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Geography and road network

vulnerability

Erik JeneliusDiv. 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)

• 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

xod = demand/hr, topen = closure duration

2. Alt. routes: Users take new shortest route, or if better, wait

• Value of alt. routes increases with closure duration

2

2opentx

T odkod

. if2

, if2

openopen

open

2open

ttx

ttx

Tkod

kodk

odod

kod

od

kod

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Regional exposure (conditional vulnerability)

• The average-case exposure of a region is the expected consequences for the region of a randomly located link closure

• Two variants:

1. User exposure: The average increase in travel time per user starting in the region

2. Total exposure: The total increase in travel time for all users starting in the region (socio-economic consequence)

ro od

odk ro od

kodk txTwrUE open)(

k ro od

kodk TwrTE )(

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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

• Two closure durations: 30 minutes and 48 hours

• Average-case user and total exposure of every municipality (289)

• Network, O-D demand and equilibrium link travel times from SAMPERS

• No congestion effects - underestimation in dense areas

• 77,769 nodes, 174,046 links, 8,764 centroids

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The road network

0 100 200 300 400 Kilometers

Population density

0 100 200 300 400 Kilometers

Population density0.3 - 1.11.1 - 2.32.3 - 10.510.5 - 26.426.4 - 4021.7

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User exposure30 mins: G = 0.35

0 100 200 300 400 Kilometers

Short user exposure1.76 - 5.915.91 - 8.058.05 - 11.6811.68 - 20.5720.57 - 52.37

0 100 200 300 400 Kilometers

Long user exposure3.9 - 15.615.6 - 3333 - 91.591.5 - 193.6193.6 - 1059.2

48 hrs: G = 0.64

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Total exposure30 mins: G = 0.43 48 hrs: G = 0.71

0 100 200 300 400 Kilometers

Short total exposure0.34 - 0.910.91 - 1.561.56 - 2.542.54 - 3.233.23 - 31.84

0 100 200 300 400 Kilometers

Long total exposure0.06 - 0.310.31 - 0.710.71 - 1.191.19 - 4.594.59 - 28.09

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Proxy variables (1)

• What affects the regional disparities in user and total exposure?

• Long closure: Location of cut links

• 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:

where Ar = surface area, Lr = length of road, lr = average link length, r = links-to-nodes ratio of region r

r

rr L

AGS

r

rr

lNS

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User exposure (30 mins)

adj R2 = 0.87

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

GPSUE (km1/2 h)

Sh

ort

use

r e

xpo

sure

(1

0-6 h

)

rr

rrr L

AGSrGPSUE )(

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Total exposure (30 mins)

adj R2 = 0.89

0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

GPSTE (km1/2 h)

Sh

ort

tota

l exp

osu

re (

10-3

h)

rr

rrr T

L

ATGSrGPSTE )(

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Conclusions

• 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