The traveler costs of unplanned transport network disruptions:

An activity-based approach

Erik Jenelius Royal Institute of Technology, SwedenLars-Göran Mattsson Royal Institute of Technology, Sweden

David Levinson University of Minnesota

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 timeaverage travel time

variability

extreme events

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

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)

Variables

• Marginal activity and travel utilities: u1(t), u2(t – ξts2), u3(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 T1, T2 (assumed exogenous here, departure time dependent in paper)

• Departure times td1, td2, arrival times ts2 = td1 + T1, ts3 = td2 + T2

The model

• Daily utility U determined by departure times

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

Delay costs

• Journey delays T1, T2

• Delay costs

• Depend on:• journey delays (magnitude and distribution)• schedule adjustments (information)• work schedule flexibility

Adjustments

• Evidence from I-35W bridge collapse

• We consider:

1. no adjustment

2. no + optimal

3. over-adjustment

4. over + optimal

5. optimal adjustment

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 functions1(t), 2(t – ts2), 3(t): min, max, steepness, location

Numerical results

• Delay on both morning and evening trip (baseline tr. time 240 min)

• Fixed (left) vs. flexible (right) work hours

Numerical results

• Delay on morning trip only or evening trip only

• Fixed (left) vs. flexible (right) work hours

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

Thank you!