
recreation, socializing
– Fundamentally spatial
• Ability to be “present” at an activity location
– Physical presence
– Tele-presence
2
Introduction
• Why is accessibility important?
– Accessibility is central to
• Cities – compress lives in space & time
• Transportation – physical access
• Communication – info access
– Accessibility in theory and application
• Theory - Central to urban, transportation, social,
economic theories
• Application - Performance & social measures
3
Introduction
• Renaissance in accessibility measurement
– Policy
• Community livability (USA)
• Social exclusion (Europe)
• Resources, opportunities, social networks, social capital
– GIS and geospatial technologies
• Detailed geographic data
• Spatial analysis, visualization
• We need better accessibility tools
– Not just better maps of old measures
4
Outline of talk
• Traditional accessibility measures
– Place-based perspective
– High mobility & connectivity
• Individual accessibility: Theories and tools
– Time geography
– Enabling geo-spatial technologies
• GIS tools for measuring individual accessibility
– Network spaces
– Multidimensional spaces
– Virtual spaces
• Locational privacy
5
Traditional accessibility measures
• Place-based methods
– Distance
• Spatial or temporal
separation
– Topological
• Network connectivity
– Attraction-accessibility
• Spatial interaction &
spatial choice
– Benefits
• Consumer surplus
6
Traditional accessibility measures
• People and place have become complex
– A shrinking but shriveling world
- Waldo Tobler
• Transport costs have collapsed
• But, relative differences are increasing
– An accelerated world
– James Gleick
• Increasing mobility at all geographic scales
• Activity organization is more complex
– A fragmenting world -
Helen Couclelis
• Information and communication technologies (ICTs)
• Activities are disconnecting from place and time
7
Individual accessibility: Theories and tools
• Time geography
– Torsten Hägerstrand (1960s)
– Spatio-temporal constraints on human
activity
• Types of constraints
– Capability – physical needs, resources
– Coupling – need to be coincident with
others
Lund, Sweden
November 2001
– Authority – fiat restrictions
8
Theories and tools
• Time geographic concepts
– Types of activities
• Fixed – e.g., home, work
• Flexible – e.g., shopping,
recreation
– Stations
• Locations and durations of
activities
– Space-time path
• Individual movement with
respect to time
9
Theories and tools
• Space-time prism
– Accessibility to environment
• Spatio-temporal region
• Activities & resources within
the region
vij max velocity
stationary
activity time
time budget
– Determined by
• Space-time anchors
anchors
– Fixed activities
• Time budget
• Min. required activity time
• Max. travel velocity
10
Theories and tools
• Classical time geography - limitations
– Uniform travel velocity
• Simplifying assumption for tractability
– Low-resolution
• Lack of rigor in basic definitions, constructs
• Cannot exploit new geospatial technologies & data
– Physically-based theory
• Does not handle information & communication
technologies well
11
Enabling geo-spatial technologies
• Location-aware technologies
(LATs)
– Global Positioning System
– Radiolocation
– Inertial navigation
• Location-based services
(LBS)
– Wireless Internet’s “killer app”
– Information based on location
in real time
12
IBM Developerworks Library
www-106.ibm.com/developerworks
Enabling geo-spatial technologies
• Space-time ecology
– Where and when do people
spend time?
– Sensitive to social factors
• Age/life cycle stage
• Socio-economic status
• Gender roles & household
organization
• Culture
– LATs allow unprecedented,
detailed analysis!
African-American women
Asian- American women
Space-time paths in Portland, Oregon
Mei-po Kwan, Ohio State University
13
Enabling geo-spatial technologies
• GIS
– Mobile objects databases
• Geosimulation
– Agent-based modeling
• High-resolution space-time
data
– Empirical and/or synthetic
– Rethink theory and analysis of
human behavior
14
EpiSims: Individual-level simulation
of disease propagation based on
contacts in space and time
episims.lanl.gov
Individual accessibility in real and virtual spaces
• Individual in space and time
– Activity schedules and locations
– Transportation resources and ICTs
• Leverages geospatial science & technology
– GIS, LATs, mobile objects, simulation
• Accessibility in three spaces
– Network – relax constant velocity assumption
– Multidimensional – rigorous measurement theory
– Virtual – relax physical space assumption
15
Accessibility in network spaces
• Transportation networks
– Realistic paths and travel times
– Linked to individual, network
referenced activity schedules
PPT
• Network time prism
– Potential path tree (PPT)
– Potential network area (PNA)
16
PNA
Accessibility in network spaces
• Dynamic networks
– Travel velocity varies by location &
time
• Congestion
• Activity timing
• Other extensions
– Multimodal networks
• O’Sullivan et al. (2000) IJGIS
– Cognitive/preference constraints
• Kwan and Hong (1998) JGS
17
Dynamic network PPT for
SLC morning commute
Accessibility in multidimensional space
• Problems with time geography
– No analytical statements of basic entities &
relationships
• Cannot support high resolution measurements
• Query and analytical tool development
– Specific to two spatial dimensions
• Cannot link 1D (networks) and 2D
• Cannot extend to 3D (natural space)
18
Accessibility in multidimensional space
• Time geographic measurement theory
– Paths, prisms etc under perfect information
• Finite but perfect instruments
• Real world instruments are finite but imperfect
– Theory properties
• Information assumptions are explicit
• Multidimensional space and time
• Supports
– Space-time query design
– High-resolution measurement
– Analysis of error & uncertainty propagation
19
Accessibility in multidimensional space
• Space-time path
– Two major components
• Control points measured
• Segments - unobserved
– Perfect info assumption
• Control points
determine segments
perfectly
Recall: Classic space-time path
20
t
sij t   1   xi  x j
 
