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Road network vulnerability: Identifying important links and

exposed regionsErik Jenelius, Tom Petersen, Lars-Göran Mattsson

Department of Transport and Economics, Royal Institute of Technology, Stockholm

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Why study road network vulnerability?

• Reliability and vulnerability important aspects of transport quality

Efficient commutingEfficient logistics (just-in-time)

• Road network is often a lifeline for other critical

infrastructure• Vulnerability a combination of probability and consequence• Conditional analysis: Given an adverse event

Which roads are particularly important?Which regions are particularly exposed?

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Methodology (1)

• Negative event: Link k in a road network is closed

• Inelastic travel demand xij• A rural uncongested network• User equilibrium (fastest route)• Travel time for undamaged network• Travel time when link k is closed• Measure of consequence

Unsatisfied demand

Travel time increase

)0(ijc

)(kijc

if0

if)(

)()(

kij

kijijk

ij c

cxu

)0()(ij

kij cc

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Methodology (2)

• Importance of link kFraction of trips that cannot reach their destinations when it is closed

and (if that fraction is zero a non-cut link)

Average increase in travel time per trip when it is closed

• Worst-case municipality exposureFraction of trips with origin in the municipality that cannot reach their destinations when the most important link is closed

andAverage increase in travel time per trip for trips with origin in the municipality when the most important non-cut link is closed

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People/sq km0.25 - 1.251.25 - 3.533.53 - 8.578.57 - 19.1219.12 - 80.1

0 200 400 Kilometers

Population density

Vehicles/day0 - 15931594 - 48114812 - 1053310534 - 1958619587 - 35742

0 200 400 Kilometers

Traffic

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Vehicle min/veh0 - 0.020.02 - 0.080.08 - 0.190.19 - 0.450.45 - 1.22

0 200 400 Kilometers

Unsatisfied veh/total00 - 0.00050.0005 - 0.00170.0017 - 0.00360.0036 - 0.00840.0084 - 0.024

0 200 400 Kilometers

Fraction of trips that cannot reach their destinations when marked link is closed

Link importance

Average increase in travel time per trip when a non-cut link is closed

Links near cities, the coast, or in the mountains

Short city links, E4

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Vehicle min/veh0.5 - 3.83.8 - 5.25.2 - 11.811.8 - 24.124.1 - 83.7

0 200 400 Kilometers

Unsatisfied veh/total0.001 - 0.0080.008 - 0.050.05 - 0.1020.102 - 0.2810.281 - 0.833

0 200 400 Kilometers

Municipality exposure

Fraction of trips that cannot reach their destinations when most important link is closed

Average increase in travel time per trip when the most important non-cut link is closed

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Conclusions

• Importance and exposure introduced

to operationalise transport quality related to reliability and vulnerability• GIS useful way of visualising results• Importance and exposure should be

considered at various planning stages Investment: improving and adding linksMaintenance: prioritisation of repairOperations: prioritisation of snow ploughing

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Further research

• Extend the analysis to the whole of Sweden• Elastic demand: accessibility changes rather than travel time increases• Application to congested networks • More realistic modelling of adverse events than just removing one link at a time• Study of probabilities for different adverse events