Stochastic departure time user equilibrium with heterogeneous trip profile

Abstract

Recently, the generalized bathtub model extended the classic bathtub model to capture various distributions of the trip length by introducing a new state variable: the number of active trips with remaining distances greater than or equal to a threshold. The traffic dynamics are reformulated by four partial differential equations that track the distribution of the remaining trip lengths. This study aims to formulate and solve stochastic user equilibrium for the dynamic departure time choice model based on the generalized bathtub model with heterogeneous trip attributes. In particular, the proposed framework is able to address any distribution for desired arrival time and trip length. We first formulate the problem in continuous form as a fixed-point problem. Then we apply a discretization method to address the trip-based setting. The proposed framework is applied to the real demand profile of the large-scale network of Lyon North for the morning peak hour.