A consistent reliability-based user-equilibrium problem with risk-averse users and endogenous travel time correlations: Formulation and solution algorithm

The traditional traffic assignment model has been extended in the literature to incorporate uncertainty and travelers who are sensitive to it. However, the proposed formulations that model risk-averse users lack (i) a consistent representation of the various stochastic quantities involved and (ii) a general solution approach. In this context, this study formulates a consistent, reliability-based user-equilibrium problem with risk-averse travelers. In the proposed formulation, various stochastic quantities are consistent with each other: the stochastic origin-destination demands result in stochastic path-flows and in turn stochastic link-flows, which result in stochastic link travel times, and travelers make decisions based on the stochasticity of travel times. The formulation also incorporates (i) endogenous link-flow variances and covariances and (ii) flow-dependent and endogenous link travel time correlations. At equilibrium - which is defined over the distributions of travel times and flows - no user can improve her travel time reliability by unilaterally changing route. The conditions for existence of a solution to the formulated problem are presented. A gradient projection based algorithm is proposed to solve the formulated problem, which is demonstrated to be correct and efficient through computational experiments. We also show that ignoring consistency in the formulation can lead to potentially erroneous conclusions. Experiments also demonstrate that the solution can be sensitive to the demand levels, stochasticity in demand, and users' degree of risk-aversion. This work has the potential to make existing reliability-based user-equilibrium formulations more general and operational. It also has important applications in reliability-based traffic planning and management.