Transport infrastructure l bilit h t KTHvulnerability research at KTH

L Gö M ttLars-Göran MattssonDepartment of Transport and Economics

Centre for Transport StudiesRoyal Institute of TechnologyRoyal Institute of Technologylars-goran.mattsson@abe.kth.se

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Transport reliability and vulnerabilityRailRail

• Empirical studies of the Swedish rail system • Empirical studies of the Swedish rail system (Wiklund)

• Railway operation analysis (O Lindfeldt)• Railway operation analysis (O Lindfeldt)• Empirical studies of delays and capacity

utilisation (A Lindfeldt)utilisation (A Lindfeldt)

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Transport reliability and vulnerabilityRoadRoad

T l ti li bilit (Bö j Eli • Travel time reliability (Börjesson, Eliasson, Franklin, Karlström)

Theoretical and empirical studies of the value – Theoretical and empirical studies of the value of reliability

– What is the cost of necessary safety margins What is the cost of necessary safety margins to cope with (known) randomness in travel times?

• Road network vulnerability (Berdica, Jenelius, Mattsson, Petersen)

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Road network vulnerabilityBased on research by Erik Jenelius

Events sometimes occur that severely • Events sometimes occur that severely disrupt transportation services

• Can have big impacts on individuals and • Can have big impacts on individuals and businesses

• For individuals: reduced accessibility to ysocial services, loss of access to/time for work, school, daycare, shopping, recreation, etcetc.

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

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Network disruptionsNetwork disruptions

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Aim

• Before occurrence identify scenarios that• Before occurrence, identify scenarios that– would have severe consequences for society– could occur in the futurecould occur in the future

• Important sub-tasks:– Identify critical points/areas where incidents 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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ValueValue

• In planning stage: • In planning stage: – Adjust location/structure of roads to risks– Support road projects providing redundancy Support road projects providing redundancy

to existing network

• In maintenance/operations stage: p g– Probability of disruption can be reduced by

upgrades and maintenance– Consequences can be reduced by information

and swift restoration

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ImportanceImportance

• A link or larger area is important if disruption • 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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ExposureExposure

• A group of users is exposed to a certain • A group of users is exposed to a certain scenario if it would have severe impacts for the groupg p

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

• User’s perspective

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Analysis focusAnalysis focus

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

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Impact modelImpact model

• Simple indicator: Delay with only route • Simple indicator: Delay with only route adjustment

• Users assumed to minimise travel timeUsers assumed to minimise travel time• For computational reasons: link travel

times assumed unchanged by disruptiong y p

• Unsatisfied demand: Users unable to Unsatisfied demand: Users unable to travel during disruption

• Calculate delay as waiting time until y greopening, assuming constant travel demand

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Link importance(Critical link analysis)

• Total delay due to link Total delay due to link closure

• 48 h closure

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Case studies – recent research Case studies recent research

1 Geographical disparities in vulnerability1. Geographical disparities in vulnerability2. Area-covering disruptions3 Secondary link importance3. Secondary link importance4. Traveller costs of unplanned transport

network disruptionsnetwork disruptions

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1 Regional disparities in vulnerability1. Regional disparities in vulnerability

• Study geographical variations in • Study geographical variations in vulnerability

• Can these differences be explained by Can these differences be explained by network structure and travel patterns?

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Regional exposure and importance

• Expected user exposure: Average delay per Expected user exposure: Average delay per traveller starting in 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 regionrandom link in the region

Delay in region

Delay in wholeregion whole

Disruption in region

Importanceeg o

Disruption in whole

Exposure

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utsatthet/resenär (10^ 6 h) betydelsefullhet (h)user exposure (10-6 h) importance (h)utsatthet/resenär (10^-6 h)1.763 - 3.8463.846 - 5.3385.338 - 7.0247.024 - 9.839

betydelsefullhet (h)0.1 - 0.3220.322 - 0.4990.499 - 0.7720.772 - 1.501

p ( ) p ( )

9.839 - 52.468

Stockholm Stockholm

1.501 - 10.085

G th b

Stockholm Stockholm

G th bGothenburg Gothenburg

170 100 200 300 400 Kilometers

NSkåne Skåne

N

0 100 200 300 400 Kilometers

Regression analysisRegression analysis

• Regress exposure on variables capturing • Regress exposure on variables capturing network structure and travel patterns of the own regiong

• Exposure should be high if network density low (low -index = #links / #nodes and high average link length)

