Stochastic traffic assignment with endogenous route sets: Relative versus absolute cost measures

Recently there has been a growing interest in stochastic traffic assignment with endogenous route sets aiming to secure consistency between route set determination and equilibrium assignment. However, existing related studies commonly assume travelers have identical perception errors of route costs. This assumption leads to endogenous route sets determined solely by absolute cost differences, despite substantial evidence suggesting that travelers consider the relative significance of route costs to different trip lengths. Motivated by this gap, our study aims to model non-identical perception errors in endogenous route set determination via relative cost measures. We develop a relative-measure truncated stochastic user equilibrium (SUE) model, where route costs are compared against an endogenous threshold in relative terms for route set determination and flow assignment. Desirably, the relative-measure truncated SUE model is invariant to the measurement scale of travel costs. Further, we provide a tractable formulation for the developed SUE model, which guarantees a unique equilibrium solution under mild conditions. In addition, a provably convergent algorithm is presented to solve the model across the entire network without enumeration of all possible routes, with applications to a realistic transportation network.