Travel-time uncertainty, departure time choice, and the cost of morning commutes

Existing models of the commuting time-of-day choice are extended in order to analyze the effect of uncertain travel times. Travel time includes a time-varying congestion component and a random element specified by a probability distribution. Results from the uniform and exponential probability distributions are compared and the optimal "head start" time that the commuter chooses to account for travel time variability, i.e., a safety margin that determines the probability of arriving late for work, is derived. The model includes a one-time lateness penalty for arriving late as well as the per minute penalties for early and late arrival that other investigators have included. It also generalizes earlier work by accounting for the time variation in the predictable component of congestion, which interacts with uncertainty in interesting ways. A brief numerical analysis of the model reveals that uncertainty can account for a large proportion of the costs of the morning commute.

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