Compartmental model and fleet-size management for shared mobility systems with for-hire vehicles
Compartmental model and fleet-size management for shared mobility systems with for-hire vehicles
复制标题
出租车辆共享移动系统的车厢模型和车队规模管理
DOI：
10.1016/j.trc.2021.103236
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Menendez, Monica
中科院分区：
文献类型：
--
作者：
Jin, Wen-Long;Martinez, Irene;Menendez, Monica
关于租赁车辆（FHVs）共享出行系统对拥堵的影响，文献中存在相互矛盾的结果。据我们所知，没有物理上有意义和数学上可处理的模型来解释这些相互冲突的结果或为此类移动系统设计有效的管理方案。在本文中，我们试图通过提出具有FHVs的共享移动系统中乘客旅行和车辆动力学的隔间模型来填补这一空白，并讨论不同车队规模管理方案的影响。为了建立车厢模型，我们首先将乘客的旅行分为四个车厢：计划、等待、旅行和完成。我们用点队列模型描述了等待行程的动力学，用扩展浴盆模型描述了出行行程的动力学。与传统的车辆出行浴盆模型一样，扩展浴盆模型是在相对于个人出行到目的地距离的相对空间中推导出来的。然而，与传统的浴缸模型不同，扩展浴缸模型中的车辆动力学和行程动力学并不重叠，因为fhv的动力学是由车队规模管理方案控制的；但它们是相关的，因为旅行的旅行伴随着被占用的fhv，而空的fhv为等待的旅行提供座位。在该建模框架中，对候车乘客与fhv的匹配过程在集合层面进行建模，使得从候车车厢到旅行车厢的乘客行程流等于由旅行行程完成率和车队规模管理方案决定的候车行程的座位需求和座位供应的最小值。除了池化比例外，与匹配过程相关的死路里程、池化服务导致的绕行里程以及其他额外里程都由另一个外生参数即额外里程比来捕获。通过这些假设和简化，得到的区隔模型是一个确定性的耦合排队模型，可以写成微分方程系统。并给出了该模型可定义的船队规模管理方案的充要条件。通过简化的封闭式隔间模型，我们从理论上证明了限制等待时间导致与私人运营车辆（POV）相同的车队规模管理方案，即POV方案。在这种系统中，完成率取决于额外行程里程比，以及合用比例。对于100%自主的fhv，在最大流量和自由流速度下，能够将总成本降至最低的最佳车队规模。对于混合动力车辆和混合动力车辆，我们扩展了舱室模型，并数值求解了不同市场渗透率下的最优车队规模。本研究调和了文献中相互矛盾的结果。我们发现，当池化率较低时，系统的整体性能可能会恶化或改善，具体取决于车队规模管理方案：使用POV方案时，系统可能会变得更加拥挤；但是，通过适当的机队规模上限，系统的性能可以大大提高。本研究的一个主要政策含义是，对FHV车队规模实施上限是一种可行的措施，可以减轻FHV造成的额外的死路和绕行里程的拥堵效应。
There have been conflicting results in the literature regarding the congestion impacts of shared mobility systems with for-hire vehicles (FHVs). To the best of our knowledge, there is no physically meaningful and mathematically tractable model to explain these conflicting results or devise efficient management schemes for such mobility systems. In this paper, we attempt to fill the gap by presenting a compartmental model for passenger trip and vehicle dynamics in shared mobility systems with FHVs and discussing the impacts of different fleet-size management schemes.To develop the compartmental model, we first divide passenger trips into four compartments: planned, waiting, traveling, and completed. We describe the dynamics of the waiting trips by the point queue model, and those of the traveling trips by an extended bathtub model. As the traditional bathtub model for vehicular trips, the extended bathtub model is derived in a relative space with respect to individual trips’ distances to their destinations. However, different from the traditional bathtub model, vehicular dynamics and trip dynamics in the extended bathtub model are not overlapping, as the dynamics of FHVs are controlled by the fleet-size management scheme; but they are related, as traveling trips travel with occupied FHVs, and empty FHVs supply seats to waiting trips. Within this modeling framework, the matching process between waiting passengers and FHVs is modeled at the aggregate level, such that the passenger trip flow from the waiting compartment to the traveling compartment equals the minimum of the waiting trips’ demand of seats and the supply of seats determined by the completion rate of traveling trips and the fleet-size management scheme. In addition to the pooling ratio, the deadhead miles, the detour miles caused by pooling services, and other extra miles associated with the matching process are captured by another exogenous parameter, namely, the extra mileage ratio. With these assumptions and simplifications, the resulting compartmental model is a deterministic, coupled queueing model, which can be written as a system of differential equations. We also present the sufficient and necessary condition on the fleet-size management scheme for the model to be well-defined.With the parsimonious, closed-form compartmental model, we demonstrate theoretically that limiting the wait time leads to a fleet-size management scheme equivalent to that of the privately operated vehicles (POVs), i.e., the POV scheme. In such a system, the completion rate depends on the extra trip mileage ratio, as well as the pooling ratio. With 100% autonomous FHVs, the optimal fleet size that minimizes the total costs occurs at the maximum flow-rate and the free-flow speed. With mixed POVs and FHVs, we extend the compartmental model and numerically solve for the optimal fleet sizes under different market penetration rates. This study reconciles the conflicting results in the literature. We find that, with a low pooling ratio, the overall system’s performance can be deteriorated or improved, depending on the fleet-size management scheme: with the POV scheme, the system could become more congested; but with an appropriate fleet-size cap, the system’s performance can be substantially improved. A major policy implication of this study is that implementing a cap for the FHV fleet size is a viable measure to mitigate the congestion effects of extra deadhead and detour miles caused by FHVs.
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