Integrating the mean–variance and scheduling approaches to allow for schedule delay and trip time variability under uncertainty

Document Type

Journal Article

Publication Date


Subject Area

place - asia, place - australasia, ridership - behaviour, operations - scheduling


Uncertainty, Trip time variability, Departure time choice, Scheduling approach, Generalized approach, Mean–variance approach


Uncertainty of travel times and the impact on travel choice behavior has been recognized as an increasingly important research direction in the past decade. This paper proposes an extension to the popular scheduling approach to model traveler’s departure time choice behavior under uncertainty, with the main focus on a richer representation of uncertainty. This more general approach incorporates a separate term to reflect the risk aversion associated with uncertainty. Recognizing the correlation between expected schedule delay and travel time variability, the schedule delay components in the generalized approach are defined in terms of expected travel time, which differs from the scheduling approach. This approach is developed based on the analytical investigation of the relationship between the expected schedule delay and the mean and standard deviation of travel time. An analytical equivalence was found between the scheduling approach and the general approach given a departure time t. To investigate the empirical performance of the generalized approach, two state preference (SP) data sets are used; one from China with a symmetric travel time distribution and the other from Australia with an asymmetric distribution. Both studies show empirical evidence of an equivalence in respect of statistical fit between the generalized and the scheduling approaches, as found from analytical investigations. The Chinese study gives support in the generalized model to including both the mean–variance and the scheduling effects; whereas the Australian study finds only the mean–variance specification has statistical merit. Despite the different travel contexts, it is noteworthy in both empirical settings, that the parameter estimate for arriving earlier than the preferred arrival time (PAT) in the generalized model is positive. This suggests that commuters tend to prefer to arrive earlier in order to guarantee he/she will not be late. This paper contributes to a better understanding of performances of different reliability measures and their relationships. The practical value of the various unreliability measures is provided showing that these indicators are easy to obtain for inclusion in project appraisal.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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