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The traveler costs of unplanned transport network disruptions: An activity-based approach Erik Jenelius Royal Institute of Technology, Sweden Lars-Göran Mattsson Royal Institute of Technology, Sweden David Levinson University of Minnesota

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Background How to value increases in travel time due to unplanned transport network disruptions (floods, snowfall, severe car crashes etc.)? In cost-benefit analysis For bonus provision for restoration work State of practice: Standard value of time Related but different: Value of reliability/variability travel time average travel time variability extreme events

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Aim Build theoretical foundation for the traveller delay costs of unplanned transport network disruptions Capture the following aspects: Large delays – marginal values may be misleading Long disruptions – more than one trip may be affected Unexpected events, imperfect information – less ability to adjust travel and daily schedule optimally Flexibility – smaller intrusion of delay Time of day – less room for schedule adjustments later

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Framework Trips are made between two activities, e.g., home and work Costs arise as we rather spend time at home or at work than in car Schedule preferences expressed as utility maximization We consider three activities (”morning”, ”work”, ”evening”), two trips (”morning commute”, ”evening commute”) Calibration against empirical results from Tseng & Verhoef (2008)

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Variables Marginal activity and travel utilities: u 1 (t), u 2 (t – ξt s2 ), u 3 (t), ν Marginal utility of activity 2 (work) may depend on arrival time: Parameter ξ controls schedule flexibility: ξ = 0 clock-time only ξ = 1 duration only Travel times T 1, T 2 (assumed exogenous here, departure time dependent in paper) Departure times t d1, t d2, arrival times t s2 = t d1 + T 1, t s3 = t d2 + T 2

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The model Daily utility U determined by departure times

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Travel costs To avoid new notation, assume utility is money metric. Marginal WTP functions for activity/travel transitions: Assume optimally timed trips normally FOC and marginal VOT can be found Travel cost

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Delay costs Journey delays T 1, T 2 Delay costs Depend on: journey delays (magnitude and distribution) schedule adjustments (information) work schedule flexibility

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Adjustments Evidence from I-35W bridge collapse We consider: 1.no adjustment 2.no + optimal 3.over-adjustment 4.over + optimal 5.optimal adjustment

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Calibration Calibrated against time-varying WTP for home/work from Tseng & Verhoef (2008) and some findings from Hess et al. (2007) Parameterized logistic functions for marginal WTP functions 1 (t), 2 (t – t s2 ), 3 (t): min, max, steepness, location

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Numerical results Delay on both morning and evening trip (baseline tr. time 2 40 min) Fixed (left) vs. flexible (right) work hours

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Numerical results Delay on morning trip only or evening trip only Fixed (left) vs. flexible (right) work hours

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Some conclusions Delay costs increase rapidly with length of delay Better adjustments (information) can reduce costs significantly Flexible work hours great if journey delay occurs early Previous model-based valuations of disruption impacts (I-35W bridge collapse etc.) have probably underestimated delay costs We here only considered work trips and individuals’ own stated costs

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Thank you!

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