UC Berkeley

Previous research studies have provided evidence of the non-uniformity of the value of time, which usually shows a decreasing trend as travel time increases. This work takes an in-depth look at thresholds and discontinuities in the value of time function. A theoretical framework is provided based on microeconomic theory. It is postulated that because of the multiple activities involved in an individual's activity pattern, and the minimum time requirements associated with these activities, there exist discontinuities in the travel cost function as the travel time encroaches upon the time originally assigned to other activities. The derivation of the indirect utility function of a trip is made in a multi-activity scenario, which shows the existence of discontinuous changes when the lowest time requirements of one or more activities are violated. In such cases, the activity may or may not be canceled. Two models are constructed depending on whether the cancellation is included. In Model 1, which assumes that the activity (of which the lowest time requirement is to be violated) cannot be canceled, the time assigned to the activity cannot be further reduced. As a result, further increase in travel time is at the expense of another activity. Therefore, Model 1 reflects a change of slope in the utility function. In the case of Model 2, the activity can be canceled. The cancellation of the activity results in a quantum change in utility function. Consequently, Model 2 reflects a change in slope together with a quantum decrease in utility.

The impact of the thresholds and discontinuities has long been overlooked, especially in intercity transportation. Using discrete choice modeling, empirical evidence of these discontinuities is found in air travel route choice. The thresholds where the discontinuities occur change with trip characteristics such as direction, and travel purpose. In general, the thresholds of business travelers are lower than those of leisure travelers. Additionally, there is evidence of a second threshold in the data. This is because as travel time keeps increasing after the first threshold is met, travel time starts to encroach on a second activity. The second threshold is hence possible as the binding condition may change again.

Because of the fewer variables involved in the estimation process, Model 1 is generally more stable and requires less computational effort. Based on the estimation results, whether the changes of utility at the thresholds are quantum (model 2) or not (model 1) remains an open question. Due to the limited data available for this study, the comparison results between the two models are tentative. More detailed data and in-depth research are needed to ascertain these results.

Numerical examples are used to illustrate the proposed models' impact on airline network design in the choice of hub location. For future research, suggestions are made to incorporate the notion of thresholds in travel survey design in order to provide better bases for estimating their values and their impact on traveler behavior.