The value of travel time variability with trip chains, flexible scheduling and correlated travel times

This paper extends the analysis of the value of mean travel time (VMTT) and day-to-day travel time variability (VTTV) from single, isolated trips to daily trip chains, considering the effects of flexibility in activity scheduling and within-day correlation of travel times. Using a multi-stage stochastic programming approach, we show that the VMTT and VTTV on a trip is conditional on the realized travel times on preceding trips, first through the arrival time to the preceding activity and second through the information provided about subsequent travel times. Analytical formulas for the VMTT and VTTV are obtained for two special cases with piecewise constant and linear marginal cost functions, respectively. With flexible scheduling, there is typically a cost associated with a positive correlation of travel times, arising from persistent deviations from typical travel demand or supply on a given day. However, there is also a strict benefit in the dependence since it allows for a more efficient scheduling of later trips.