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Road network vulnerability Important links and areas, exposed users

Erik JeneliusDept. of Transport and Economics

Royal Institute of Technology (KTH)Stockholm

jenelius@infra.kth.se

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The project• Dep. of Transport and Economics, KTH• Supervisor Prof. Lars-Göran Mattsson

Assist. supervisor Dr. Katja Vourenmaa Berdica• Time period 2007-2010• Funded by Swedish Road Administration and

Swedish Agency for Innovation Systems

http://www.infra.kth.se/tla/projects/vulnerability/index_eng.html

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Vulnerability analysis

Motivation• Events sometimes occur that severely disrupt

transportation services• Can have big impacts on individuals and

businesses• For individuals: reduced accessibility to social

services, loss of access to/time for work, school, daycare, shopping, recreation, etc.

• For businesses: loss of manpower/customers, delayed deliveries, increased freight costs, etc.

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Network disruptions

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Vulnerability analysis

Aim• Before occurrence, identify scenarios that

– would have severe consequences for society

– could occur in the future• Important sub-tasks:

– Identify critical points/areas where incidents are likely and/or could have particularly severe impacts

– Identify users/regions that would be particularly affected by an incident

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Vulnerability analysis

Value• In planning stage:

– Adjust location/structure of roads to risks– Support road projects providing

redundancy to existing network• In maintenance/operations stage:

– Probability of disruption can be reduced by upgrades and maintenance

– Consequences can be reduced by information and swift restoration

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Concepts

Importance• A link or larger area is important if disruption

there would have severe impacts for users overall• An operator’s perspective of vulnerability

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Concepts

Exposure• A group of users is exposed to a certain

scenario if it would have severe impacts for the group

• We study regional exposure: users grouped according to municipality/county of trip origin

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Analysis focus• Large-scale real-world road networks• Full-range analysis (”all links”)• Draw generalizable conclusions

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Impact model• Simple indicator: Delay with only route

adjustment• Users assumed to minimize travel time• In Swedish applications, link travel times

assumed unchanged by disruption• Data requirements:

– Network (nodes, links)– Link travel times– Travel demand between zones (demand

nodes)

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Impact model• Unsatisfied demand: Users unable to travel

during disruption• Calculate delay as waiting time until

reopening, assuming constant travel demand (to be revised in future applications)

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Case studies

1. Geographical disparities in vulnerability2. Area-covering disruptions

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Link importance• Total delay due to link

closure• 48 h closure

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1. Regional disparities in vulnerability

Motivation• Study geographical variations in vulnerability• Can these differences be explained by network

structure and travel patterns?• Can we find simple proxy variables?

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Regional exposure and importance• Expected user exposure: Average delay per

traveller starting the region due to disruption of random link in the whole network

• Expected importance: Total delay for travellers in the whole network due to disruption of random link in the region

Delay in region

Delay in whole

Disruption in region

Importance

Disruption in whole

Exposure

170 100 200 300 400 Kilometers

utsatthet/resenär (10^-6 h)1.763 - 3.8463.846 - 5.3385.338 - 7.0247.024 - 9.8399.839 - 52.468

N

Gothenburg

Skåne

Stockholm Stockholm

Skåne

Gothenburg

N

betydelsefullhet (h)0.1 - 0.3220.322 - 0.4990.499 - 0.7720.772 - 1.5011.501 - 10.085

0 100 200 300 400 Kilometers

user exposure (10-6 h) importance (h)

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Regression analysis• Regress exposure and importance on variables

capturing network structure and travel patterns of the own region

• Both exposure and importance should be high if network density low

• Exposure high if average user travel time long• Importance high average link flow large

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Network density• Three measures of increasing simplicity and

data availability:1. Redundancy and scale:

#links / #nodes and average link length2. Road density:

Total network length / region area3. Population density

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0 100 200 300 400 Kilometers

vägtäthet (km/km^2)0.073 - 0.5580.558 - 0.8340.834 - 1.0241.024 - 1.3531.353 - 7.306

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Gothenburg

Skåne

Stockholm Stockholm

Skåne

Gothenburg

N

befolkn.täthet (inv./km^2)0.26 - 10.4810.48 - 19.6419.64 - 34.6834.68 - 81.9281.92 - 4021.67

0 100 200 300 400 Kilometers0 100 200 300 400 Kilometers

beta index1.036 - 1.2771.277 - 1.3431.343 - 1.3881.388 - 1.4341.434 - 1.554

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Gothenburg

Skåne

Stockholm Stockholm

Skåne

Gothenburg

N

länklängd (km)0.422 - 1.8381.838 - 2.4312.431 - 3.0253.025 - 3.8583.858 - 11.005

0 100 200 300 400 Kilometers

link length (km) road density (km-1)

210 100 200 300 400 Kilometers

genomsn. restid (h)0.118 - 0.2360.236 - 0.2750.275 - 0.3250.325 - 0.370.37 - 0.783

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Gothenburg

Skåne

Stockholm Stockholm

Skåne

Gothenburg

N

genomsn. flöde (frdn/h)1.01 - 10.90310.903 - 17.72217.722 - 28.86428.864 - 54.82154.821 - 502.054

0 100 200 300 400 Kilometers

aver. user travel time (h) aver. flow (veh/h)

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Conclusions• Long-term vulnerability strongly determined

by network structure and travel patterns• Complex measures can be approximated with

simple variables• Difficult to affect patterns with infrastructure

investments

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2. Area-covering disruptions

Motivation• Extend single-link analysis to areas• Develop methodology for systematic analysis• Apply to large real-world road networks• Where are area-covering disruptions most

severe?• What differs from single-link failures?

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Methodology• Study area is covered with grid of equally

shaped and sized cells• 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

• No coverage bias: Each point in study area equally covered

• Avoids combinatioral issues with multiple link failures

• Easy to combine with frequency data

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Case study• Cell importance:

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

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

Cell size # cells/grid # grids

12.5 km 3170 4

25 km 853 4

50 km 241 16

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Cell importance• 25 km grids• Each small square shows

mean importance of the four intersecting cells

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Cell importance• Unsatisfied demand constitutes on average 60% - 90% of

total delay• For most important cells, almost all delay due to

unsatisfied demand• Unsatisfied demand consists of internal,

inbound/outbound and crossing demand

I (veh h) Cell size (km) Mean Median Coeff. of

var.

Internal (%)

In+out (%)

Crossing unsat. (%)

Crossing detours (%)

Cell/link I

12.5 14600 224 4.90 4.20 49.2 7.15 39.4 282 25 47500 3790 3.57 13.5 60.2 5.73 20.5 701 50 148000 19700 2.51 30.6 56.1 3.77 9.56 1780

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Ratio cell/mean link importance• Ratio largest where both

demand and network are dense

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Conclusions• Other factors behind vulnerability to area-

covering disruptions compared to single link failures: demand concentration

• Vulnerability reduced through allocation of restoration resources rather than increasing redundancy

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

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Thank you!• Papers:

• Jenelius, E., Petersen, T. & Mattsson, L.-G. (2006), ”Importance and exposure in road network vulnerability analysis”, Transportation Research Part A 40, 537-560.

• Jenelius, E. (2009a), ”Network structure and travel patterns: Explaining the geographical disparities of road network vulnerability”, Journal of Transport Geography 17, 234-244.

• Jenelius, E. (2009b), ”Considering the user inequity of road network vulnerability”, Journal of Transport and Land Use, forthcoming.

• Jenelius, E. (2009c), ”Road network vulnerability analysis of area-covering disruptions: A grid-based approach with case study”, submitted.

http://www.infra.kth.se/tla/projects/vulnerability/index_eng.html