1 Road network vulnerability Important links and areas, exposed users Erik Jenelius Dept. of Transport and Economics Royal Institute of Technology (KTH) Stockholm

2 The project Dep. of Transport and Economics, KTH Supervisor Prof. Lars-Göran Mattsson Assist. supervisor Dr. Katja Vourenmaa Berdica Time period Funded by Swedish Road Administration and Swedish Agency for Innovation Systems

3 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.

4 Network disruptions

5 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

6 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

7 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

8 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

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

10 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)

11 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)

12 Case studies 1.Geographical disparities in vulnerability 2.Area-covering disruptions

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14 Link importance Total delay due to link closure 48 h closure

15 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?

16 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

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

18 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

19 Network density Three measures of increasing simplicity and data availability: 1.Redundancy and scale: #links / #nodes and average link length 2.Road density: Total network length / region area 3.Population density

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

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

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23 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

24 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?

25 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

26 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

27 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 km km24116

28 Cell importance 25 km grids Each small square shows mean importance of the four intersecting cells

29 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

30 Ratio cell/mean link importance Ratio largest where both demand and network are dense

31 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

32 Thank you! Papers: Jenelius, E., Petersen, T. & Mattsson, L.-G. (2006), ”Importance and exposure in road network vulnerability analysis”, Transportation Research Part A 40, Jenelius, E. (2009a), ”Network structure and travel patterns: Explaining the geographical disparities of road network vulnerability”, Journal of Transport Geography 17, 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.