共乘出行是城市共享交通的重要出行方式之一。共乘出行可以减少道路上的机动车数量,也常被认为是缓解交通拥堵的有效方式。相比于传统的共乘出行,专车共乘出行能进一步提升出行体验的舒适程度,提高出行者的共乘积极性,促进城市共享交通的良性发展。研究共乘出行的交通分配问题对于预测交通流量和制定管理政策具有重要意义。该文以专车共乘出行为研究对象,提出了多模式随机共乘用户均衡(stochastic ridesharing user equilibrium,SRUE)问题;基于Logit模型建立了该问题的变分不等式(variational inequality,VI)模型,并验证了解的等价性、存在性和唯一性;通过并行自适应投影算法(parallel self-adaptive projection,PSAP)获得模型的解,通过数值实验对模型和算法的有效性进行评估。实验结果表明：专车共乘出行能有效减少路面行驶的车辆、降低出行时间;乘客在专车共乘出行市场中占据主导地位;制定的合理公交票价能协同常规公交与专车共乘出行从而缓解交通拥堵。
[Objective] 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. [Methods] 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. [Results] 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. [Conclusions] 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.
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