• Exposure high if average user travel timelong

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link length (km) genomsn. restid (h)0.118 - 0.2360 236 0 275

aver. user travel time (h)beta index1.036 - 1.2771 277 1 343

länklängd (km)0.422 - 1.8381 838 2 431

link length (km)

0.236 - 0.2750.275 - 0.3250.325 - 0.370.37 - 0.783

1.277 - 1.3431.343 - 1.3881.388 - 1.4341.434 - 1.554

1.838 - 2.4312.431 - 3.0253.025 - 3.8583.858 - 11.005

StockholmStockholm Stockholm

Gothenburg GothGothenburg Gothenburg

0 100 200 300 400 Kilometers

NSkåne

0 100 200 300 400 Kilometers

NSkåne Skåne

N

0 100 200 300 400 Kilometers

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Explaining user exposure (UE)

Adj. R2 = 0.90

ln 4.8 2.1ln 0.70ln 0.83lnr r r rUE l T

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ConclusionsConclusions

• Long-term vulnerability strongly • Long term vulnerability strongly determined by network structure and travel patternsp

• Complex measures can be approximated with simple variables

• Difficult to affect patterns with infrastructure investments

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2 Area-covering disruptions2. Area covering disruptions

• Extend single-link analysis to areas• Extend single link analysis to areas• Develop methodology for systematic

analysisanalysis• Apply to large real-world road networks• Where are area-covering disruptions most • Where are area covering disruptions most

severe?• What differs from single-link failures?What differs from single link failures?

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Methodology

• Study area is covered with grid of equally h d d i d llshaped and sized cells

• Each cell represents spatial extent of disruptive eventdisruptive event

• Event representation: All links intersecting cell are closed remaining links unaffectedcell are closed, remaining links unaffected

Square

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Cell importanceCell importance

• 25 km grids• 25 km grids• Each small square shows

mean importance of the mean importance of the four intersecting cells

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Cell importanceCell importance

• Unsatisfied demand constitutes on 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 demandinbound/outbound and crossing demand

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Ratio cell/mean linkimportance• Ratio largest where both • Ratio largest where both

demand and network are dense

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ConclusionsConclusions

• Other factors behind vulnerability to area-• Other factors behind vulnerability to areacovering 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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3 Secondary link importance3. Secondary link importance

• To allocate resources for maintenance, To allocate resources for maintenance, operations and upgrades, it is useful to rank road links according to importance

• Measures of link importance usually reflect role under normal conditions

• Here we are interested in measuring link

importance as rerouting alternative to importance as rerouting alternative to

other links during disruptions

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Primary and secondary importancePrimary and secondary importance

• Primary importance: Total travel delay caused Primary importance: Total travel delay caused by disruption of link k (typical vulnerability analysis)

• Captures availability of alternatives• Secondary importance: Additional delay for

e o ted flo if link k also o ld be dis pted rerouted flow if link k also would be disrupted • Captures quality of next-best alternatives• Some similarity with synergistic consequences • Some similarity with synergistic consequences

analysis

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Original link flowsOriginal link flows

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Primary importancePrimary importance

• 12 h closure duration• 12 h closure duration• Link important if average

user delay is largeuser delay is large

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Secondary importanceSecondary importance

• Link important if • Link important if average difference in delay ywith/without link is large

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ConclusionsConclusions

• Identify links important as rerouting • Identify links important as rerouting alternatives

• May motivate extra maintenance although May motivate extra maintenance although normal traffic is not particular high

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4. Traveller costs of unplanned transport network disruptionstransport network disruptions

• Monetary values for delays needed for e.g. y y gcost-benefit assessment of mitigation measures

• User’s cost per unit of delay may depend on– Characteristics of the user and her

situationWhat information the user has– What information the user has

– When the delay occurs– How long the delay lasts– How long the delay lasts– What adjustments the user can make

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Average delay cost per hour delayA two way work trip

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Fixed work schedule Flexible work schedule

ConclusionsConclusions

• Travel time value of unplanned disruptions • Travel time value of unplanned disruptions could be up to 6 times normal value of travel time

• Cost is less if user is informed about the disruption

• Cost is less if user has flexible work schedule

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Thank you!y

For papers and more information see:

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

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Not only transport

• Also electric power networks (Holmgren, Jenelius, Molin, Thedéen, Westin)– Framework for vulnerability assessment

– Empirical studies of disturbance data– Application of graph models– Branching network models to explain power laws– Optimal defence against antagonistic attacks– Game theoretic applications to infrastructure

protection under imperfect attacker perceptionprotection under imperfect attacker perception

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