This paper presents an Aggregate Matching and Pick-up (AMP) model to delineate the matching and pick-up processes in mobility-on-demand (MoD) service markets by explicitly considering the matching mechanisms in terms of matching intervals and matching radii. With passenger demand rate, vehicle fleet size and matching strategies as inputs, the AMP model can well approximate drivers’ idle time and passengers’ waiting time for matching and pick-up by considering batch matching in a stationary state. Properties of the AMP model are then analyzed, including the relationship between passengers’ waiting time and drivers’ idle time, and their changes with market thickness, which is measured in terms of the passenger arrival rate (demand rate) and the number of active vehicles in service (supply). The model can also unify several prevailing inductive and deductive matching models used in the literature and spell out their specific application scopes. In particular, when the matching radius is sufficiently small, the model reduces to a Cobb–Douglas type matching model proposed by Yang and Yang (2011) for street-hailing taxi markets, in which the matching rate depends on the pool sizes of waiting passengers and idle vehicles. With a zero matching interval and a large matching radius, the model reduces to Castillo model developed by Castillo et al. (2017) that is based on an instant matching mechanism, or a bottleneck type queuing model in which passengers’ matching time is derived from a deterministic queue at a bottleneck with the arrival rate of idle vehicles as its capacity and waiting passengers as its customers. When both the matching interval and matching radius are relatively large, the model also reduces to the bottleneck type queuing model. The performance of the proposed AMP model is verified with simulation experiments.

中文翻译：

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按需移动服务的聚合匹配和拾取模型


本文提出了一个聚合匹配和拾取 （AMP） 模型，通过明确考虑匹配间隔和匹配半径方面的匹配机制，来描述移动按需 （MoD） 服务市场的匹配和拾取过程。以乘客需求率、车队规模和匹配策略为输入，AMP 模型可以通过考虑静止状态下的批量匹配，很好地估计驾驶员的空闲时间和乘客的匹配和接送等待时间。然后分析 AMP 模型的属性，包括乘客等待时间和驾驶员空闲时间之间的关系，以及它们随市场厚度的变化，市场厚度以乘客到达率（需求率）和在役活跃车辆数量（供应）来衡量。该模型还可以统一文献中使用的几种流行的归纳和演绎匹配模型，并阐明它们的具体应用范围。特别是，当匹配半径足够小时，该模型简化为 Yang 和 Yang （2011） 针对街头叫车出租车市场提出的 Cobb-Douglas 型匹配模型，其中匹配率取决于等待乘客和闲置车辆的池大小。该模型具有零匹配间隔和较大的匹配半径，可简化为 Castillo 等人（2017 年）开发的基于即时匹配机制的 Castillo 模型，或瓶颈型排队模型，其中乘客的匹配时间来自瓶颈处的确定性队列，以闲置车辆的到达率为容量，等待的乘客为客户。当匹配间隔和匹配半径都比较大时，模型也会简化为瓶颈型排队模型。 通过仿真实验验证了所提出的 AMP 模型的性能。