t  ti
t j  ti
c j  x j , t j 
ci  xi , ti 
X
21
Accessibility in multidimensional space
• Space-time prism
vij max velocity
– Temporally adjacent
control points
– Maximum velocity:
Assumed or measured
stationary
activity time
time budget
anchors
• Temporally disaggregate
prism
– Prism at time t
– Intersection of simple
objects in n - dimensional
space
Recall: Classic space-time prism
22
tj
Zij t 
t
ti
xi
xj
Case 1: No activity time
Zij (t) : A time “slice” of the prism
23
t
ti
xi
xj
“Future disc” of ci

fi t   x x  xi  t  ti vij
24

tj
t
xi
xj
“Past disc” of cj

p j t   x x j  x  t j  t vij
25

tj
Zij t 
t
ti
xi
xj
Prism at time t: Intersection of two discs
Zij t   fi (t )  p j (t )
26
tj
Past disc
t 
t
Disc intersection
Future disc
ti
xi
xj
Evaluating the prism using time boundaries
27
Accessibility in multidimensional space
Disc
Intersection
1D
Line segment
Line segment
2D
Circle
Lens-shaped region
3D
Sphere
Lens-shaped volume
Simple geometric objects - easy to compute
28
Zij t 
“Potential path ellipse”
(aka PPA)
gij  x x  xi  x j  x   tij  aij vij 

