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Secondary link importance:Links as rerouting alternatives during road network disruptions

Erik JeneliusCentre for Transport Studies /

Royal Institute of Technology (KTH)Stockholm, Sweden

jenelius@infra.kth.se

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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

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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

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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

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

An example

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• f is normally used (only) for trips from B to C

• Normal link flow: ff = fBC

• Flow-based primary importance: I1flow(f) = ff = fBC

An examplePrimary importance

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An examplePrimary importance

• Disruption of f: flow reroutes to (d,b)• Delay-based primary importance:

I1delay(f) = ΔTf = fBC·ΔtfBC

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• Still interested in link f• Trips from A to B normally use route (a,d)

An exampleSecondary importance

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• Trips from A to B normally use route (a,d)• If a is disrupted, f is on alternative route

• Added flow on f: faf+ = fa = fAB

An exampleFlow-based secondary importance

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Secondary importance• To find total flow-based secondary importance

of f, we summarize over all OD pairs and other links

• Flow-based secondary importance: I2flow(f) = Σkf wk·fkf+

• Weight wk reflects influence of link k

• Here: wk proportional to link length

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• Total delay for rerouted traffic: ΔTaf+ = fAB·Δta

AB

An exampleDelay-based secondary importance

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An exampleDelay-based secondary importance

• Total delay for rerouted traffic: ΔTaf+ = fAB·Δta

AB

• If both a, f are disrupted: (c,b,d) is alternative• Difference in delay with/without f:

ΔTaff+ - ΔTa

f+ = fAB·(ΔtafAB - Δta

AB)

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Secondary importance• Again, we summarize over all other links:• Delay-based secondary importance:

I2delay(f) = Σkf wk·(ΔTkff+ - ΔTk

f+)

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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 ΔTdff+ = (fAB+fBC)·τ2/2

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Case study Northern Sweden

• Study area: 18 municipalities

• 12 h closure duration• Travel time minimization• Travel demand, travel

times from transport modelling system SAMPERS

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ResultsFlow-based primary importance

• Normal link flows show backbone road network

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ResultsDelay-based primary importance

• Link important if flow and/or average user delay is large

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ResultsFlow-based secondary importance

• Links along coastal motorway, around towns important

• Links being alternatives for long links important

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ResultsDelay-based secondary importance

• Link important if weighted redirected flow and/or average difference in delay with/without link is large

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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

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Thank you!