Commuter behavior under travel time uncertainty

We investigate the impact of random deviations in planned travel times using an extension of Vickrey's celebrated bottleneck model. The model is motivated by the fact that in real life, users can neither exactly plan the time at which they depart from home, nor the delay they experience before they join a particular congestion bottleneck under investigation. We show that the strategy advocated by the Nash equilibrium in Vickrey's model is not a user equilibrium in the model with travel time uncertainty. We then investigate the existence of a user equilibrium for the latter and show that in general such an equilibrium can neither be a pure Nash equilibrium, nor a mixed equilibrium with a continuous density. Our results imply that when random distortions influence user decisions, the dynamics of deterministic bottleneck models are inadequate to describe this more complex situation. We illustrate with numerical analysis how the mechanics of a bottleneck with delayed arrivals are unstable for any continuous strategy, thus shedding more light on the non-existence result. Alternatively, we formulate a logit model for the day-to-day dynamic adjustment in response to previous travel experiences. We further investigate the conditions for convergence of the dynamic choice model and numerically illustrate the resulting equilibrium strategy.

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