Transcript Network Analysis

Network Analysis
Hong Kong Hospital Coverage
Surveyed Hospitals
Population Density
0 - 12700
12700 - 36900
36900 - 68700
68700 - 110700
110700 - 193700
Distance Zones to Hospital
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TPU-based Population Density
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12000 - 35200
35200 - 59200
59200 - 102400
102400 - 193700
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24 Kilometers
Copyright, 1998-2014 © Qiming Zhou
GEOG3600. Geographical Information Systems
Network Analysis
 What
is network?
 Why use networks?
 Network data structure
 Network data models
 Network analysis capabilities
Network Analysis
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What is network?
 Much
of the economic and social activity
of the world is organised into networks.
 The form, capacity and efficiency of
these networks have a substantial
impact on our standard of living and
affect perception of the world around us.
 Networks also exist in the physical
world,
 e.g.
networks of streams and rivers.
Network Analysis
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Examples of networks

rail network (MTR)
 road and highway network (KMB)
 electricity network (CLP)
 telephone network (PCCW)
 pile line network (Water Supplies Department)
 air transportation network (Cathay Pacific)
 parcel delivery network (DHL Courier)
 street network (Emergency Services, Police
Department, etc.)
Network Analysis
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Questions that require use
of network
 What
is the best route from a location to a
given destination?
 Where should I locate a service centre?
 Which centre serves a particular location?
 How accessible is a location to other
locations?
 How many trips will be generated between
origins and destinations?
 Given street addresses, how can I map
occurrence of given events on a street map?
Network Analysis
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Network data structure
A
network can be represented digitally
by nodes and links.
 Nodes
represent intersections,
interchanges and confluence points.
 Links represent transportation facility
segments between nodes.
Network Analysis
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Nodes and links
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2
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4
Node
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Network Analysis
Link
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Topological classification
of networks

Planar networks:
No links intersect
except at nodes


e.g. road and
highway networks
Non-planar
networks: Links
intersect

e.g. Airline
networks
Network Analysis
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Network classification and
applications
Networks
Planar
networks
Paths
Trees
Circular
Linear
flows
Non-planar
network
Cells
Linear
barriers
Network Analysis
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Network level of details



The fine level is nearly identical to the actual street
network
The medium level corresponds to transportation planning
practice
The coarse level only represents the arterial roads
Coarse level network
Medium level network
2039
2039
11
2035
Fine level network
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2065
2035
2033
2065
2033
3636
3636
2051
12
2051
12
Network Analysis
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Link versus node based
approaches

Most networks are entered as line graphs in a
vector GIS and attribute data is recorded with
links rather than with nodes.
 Example for link description include traffic load,
capacity of the road segment, etc.
 The link based approaches is not entirely
suitable for applications that deal directly with
nodes in a network.
 A typical example is the air passenger volume
between cities where there is no direct link
(multiple routes).
Network Analysis
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Network data models




Network Links
 linear entities through which movement and
communications takes place (e.g. road segment)
Network Nodes
 end points of network links (e.g. towns, cities, etc)
Stops
 locations visited in a path (e.g. customers on a
delivery route)
Centres
 discrete locations where there exists a supply or
attraction (e.g. shopping centres, airports, fire
stations)
Network Analysis
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Turns

represent relationships between network links
 can affect movement through a network (e.g. a
right hand turn against on-coming traffic takes more
time than proceeding straight through)
There are n2 possible
turns at every network
node, where n is the
number of links
connected at that node.
Even at a node with a
single link, it is possible
to make one u-turn.
U-turn
Left
Right
Straight transition
Network Analysis
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Links


Link Attributes
 attributes describing links (e.g. one- or two-way,
number of lanes, etc.)
Link Impedance
 the cost of moving on a network link, usually given in
terms of time or money cost or a generalised cost
 The impedance depends on the direction of travel
45 sec
60 sec
70 sec
70 sec
Network Analysis
60 sec
45 sec
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Link demand

the level of the resource that is associated with a
particular network link.

e.g. the number of school children residing on a
street (link demand) which are assigned to a
centre (school).
The children who live
along the streets of the
network utilise the
resources of the
school, creating a link
demand
School
5 children
Network Analysis
2 children
3 children
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Centres

Supply: total quantity of resource available to
satisfy the demand associated with links of network
 Maximum Impedance: is the maximum total
impedance that may be encountered between the
centre and the end of any allocated sequence of
links
2
2
6
2
7
1
2
Maximum impedance = 15
8
5
5
10
2
3
Network Analysis
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3
10
5
10
5
2
5
5
7
3
2
2
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Analysis capabilities

Location/Allocation


Routing


finding shortest (or cheapest or quickest) route
between locations
Accessibility


optimally locating a set of objects so that
variable or variables will achieve a maximum or
minimum value
providing an aggregate measure of how
accessible a location is to other locations
Address Matching

finding spatial locations based on address
descriptions
Network Analysis
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Location/allocation

The problem to be addressed
 Private sector

e.g. optimum location of a factory for minimising
the cost of getting products to consumers
 e.g. optimum locations of warehouses in
territory for minimising transportation costs

