机场出租车阈值决策与短途优先的随机排队模型研究

Research on Threshold Decision and Short-Trip Priority Stochastic Queueing Models for Airport Taxi Operations

摘要: 针对“机场的出租车问题”，本文从出租车司机和机场管理者两个视角出发，分别构建了出租车司机在送客到机场后“排队等客”与“空驶返城”之间的决策模型，以及管理部门实施“短途优先权”以平衡司机收益的排队优化模型。在问题一中，本文以“单周期期望单位时间净收益最大化”为目标，综合考虑蓄车池当前排队车辆数、机场乘客到达与放行规律、市区营运收益等因素，建立了出租车司机的收益率比较模型。推导表明，存在一个与机场单次平均收益、市区平均收益率、放行率和机场行驶时间等参数相关的临界排队车数阈值N^*：当现场排队车辆数不超过N^*时，司机选择留在机场排队更有利；当排队车辆数超过N^*时，空驶返回市区运营更有利。该阈值清晰刻画了航班规模、时段、季节等因素对司机决策的影响机理。在问题二中，本文根据乘客目的地远近划分短途与长途，构建了“短途优先队列 + 普通队列”的双队列M/M/1排队模型，将总放行能力在两条队列之间按比例β分配。通过分析短途司机和长途司机在优先机制下的单位时间平均净收益，提出了以“短途与长途收益率差最小”为目标的参数寻优模型，给出最优放行比例β^*的求解过程，并据此设计了可操作的“短途优先放行规则”。数值算例表明，在合理设定参数的情况下，适当的优先比例可以显著缩短短途司机的排队等待时间，使短途与长途司机的收益率接近，从而兼顾整体效率与收益公平。

Abstract: Focusing on the “airport taxi problem”, this paper examines the issue from the perspectives of taxi drivers and airport managers. We first construct a decision model for taxi drivers who, after dropping off passengers at the airport, must choose between “queuing for passengers” and “returning empty to the city”, and then build a queuing optimization model for the management authority to implement a “short-trip priority” policy so as to balance drivers’ incomes. In Problem 1, taking the maximization of the expected net income per unit time over a single operating cycle as the objective, we comprehensively consider the current number of vehicles in the holding pool, passenger arrival and release patterns at the airport, and operating revenue in the urban area, and establish a comparative model for the driver’s income rate. The analysis shows that there exists a critical queue-length threshold N^*, which depends on parameters such as the average income per airport trip, the average income rate in the city, the passenger release rate, and the travel time between the city and the airport. When the on-site queue length does not exceed N^*, it is more profitable for drivers to stay and queue at the airport; when the queue length exceeds N^*, it is more profitable to return empty to the city to operate. This threshold clearly characterizes the influence mechanism of flight volume, time of day, season and other factors on drivers’ decisions. In Problem 2, passengers are classified into short-distance and long-distance trips according to their destinations, and a two-queue M/M/1 model consisting of a “short-trip priority queue” and a “regular queue” is constructed, where the total service capacity is allocated between the two queues in proportion β. By analyzing the average net income per unit time of short-trip and long-trip drivers under the priority mechanism, we propose a parameter-optimization model with the objective of minimizing the difference between the income rates of short-trip and long-trip drivers, and derive the solution procedure for the optimal release proportion β^*. On this basis, an operational “short-trip priority dispatching rule” is designed. Numerical examples show that, under reasonable parameter settings, an appropriate priority proportion can significantly reduce the waiting time of short-trip drivers, make the income rates of short-trip and long-trip drivers close to each other, and thus balance overall efficiency and income fairness.