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Sårbarhetsanalyser av vägnät- gjort sedan förra mötet

Referensgruppsmöte 18 december 2008

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Sårbarhetsanalys av utbredda avbrott

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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

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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

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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

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Consequence model

• Indicator: Increase in travel time for users

• Constant, inelastic travel demand

• Initial travel times estimated with congestion, no change during closure

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Consequence model

• During disruption of cell, two possibilities:

1. No alternative routes

Unsatisfied demand, must delay tripuntil after closure

2. Alternative routes

Users choose new shortest route, or if faster delay trip

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System and user perspectives

• Cell importance:

Total increase in travel time for all users when cell is disrupted

• Worst-case regional user exposure:

Mean increase in travel time per user starting in region when most important cell for region is closed

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Case study

• Swedish road network: 174,044 directed links, 8,764 origins/destinations

• Matrix of estimated travel demand (vehicles/hour) between every origin/destination pairPersonal cars and light and heavy trucks

• Three square cell sizes: 12.5 km, 25 km, 50 km

• 12 hour closure duration

Cell size # cells/grid # grids

12.5 km 64 x 128 4

25 km 32 x 64 4

50 km 16 x 32 16

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Cell importance12.5 km grid

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Cell importance25 km grid

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Cell importance50 km grid

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Cell importance

• Unsatisfied demand constitutes 60% - 90% of total increase in travel time on average

• Unsatisfied demand consists of internal, inbound/outbound and transit demand

• Consequences as function of cell size

cell size (km)

#grids #inters. cells/grid

I (veh h) uns. dem. of I (%)

internal (%)

in+out (%)

transit (%)

cell/link I

mean median coeff. of var.

12.5 4 3170 14600 224 4.90 60.6 4.2 49.2 46.6 282 25 4 853 47500 3790 3.57 79.5 13.5 60.2 26.2 701 50 16 241 148000 19700 2.51 90.4 30.6 56.1 13.3 1780

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Jämförelse mellan att stänga hela rutan eller slumpmässigt vald meter väg i rutan

• De 11 värsta rutorna finns i Skåne

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Worst-case county user exposure

• Exposure depends on concentrated travel demand, not network redundancy

• In most exposed county, more than 60% of demand unsatisfied

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Worst-casecell vs. link

• Area-covering disruption particularly worse in densely populated regions

• 12 of 21 counties: Worst-case link within worst-case cell

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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

• For important cells, unsatisfied demand constitutes nearly all increase in travel time

• Results depend on link and demand location and regional partition

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Sårbarhetsanalys av Mexicos vägnät

• Detaljerat (åtminstone bitvis) nätverk (23352 noder, 54172 länkar)

• Gles efterfrågematris (ca 500 start/målnoder)

• Lastbilsmatris

• Mått och metoder från tidigare studier av Sverige

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Vägnätet

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Reseefterfrågan

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Länkarnas betydelsefullhet

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Delstaternas utsatthet