Transcript Document

Geography and road network
vulnerability
Erik Jenelius
Div. of Transport and Location Analysis
Royal Institute of Technology (KTH), Stockholm
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Aims of the presentation
•
Study the vulnerability of different geographic
regions in Sweden’s road network
•
Assess the regional equity of the road network in
terms of vulnerability
•
Find properties of geography, network and traffic
that explain regional differences, develop proxy
variables
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Road network vulnerability
•
Vulnerability is a susceptibility to incidents that
can result in considerable reductions in road
network serviceability (Berdica, 2002)
•
Typical scenarios: Extreme weather, landslides,
major accidents, malevolent attacks
•
Vulnerability analysis should contain both
probability/frequency and consequence
•
In the following, we focus on consequence
(conditional vulnerability)
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Consequence measure (1)
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Considered incident: A single road link is
completely cut off/blocked/closed a certain period
•
Some assumptions:
1. Changes only in route and departure time
choices, not in trip generation, destination or
mode choices
2. Users choose shortest route
3. Perfect information on the incident
4. Constant demand/hr
•
Consequence measure: Increased travel
time/delayed arrival for car users
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Consequence measure (2)
•
Two possibilities during closure:
1. No alt. routes: Users wait until link reopened
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x
t
od
open
Todk 
xod = demand/hr, topen = closure duration
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2. Alt. routes: Users take new shortest route, or if
better, wait
Todk
•
2

xod t open


2

k



k
od
 xod  od  t open 


2

if  odk  t open ,

 if  odk  t open .

Value of alt. routes increases with closure duration
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Regional exposure
(conditional vulnerability)
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The average-case exposure of a region is the
expected consequences for the region of a
randomly located link closure
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Two variants:
1. User exposure: The average increase in
travel time per user starting in the region
UE(r )   wk  Todk
k
or d o
 x
or d o
t
od open
2. Total exposure: The total increase in travel
time for all users starting in the region
(socio-economic consequence)
TE(r )   wk  Todk
k
or d  o
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Regional inequity
•
Large regional disparities in exposure indicate
spatial inequity between users and regions
•
A measure of equity: Gini coefficient G
G = 0: perfect equity
G = 1: perfect inequity
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Case study: Sweden
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Two closure durations: 30 minutes and 48 hours
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Average-case user and total exposure of every
municipality (289)
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Network, O-D demand and equilibrium link travel
times from SAMPERS
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No congestion effects - underestimation in dense
areas
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77,769 nodes, 174,046 links, 8,764 centroids
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The road network
Population density
Population density
0.3 - 1.1
1.1 - 2.3
2.3 - 10.5
10.5 - 26.4
26.4 - 4021.7
0
100
200
300
400 Kilometers
0
100
200
300
400 Kilometers
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User exposure
30 mins: G = 0.35
48 hrs: G = 0.64
Long user exposure
3.9 - 15.6
15.6 - 33
33 - 91.5
91.5 - 193.6
193.6 - 1059.2
Short user exposure
1.76 - 5.91
5.91 - 8.05
8.05 - 11.68
11.68 - 20.57
20.57 - 52.37
0
100
200
300
400 Kilometers
0
100
200
300
400 Kilometers
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Total exposure
30 mins: G = 0.43
48 hrs: G = 0.71
Long total exposure
0.06 - 0.31
0.31 - 0.71
0.71 - 1.19
1.19 - 4.59
4.59 - 28.09
Short total exposure
0.34 - 0.91
0.91 - 1.56
1.56 - 2.54
2.54 - 3.23
3.23 - 31.84
0
100
200
300
400 Kilometers
0
100
200
300
400 Kilometers
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Proxy variables (1)
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What affects the regional disparities in user and
total exposure?
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Long closure: Location of cut links
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Short closure:
1. sparsity of the regional road network
2. average/total initial travel times of the users
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Proxy variables (2)
•
Two measures of road network sparsity:
1. Geographic sparsity:
2. Network sparsity:
GS r 
NS r 
Ar
Lr
lr
r
where Ar = surface area, Lr = length of road,
lr = average link length, r = links-to-nodes
ratio of region r
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User exposure (30 mins)
GPSUE(r )  GSr   r 
Ar
 r
Lr
Short user exposure (10-6 h)
60
50
40
30
20
10
0
0
0.5
1
GPSUE (km
1.5
1/2
2
2.5
h)
adj R2 = 0.87
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Total exposure (30 mins)
Ar
 Tr
Lr
GPSTE(r )  GSr  Tr 
Short total exposure (10-3 h)
35
30
25
20
15
10
5
0
0
500
1000
1500
GPSTE (km
2000
1/2
2500
3000
h)
adj R2 = 0.89
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Conclusions
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Considerable regional disparities in exposure and
importance, larger for longer closures
•
Results are robust to change of partition
•
Interesting topics for further research:
• How would congestion effects, more realistic
closure probabilities etc affect the results?
• Compare with other countries
• Universality of proxy variables?
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Thank you
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