Multimodal stochastic ridesharing user equilibrium model with tailored service

Ridesharing is considerably reforming urban transportation networks. It is considered an effective measure to alleviate traffic congestion and vehicle emissions and is supported by many governments and residents globally. It also encourages travelers with the same or similar origin and destination to share vehicles to reduce on-road vehicles. Unlike traditional ridesharing services, which place as many ridesharing participants as possible inside ridesharing vehicles, tailored ridesharing prioritizes the comfort and convenience of travelers and predominantly offers one-to-one ridesharing services. However, the emerging tailored ridesharing mode makes traditional methods of predicting traffic flow ineffective. Therefore, it is crucial to investigate a traffic assignment problem to predict traffic flow and formulate traffic management policies.

First, we clarify a multimodal stochastic ridesharing user equilibrium (SRUE) problem, where the network topology, flow constraints, and generalized travel cost functions are specified. Travelers can choose to be solo drivers, ridesharing drivers, riders, or public transport passengers, considering a network with tailored ridesharing and public transit services. Consideration is given to the travel demands of car owners and noncar owners. The flow conservation and ride-matching constraints are formulated. Furthermore, a path-based generalized travel cost function is proposed for each mode, including time costs, inconvenience costs, ridesharing prices, compensation, and miscellaneous costs. The SRUE flow distribution principle states that travelers will always select the alternative, where an alternative consists of a route and a mode with the minimum perceived travel cost. Second, we formulate an equivalent variational inequality (VI) model for the above SRUE problem, refer to as the VI-SRUE model. Moreover, the equivalence, existence, and uniqueness of the model solution are demonstrated. The stochasticity is handled by introducing a random perception error that satisfies the Gumbel distribution, ensuring that the travelers' choice behavior pattern conforms to the Logit model. The equivalence is proved by checking the Karush-Kuhn-Tucker (KKT) condition and Slater's theorem. The existence is supported by the compact feasible solution set and continuous function of the VI-SRUE model. The VI-SRUE has a unique solution because its function is strictly monotonous under mild conditions. Finally, a globally convergent parallel self-adaptive projection (PSAP) algorithm is applied to find the solution to the VI-SRUE model. The algorithm combines the K-shortest path method, network decomposition, and parallel computing techniques to avoid the possible memory overflow caused by large-scale networks.

In this paper, numerical experiments were conducted to assess the proposed model and algorithm. A sensitivity analysis was performed based on the Braess network. From these experiments, the following results were obtained: (1) Tailored ridesharing could effectively reduce the travel time of on-road vehicles and travelers. (2) Riders dominated the tailored ridesharing market through high sensitivity of ridesharing flow to coefficient of inconvenience (COI). (3) Appropriate bus fares could help public transport and tailored ridesharing to further reduce the traffic congestion. Moreover, through the Sioux-Falls network, the PSAP algorithm was verified to have excellent computational efficiency for solving large-scale SRUE problems.

In summary, this paper proposes a VI-SRUE model to predict the flow pattern of urban transportation networks with tailored ridesharing services using an efficient algorithm. The proposed VI-SRUE model describes the stochasticity associated with travelers' perception of transportation network information. The contribution of this paper is to establish a traffic assignment problem that simultaneously considers various travel modes and multiple types of travelers in the ridesharing network. Through the verification, solution, and analysis of the problem and equivalent mathematical model, this paper clarifies the relation among multiple travel modes, providing an effective foundation for predicting traffic flow and formulating ridesharing management measures.