1

GIS Tools for Measuring Individual Accessibility in Real

and Virtual Spaces

Harvey J. MillerDepartment of Geography

University of UtahSalt Lake City, Utah USA

harvey.miller@geog.utah.edu

eSI Visitor Seminar, National e-Science Centre, Edinburgh, Scotland - 06 September, 2007

2

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

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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

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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

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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

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Traditional accessibility measures

• Place-based methods– Distance

• Spatial or temporal separation

– Topological• Network connectivity

– Attraction-accessibility

• Spatial interaction & spatial choice

– Benefits• Consumer surplus

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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

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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

– Authority – fiat restrictions

Lund, Sweden

November 2001

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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

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Theories and tools

• Space-time prism– Accessibility to environment

• Spatio-temporal region• Activities & resources

within the region

– Determined by• Space-time anchors

– Fixed activities

• Time budget• Min. required activity time• Max. travel velocity

t

ija

ijt

jt

jx ix

it

x

max velocity

stationaryactivity time

time budget

anchors

ijv

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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

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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

IBM Developerworks Library

www-106.ibm.com/developerworks

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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!

Space-time paths in Portland, Oregon Mei-po Kwan, Ohio State University

African-American womenAsian- American women

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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

EpiSims: Individual-level simulation of disease propagation based on contacts in space and time

episims.lanl.gov

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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

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Accessibility in network spaces

• Transportation networks – Realistic paths and travel

times – Linked to individual,

network referenced activity schedules

• Network time prism– Potential path tree (PPT)– Potential network area

(PNA)

PPT

PNA

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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

Dynamic network PPT for SLC morning commute

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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)

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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

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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

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jjj tc ,x

iii tc ,x

jij ts xxi 1

ij

i

tt

tt

X

t

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Accessibility in multidimensional space

• Space-time prism– Temporally adjacent

control points– Maximum velocity:

Assumed or measured

• Temporally disaggregate prism– Prism at time t– Intersection of simple

objects in n - dimensional space

t

ija

ijt

jt

jx ix

it

x

max velocity

stationaryactivity time

time budget

anchors

ijv

Recall: Classic space-time prism

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jx

t

jt

ix

tijZ

)(tZij : A time “slice” of the prism

Case 1: No activity time

it

24

jx

it

ix

ijiii vtttf xxx

“Future disc” of ci

t

25

jx

jt

ix

ijjjj vtttp xxx

“Past disc” of cj

t

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jx

t

jt

ix

)()( tptftZ jiij

Prism at time t: Intersection of two discs

it

tijZ

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jx ix

Evaluating the prism using time boundaries

tt

jt

it

Future disc

Disc intersection

Past disc

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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

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jx ix

Case 2: Stationary activity time

ijijijjiij vatg xxxxx

“Potential path ellipse” (aka PPA)

ijjiij gtptftZ x

tZij

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jx ix

it

0t

t

t

t

jt

Future disc & PPA

Future disc

PPA

Past disc & PPA

Past disc

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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

rkc

qic

rlc

qjc

Prism-prism intersection – Worse case in 2D

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Accessibility in multidimensional space

• Example– Future and past

discs based on network travel

– Phoenix, Arizona USA

ij

Past disc(t’)

PPAij

Future disc(t’’)

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Accessibility in virtual space

• Virtual interaction– Accessibility to

information and people using ICTs

– ICT modes • Spatial constraints

– Presence– Telepresence

• Temporal constraints– Synchronous– Asynchronous

Temporal Spatial

Presence Telepresence

Synchronous SPFace-to-face

STTelephoneTV

Asynchronous APPost-it notes

ATMailEmailWebpages

Donald Janelle (1995)

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Accessibility in virtual space

• New time geographic objects– Portal

• A station that allows virtual interaction

– 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

Spatial footprint of a portal

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Accessibility in virtual space

A path and portals

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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

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Accessibility in virtual space

• Virtual interaction constraints– Space

• Easy! - Presence or not

– Time• More difficult• Allen time predicates applied to message windows

Predicate Definition

st BEFORE rt rk

sj tt

st BEFORE-1 rt rl

si tt

st MEETS rt rk

sj tt

st MEETS-1 rt rl

si tt

st EQUAL rt rl

sj

rk

si tttt

st OVERLAP rt rl

sj

rk

si tttt

st OVERLAP-1 rt rl

sj

rk

si tttt

st DURING rt rl

sj

rk

si tttt

st DURING-1 rt rl

sj

rk

si tttt

st STARTS rt rl

sj

rk

si tttt

st STARTS-1 rt rl

sj

rk

si tttt

st FINISHES rt rl

sj

rk

si tttt

st FINISHES-1 rt rl

sj

rk

si tttt

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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

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Locational privacy

• Privacy protocols– Notify– Opt-in/out– Security & authorization– Build privacy into spatial

representations

• Spatio-temporal masking– Controlled noise into space-

time trajectories

Random perturbation

mask

Spatio-temporal weeding

Scott Bridwell & Harvey

Miller

U of U Geography

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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

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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

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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 .