The vulnerability of road networks under area-covering disruptions

1. The vulnerability of road networks under area-covering disruptions Erik JeneliusLars-Göran MattssonDiv. of Transport and Location AnalysisDept. of Transport and EconomicsRoyal Institute of Technology (KTH)Stockholm, Sweden INFORMS Annual Meeting 2008, Washington D.C., USA

2. Background • Road network a fundament of modern society • Disruptions and closures can cause severe consequences for people and businesses • Disruptive events may affect extended areas in space,e.g. extreme snowfall, hurricanes, floods, forest fires

3. Background • Past applied vulnerability studies focused on identifying important (critical, significant, vital) links • Our aim: Study vulnerability to area-covering disruptions • Provide complement to single link failure analysis • Develop methodology for systematic analysis • Apply to large real-world road networks • Gain general insights

4. Methodology • Study area is covered with grid of equally shaped and sized cell • Each cell represents spatial extent of disruptive event • Event representation: All links intersecting cell are closed, remaining links unaffected Square Hexagonal

5. Methodology • Multiple, displaced grids used to increase accuracy • Advantages of grid approach: • No coverage bias: Each point in study area equally covered • Avoids combinatioral issues with multiple link failures • Easy to combine with frequency data • Disadvantages: • Results depend on rotation

6. delay/user τ dept. time τ 0 Consequence model • Indicator: Increase in travel time for users • Constant, inelastic travel demand xij • Initial link travel times from equilibrium assignment, no change during closure • During disruption of cell, two possibilities: • No alternative routesUnsatisfied demand, must delay tripuntil after closureTotal delay:

7. delay/user τ dept. time τ 0 Consequence model • Alternative routesUsers choose new shortest route, or if faster delay tripTotal delay:

8. Importance and exposure • Cell importance: Total increase in travel time for all users when cell is disrupted • Given collection of grids G and closure duration τ, Importance of cell c: • Worst-case regional user exposure: Mean increase in travel time per user starting in region when most important cell for region is closed

9. L Calculations • Initial SP tree from start node using Dijkstra • Remove link k in cell by setting long length L • If k in SP tree, update tree under k • If distance to node L: no alternative route • Repeat for all links in cell • Repeat for all cells in grids • Repeat for all start nodes • Calculation time independent of grid size

10. Case study • Swedish road network: 174,044 directed links, 8,764 centroids • Three square cell sizes: 12.5 km, 25 km, 50 km • 12 hour closure duration

12. Cell importance12.5 km grid

13. Cell importance25 km grid

14. Cell importance50 km grid

15. Cell importance • Consequences as function of cell size • Unsatisfied demand constitutes 97.6% - 99.3% of total increase in travel time

16. Worst-case county user exposure • Exposure depends on concentrated travel demand, not network redundancy • In most exposed county, more than 60% of demand unsatisfied

17. Worst-casecell vs. link • Area-covering disruption particularly worse in densely populated regions • 12 of 21 counties: Worst-case link within worst-case cell

18. Some insights • Other factors behind vulnerability to area-covering disruptions compared to single link failures • Vulnerability reduced through allocation of restoration resources rather than increasing redundancy • Unsatisfied demand constitutes nearly all increase in travel time • Unchanged link travel times may be reasonable assumption • Duration not significant for relative comparisons • Results depend on link and demand location and regional partition

19. Thank you!