Existing models of the commuting time-of-day choice were used to analyze the effect of uncertain travel times. Travel time included a time-varying congestion component and a random element specified by a probability distribution. The results from the uniform and exponential probability distributions were compared and the optimal 'head-start' time that the commuter chooses to account for travel time variability, that is, a safety margin that determines the probability of arriving late for work, was 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 are included by other investigators. 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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