Public sector

Ordinary services: health, education and welfare
facilities
 Emergency services: medical, ambulance,
police, fire, vehicle breakdown services
Network Analysis
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Meaning of most accessible
A location pattern is most acceptable to people when:
 the total of the distances of all people from their closest
facility is minimum (aggregate distance minimisation
criterion).
 the farthest distance of people from their closest facility
is minimum (minimax distance criterion).
 the number of people in the proximal area surrounding
each facility is approximately equal (equal assignment
criterion).
 the number of people in the proximal area surrounding
each facility is always greater than a specified number
(threshold constraint criterion).
 the number of people in the proximal area surrounding
each facility is never greater than a specified number
(capacity constraint criterion).
Network Analysis
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Location

Single source location problems


find a location from which the sum of the
distances to all other points is least (median of
the graph).
Multi-facility location problems


Minimising average distance
Minimising the maximum distance to closest
supply centre
 Minimising the number of centres required for
every demand point to be within a critical
distance of a supply point
 Minimising average distance subject to a
maximum distance constraint
Network Analysis
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Site demand-supply analysis
Network Analysis
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Allocation

Which centre serves a particular link?
 Two criteria are used for allocation:
supply: amount of resource a facility (centre) has
available
 demand: amount of the resource demanded on the
links or nodes
Allocation works by assigning demand to a centre until
the demand matches the supply of the centre.
 e.g. A school (centre) has a quantity of spaces
available for children. The number of children living
on each street form the demand. Streets are
assigned to the school until the total number of
children on those streets equals the number of
available spaces.


Network Analysis
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Service area
School 2
Service Area
of School 1
2
2
6
2
7
1
2
School 1
5
8
5
10
2
3
2
3
10
5
10
5
2
5
5
7
3
2
2
Network Analysis
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Service area analysis
Network Analysis
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Routing with unordered
stops
(Also known as postman problem)


How to cover all the streets in the route
and return back to the starting point
with as little travelling as possible.
This is the problem of finding the
shortest route for the postman so that F
he traverses each link at least once
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and returns to his starting node.
7
A
3
E
Network Analysis
2
4
9
B
1
D
6
5
C
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Routing with
ordered stops
Stops
2
5
4
6
3
1
(Also known as travelling salesman problem)


to call at each town before returning home.
This is the problem of finding a route that
minimises the total distance (or time or cost)
needed to visit all the towns in his district.
Network Analysis
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Optimum route analysis
Network Analysis
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Accessibility


Accessibility provides an aggregate measure of how
accessible a location is to other locations. It can be
defined as the ease of participating in activities.
Types of accessibility measures:
 Topological accessibility: states whether two
points in space are physically connected by a
transport system thus enabling movement to take
place between them.
 Relative accessibility: a measure of the degree of
connectivity or accessibility between places.
 Integral accessibility: measures the accessibility of
a site to a number of other sites or activities.
Network Analysis
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Measuring accessibility
Relative accessibility
Integral accessibility
4
j
i
3
2
i
1
Ai  Cij
C

A 
ij
i
e.g. travel time to nearest health clinic
distance to Central Business
District
Network Analysis
n
e.g. mean travel time to all health
clinics in the region
mean distance to all other zones
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Computing origin accessibility
The basic principle is that the effect of one
location on another is directly proportional to its
supply (attractiveness) and inversely
proportional to its distance
Origin
Destination
A
B
M1
M2
0.5
0.7
1.6
Attraction
Production
M1
M2
A
B
3.0
5.0
2
3
2.1
The distance between the origins A
and B and destinations M1 and M2
in kilometres
To compute accessibility, each market is given an
index of how attractive it is and the population (or
production) at each location is determined
Network Analysis
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Computing origin accessibility

Assume a distance decay exponent of 2, the
accessibility of A to M1 is computed as:
attractiveness index of market centre
(distance between location and market)2

The total accessibility can be expressed as:
where
n
Pi  
Wj

d
j 1 ij
Pi is the accessibility at point i
Wj is the attractiveness of location j
dij is the distance between location i and j
 is the exponent for distance decay
n is the number of locations in the region
Network Analysis
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Spatial interaction

How accessible is one location to all other
locations?
 Computing interaction
Interaction =
production  attractiveness
(distance between origin and destination)2
Origin
Destination
M1
M2
A
24.0
20.4
B
3.5
3.4
The raw interactions between the
two locations A and B and centres
M1 and M2 result in a 2 by 2
matrix.
Network Analysis
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Address matching

Address can be interpreted to give approximate
spatial location on a network.
 Spatial locations can be interpreted based on
the street names assigned to the links and
street numbers recorded at nodes.
 The technique is widely used in, for example,
direct marketing, crime control, and supply and
demand analysis.
Network Analysis
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Display of matched cases
Network Analysis
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Map of Incidents
Crime cases
Traffic accidents
Network Analysis
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Summary

Much of our life involves network problems.
 GIS network analysis attempts to solve network
problems using network data model, which is
composed of nodes and links with variables
such as centre, stop, impedance, supply and
demand.
 Typical network analysis functions include:

Location/allocation
 Routing
 Accessibility
 Address matching
Network Analysis
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