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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
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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!