1 Secondary link importance: Links as rerouting alternatives during road network disruptions Erik Jenelius Centre for Transport Studies / Royal Institute of Technology (KTH) Stockholm, Sweden

2 Motivation 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 Link’s role for transport efficiency We are interested in measuring link importance as rerouting alternative to other links during disruptions Link’s role for transport robustness

3 Primary importance: Importance under normal conditions Flow-based primary importance: Number of travellers using the link per unit time (flow centrality) Captures how many rely on the link Delay-based primary importance: Total travel delay caused by disruption of link (typical vulnerability analysis) Also captures availability of alternatives

4 Secondary importance: Importance as rerouting alternative Flow-based secondary importance: Flow rerouted to link k during disruption of other link Captures how many could come to rely on the link Delay-based secondary importance: Additional delay for rerouted flow if link k also would be disrupted Also captures quality of next-best alternatives

5 Three origins/destinations: A, B, C Six links: a, b, c, d, e, f Consider link f An example

6 f is normally used (only) for trips from B to C Normal link flow: f f = f BC Flow-based primary importance: I 1 flow (f) = f f = f BC An example Primary importance

7 Disruption of f: flow reroutes to (d,b) Delay-based primary importance: I 1 delay (f) = ΔT f = f BC ·Δt f BC

8 Still interested in link f Trips from A to B normally use route (a,d) An example Secondary importance

9 Trips from A to B normally use route (a,d) If a is disrupted, f is on alternative route Added flow on f: f a f+ = f a = f AB An example Flow-based secondary importance

10 Secondary importance To find total flow-based secondary importance of f, we summarize over all OD pairs and other links Flow-based secondary importance: I 2 flow (f) = Σ kf w k ·f k f+ Weight w k reflects influence of link k Here: w k proportional to link length

11 Total delay for rerouted traffic: ΔT a f+ = f AB ·Δt a AB An example Delay-based secondary importance

12 An example Delay-based secondary importance Total delay for rerouted traffic: ΔT a f+ = f AB ·Δt a AB If both a, f are disrupted: (c,b,d) is alternative Difference in delay with/without f: ΔT af f+ - ΔT a f+ = f AB ·(Δt af AB - Δt a AB )

13 Secondary importance Again, we summarize over all other links: Delay-based secondary importance: I 2 delay (f) = Σ kf w k ·(ΔT kf f+ - ΔT k f+ )

14 Example cont. No available routes If both d, f disrupted, no routes from A to B or from B to C We calculate delay as time until disruption is lifted (duration τ) Here, total delay is ΔT df f+ = (f AB +f BC )·τ 2 /2

15 Case study Northern Sweden Study area: 18 municipalities 12 h closure duration Travel time minimization Travel demand, travel times from transport modelling system SAMPERS

16 Results Flow-based primary importance Normal link flows show backbone road network

17 Results Delay-based primary importance Link important if flow and/or average user delay is large

18 Results Flow-based secondary importance Links along coastal motorway, around towns important Links being alternatives for long links important

19 Results Delay-based secondary importance Link important if weighted redirected flow and/or average difference in delay with/without link is large

20 Conclusions Identify links important as rerouting alternatives Can also be used under emergency rerouting schemes If single link failure is isolated event: Use flow-based secondary importance If risk for multiple failures: Use delay-based secondary importance Can be extended to more than two simultaneous failures

21 Thank you!