Ride-sharing with travel time uncertainty

Abstract

Travel time uncertainty has significant effects on travel reliability and travelers’ generalized trip cost. However, travel time uncertainty has not been considered in existing ride-sharing models, leading to an inaccurate estimation of the benefit from ride-sharing and irrational ride-sharing matches. To fill in the gap, this paper proposes a stochastic ride-sharing model, in which travel time is assumed to be stochastic and follow a time-independent general distribution that has a positive lower bound. Due to travel time uncertainty, travelers may not arrive at their destinations on time. Different from the traditional models taking time windows as hard constraints, the proposed ride-sharing system only requires each participant announcing a role and the desired arrival time window. In the model, the generalized trip cost consists of the cost of driving a vehicle, the cost of travel time, and the cost of schedule delay early and late. This study investigates the effect of the unit variable cost of driving, travelers’ values of time (VOTs), and travel time uncertainty on the cost saving of ride-sharing trips compared to driving-alone trips. A bi-objective ride-sharing matching model is proposed to maximize both the total generalized trip cost saving and the number of matches. The proposed ride-sharing model is further extended to consider time-dependent travel time uncertainty, and the Monte Carlo simulation (MCS) method is developed to evaluate the mean generalized trip cost. Finally, numerical examples are provided to illustrate the properties of the two proposed models. The results show that the unit variable cost of driving, travelers’ VOTs, travel time uncertainty, and the selection of the weight in the objective function have significant impacts on the performance of the proposed ride-sharing system with travel time uncertainty. The results also show that a feasible ride-sharing match based on deterministic travel time can become infeasible in a stochastic ride-sharing system. It is therefore important to consider travel time uncertainty when determining the matches.