xj
xi
Case 2: Stationary activity time
Zij t   x f i t  p j t  gij 


29



tj
Past disc
t 
Past disc & PPA
t 
PPA
t
t
Future disc & PPA
0
Future disc
ti
xi
xj
30
Accessibility in multidimensional space
• Intersections
– Path-prism intersections
• Is a path or station within a
prism at time t ?
– Point in disc and/or ellipse
problem
– Prism-prism intersections
• Do two prisms intersect at
time t ?
– Intersection of discs and or
ellipses
– n-disc case: Helly’s theorem
31
Prism-prism intersection –
Worse case in 2D
Accessibility in multidimensional space
• Example
Future disc(t’’)
– Future and past
discs based on
network travel
Past disc(t’)
i
j
– Phoenix, Arizona
USA
PPAij
32
Accessibility in virtual space
• Virtual interaction
Temporal
– Accessibility to information
and people using ICTs
Presence
Telepresence
Synchronous
SP
Face-to-face
ST
Telephone
TV
Asynchronous
AP
Post-it notes
AT
Mail
Email
Webpages
– ICT modes
• Spatial constraints
– Presence
– Telepresence
Spatial
• Temporal constraints
– Synchronous
– Asynchronous
Donald Janelle (1995)
33
Accessibility in virtual space
• New time geographic objects
– Portal
• A station that allows virtual
interaction
Spatial footprint of a portal
– A point location
– A service radius
• Examples:
– Internet connection (point w/ zero
radius)
– WAP (point w/ positive radius)
– Cell phone base station (point w/
positive radius)
A path and portals
34
Accessibility in virtual space
A path and portals
35
Accessibility in virtual space
– Message windows
• Communication events
• Defined by a portal and a
time span
• Send and receive windows
– Two types
• General: An actor
interacting with a portal
• Strict: An actual message
36
Accessibility in virtual space
• Virtual interaction constraints
– Space
• Easy! - Presence or not
– Time
• More difficult
• Allen time predicates applied to
message windows
37
Predicate
Definition
t s BEFORE t r
t sj  t kr
t s BEFORE-1 t r
t is  t lr
t s MEETS t r
t sj  t kr
t s MEETS-1 t r
t is  t lr
t s EQUAL t r
t is  t kr  t sj  t lr
t s OVERLAP t r
t is  t kr  t sj  t lr
t s OVERLAP-1 t r
t is  t kr  t sj  t lr
t s DURING t r
t is  t kr  t sj  t lr
t s DURING-1 t r
t is  t kr  t sj  t lr
t s STARTS t r
t is  t kr  t sj  t lr
t s STARTS-1 t r
t is  t kr  t sj  t lr
t s FINISHES t r
t is  t kr  t sj  t lr
t s FINISHES-1 t r
tis  tkr  t sj  tlr
Accessibility in virtual space
• Example: Who can receive a given message?
– Synchronous
• “Actor must interact with a portal during the entire
message”
– Asynchronous
• “Actor must interact with a portal anytime after the
message is sent”
• Side conditions (not shown):- There must be enough time
Sent message
Possible receive window
38
Locational privacy
Random
perturbation
mask
• Privacy protocols
–
–
–
–
Notify
Opt-in/out
Security & authorization
Build privacy into spatial
representations
• Spatio-temporal masking
– Controlled noise into spacetime trajectories
Spatiotemporal
weeding
Scott Bridwell &
Harvey Miller
U of U
Geography
39
Conclusion
• Traditional accessibility measures
– Still important, but incomplete
– High mobility and ICTs
• Complex relationships between person, place & activities
• Individual accessibility measures
– Activities in space and time
• Transportation networks
• High-resolution measurement using LATs
• Virtual interaction using ICTs
– GIS tool development for accessibility analysis
• Space-time activity queries, toolkits
40
Conclusion
• Future research
– Synoptic measures
• Aggregate accessibility patterns
• Make sense of large space-time activity datasets
– Imperfect measurement
• Error propagation in time geographic queries
– Applications: Theory and models
• Accessibility-related phenomena
– Travel demand, urban dynamics, social networks, social
exclusion, epidemiology
41
Questions?
• Here and now?
– or asynchronous telepresence?
• harvey.miller@geog.utah.edu
• Related papers
(available at: www.geog.utah.edu/~hmiller)
– 2007. “Place-based versus people-based geographic information
science,” Geography Compass, 1, 503-535.
– 2005. "A measurement theory for time geography," Geographical
Analysis, 37, 17-45
– 2005. "Necessary space-time conditions for human interaction,"
Environment and Planning B: Planning and Design, 32, 381-401 .
42