1 Importance and Exposure in Road Network Vulnerability Analysis: A Case Study for Northern Sweden Erik Jenelius Transport and Location Analysis Dept. of Transport and Economics Royal Institute of Technology, Stockholm

2 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

3 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

4 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

5 Assumptions for the measures Incident: a link k is closed Travel demand x ij is fixed during event User equilibrium Measure of reduced operability: increased generalised travel cost

6 Different perspectives Aggregation: is averaged over OD pairs (i, j) Unweighted average: Average cost increase per OD pair Measure of regional accessibility Travel demand-weighted average: Average cost increase per trip Measure of economic efficiency

7 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

8 Road network of northern Sweden Six northernmost counties of Sweden Original size: c. 26,989 nodes and c. 60,752 directed links 2.0·10 6 OD pairs After simplification: 4,470 nodes and 6,362 undirected links 1.3·10 6 OD pairs Travel demand data: vehicles on an annual daily average

9 Population density Traffic load

10 The case study: Methods and measures No congestion effects: fast, exact shortest path algorithm Travel time t ij is used as generalised travel cost Link travel time = length / (free flow speed from vd-function) Travel time matrix T = (t ij ) is calculated initially and after every removed link Total time consumption: 9-10 hours New implementation: minutes

11 Simplification of the network Make undirected Remove centroids and network outside study area Move demand to closest node within study area Update demand matrix X = (x ij ) Remove dead-end nodes and joint nodes t1t1 t2t2 t 1 + t 2

12 Unweighted link importance for the whole network: Average time increase per OD pair E4 European highway

13 Demand-weighted link importance for the whole network: Average time increase per trip City segments of E4: Local and regional traffic

14 Unsatisfied demand-related link importance for the whole network: Average fraction of trips cut off Roads near the coast Boundary effects Sensitive measure

15 Worst-case scenario: most important link closed Unweighted 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

16 Worst-case scenario: most important link closed Demand-weighted municipality exposure: Average time increase per trip Local density important Northwestern parts the most exposed

17 Worst-case scenario: most important link closed Unsatisfied demand-related municipality exposure: Average fraction of trips cut off Northwestern region highly exposed Middle region unexposed

18 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