A bi-objective user equilibrium model of travel time reliability in a road network

•We illustrate shortcomings of existing travel time reliability UE models.•We introduce bi-objective user equilibrium models to overcome the shortcomings.•We formulate bi-objective versions of two travel time reliability UE models.•We prove that the UE models are special cases of the bi-objective formulations.•We propose a general bi-objective formulation as a general modelling framework. Travel time, travel time reliability and monetary cost have been empirically identified as the most important criteria influencing route choice behaviour. We concentrate on travel time and travel time reliability and review two prominent user equilibrium models incorporating these two factors. We discuss some shortcomings of these models and propose alternative bi-objective user equilibrium models that overcome the shortcomings. Finally, based on the observation that both models use standard deviation of travel time within their measure of travel time reliability, we propose a general travel time reliability bi-objective user equilibrium model. We prove that this model encompasses those discussed previously and hence forms a general framework for the study of reliability related user equilibrium. We demonstrate and validate our concepts on a small three-link example.