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Importance and Exposure in Road Network Vulnerability Analysis:

A Case Study for Northern Sweden

Erik JeneliusTransport and Location Analysis

Dept. of Transport and EconomicsRoyal Institute of Technology, Stockholm

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Vulnerability study of northern Sweden:Objectives

• Find good measures of the vulnerability of nodes, regions and whole road networks, and the criticality of links

• Calculate the measures for large regional networks in reasonable time

• Apply measures to the regional network of northern Sweden

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Vulnerability and exposure

• Vulnerability is a susceptibility to incidents that can result in considerable reductions in road network operability (Berdica, 2002)

• Vulnerability contains likelihood and consequence

• The exposure of a region to a certain incident is the consequences of that incident for that region

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Criticality and importance

• A link is weak if the probability of an incident is high, important if the consequences are great and critical if it is both weak and important (Nicholson and Du, 1994)

• Link k important for region r Region r exposed to failure of link k

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Assumptions for the measures

• Incident: a link k is closed

• Travel demand xij is fixed during event

• User equilibrium• Measure of reduced operability: increased

generalised travel cost)0()()(

ijkij

kij ccc

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Different perspectives

• Aggregation: is averaged over OD pairs (i, j)

• Unweighted average: Average cost increase per OD pairMeasure of regional accessibility

• Travel demand-weighted average: Average cost increase per tripMeasure of economic efficiency

)0()()(ij

kij

kij ccc

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Unsatisfied demand

• Closure of link may divide network into disconnected components: infinite travel cost

• Finite measure of consequences:unsatisfied demand = number of trips unable to reach their destinations

if0

if)(

)()(

kij

kijijk

ij c

cxu

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Road network of northern Sweden

• Six northernmost counties of Sweden• Original size:

c. 26,989 nodes and c. 60,752 directed links2.0·106 OD pairs

• After simplification:4,470 nodes and 6,362 undirected links1.3·106 OD pairs

• Travel demand data:vehicles on an annual daily average

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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 Traffic load

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

0 200 400 Kilometers

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The case study:Methods and measures

• No congestion effects: fast, exact shortest path algorithm

• Travel time tij is used as generalised travel cost

• Link travel time = length / (free flow speed from vd-function)

• Travel time matrix T = (tij) is calculated initially and after every removed link

• Total time consumption: 9-10 hoursNew implementation: 15-20 minutes

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Unweighted link importancefor the whole network:Average time increase per OD pair

• E4 European highway

Minutes/OD pair0 - 0.330.33 - 1.311.31 - 2.722.72 - 5.445.44 - 10.76

0 200 400 Kilometers

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Demand-weighted link importancefor the whole network:Average time increase per trip

• City segments of E4:Local and regional traffic

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

0 200 400 Kilometers

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Unsatisfied demand-related link importance for the whole network:Average fraction of trips cut off

• Roads near the coast• Boundary effects• Sensitive measure

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

0 200 400 Kilometers

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Worst-case scenario: most important link closedUnweighted municipality exposure:Average time increase per OD pair

• Southern and northern parts the most exposed

• A few links of the E4 the most important for many municipalities

Minutes/OD pair5.4 - 10.410.4 - 12.512.5 - 15.115.1 - 18.618.6 - 27.9

0 200 400 Kilometers

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Worst-case scenario: most important link closedDemand-weighted municipality exposure:Average time increase per trip

• Local density important

• Northwestern parts the most exposed

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

0 200 400 Kilometers

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Worst-case scenario: most important link closedUnsatisfied demand-relatedmunicipality exposure:Average fraction of trips cut off

• Northwestern region highly exposed

• Middle region unexposed

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

0 200 400 Kilometers

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Future work

• Study the sub-network available for heavy transports

• Study reduction of exposure by adding new links• The probability part:

- models of threats (extreme weather, major accidents, hostile attacks)- identify weak links

• Policy implications