A three‐objective user equilibrium model: Time surplus maximisation under uncertainty

In this paper, we propose a user equilibrium model considering the 3 most important factors influencing route choice behaviour in a road network, namely, travel time, travel time reliability, and monetary cost. We further develop the time surplus maximisation bi‐objective user equilibrium model and incorporate the concept of travel time budget to model how users might react to uncertainty induced by day‐to‐day variability in travel time caused by traffic incidents. This results in a three‐objective user equilibrium model, which has a possibly infinite set of equilibrium flows. To compute equilibrium flows, we introduce time budget surplus defined as the maximum travel time a user is willing to spend minus the actual time budget required for a desired level of travel time reliability. At equilibrium, for each origin–destination pair, all individuals are travelling on the path with the highest time budget surplus value among all the efficient paths between this origin‐destination pair. This becomes a time budget surplus maximisation three‐objective user equilibrium model (TBSmaxTUE). We show that the TBSmaxTUE model is a special case of three‐objective user equilibrium considering inimisation of expected travel time, travel time variance, and toll (monetary cost) as objectives. We illustrate the model and our results on a small network.