1 The vulnerability of road networks under area-covering disruptions Erik Jenelius Lars-Göran Mattsson Div. of Transport and Location Analysis Dept. of Transport and Economics Royal 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 Hexagonal Square

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 Consequence model Indicator: Increase in travel time for users Constant, inelastic travel demand x ij Initial link travel times from equilibrium assignment, no change during closure During disruption of cell, two possibilities: 1.No alternative routes Unsatisfied demand, must delay trip until after closure Total delay: 0 τ τ dept. time delay/user

7 Consequence model 2.Alternative routes Users choose new shortest route, or if faster delay trip Total delay: 0 τ τ dept. time delay/user

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 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 L

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 Cell size# cells/grid# grids 12.5 km64 x km32 x km16 x 3216

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12 Cell importance 12.5 km grid

13 Cell importance 25 km grid

14 Cell importance 50 km grid

15 Cell importance Consequences as function of cell size Unsatisfied demand constitutes 97.6% % 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-case cell 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!