Analytical Model for Optimal Departure Time Choice with Perception Errors for Planners

An extension of a recent framework for analyzing scheduling disutility with perception errors is derived. In such framework, the traveler has ( α , β , γ ) scheduling preferences. Although the actual travel time of travelers is influenced by departure time, travelers make a route-choice decision on the basis of their perceived travel time. Thus, we mainly investigate the effects of perception errors on the optimal departure time. The optimal departure time and expected disutility are obtained on the basis of the proposed scheduling disutility model with perception errors. The inverse function curve of a standardized normal distribution is introduced to geometrically analyze the positive correlation between perception errors and optimal departure time. Our empirical example further illustrates that departure time as an endogenous variable affects the expectation and variance of perceived travel time and implies that perception errors are related to departure time. The linear relationship between the mean and variance of perceived travel time and the departure time is analyzed through an empirical illustration. The expected optimal disutility and departure time are derived, provided that the mean and variance of perception errors and departure time satisfy linear dependence. Finally, the results of the analysis of scheduling services with standardized normal distributions agree with the theoretical results and linear assumption in this study.