This paper studies a large-scale ride-matching problem with a large number of travelers who are either drivers with vehicles or riders looking for sharing vehicles. Drivers can match riders that have similar itineraries and share the same vehicle; and reneging travelers, who become impatient and leave the service system after waiting a long time for shared rides, are considered in our model. The aim is to maximize the long-run average revenue of the ride service vendor, which is defined as the difference between the long-run average reward earned by providing ride services and the long-run average penalty incurred by reneging travelers. The problem is complicated by its scale, the heterogeneity of travelers (in terms of origins, destinations, and travel preferences), and the reneging behaviors. To this end, we formulate the ride-matching problem as a specific Markov decision process and propose a scalable ride-matching policy, referred to as Bivariate Index (BI) policy. The BI policy prioritizes travelers according to a ranking of their bivariate indices, which we prove, in a special case, leads to an optimal policy to the relaxed version of the ride-matching problem. For the general case, through extensive numerical simulations for systems with real-world travel demands, it is demonstrated that the BI policy significantly outperforms baseline policies.

中文翻译：

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不安分的强盗模型，与叛逆的旅行者进行动态骑行匹配


本文研究了一个大规模的乘车匹配问题，该问题涉及大量旅行者，这些旅行者要么是有车辆的司机，要么是寻找共享车辆的乘客。合作车主可以匹配行程相似且共享同一车辆的乘客;而违背的旅客，他们变得不耐烦，在等待很长时间后离开服务系统，在我们的模型中被考虑在内。其目的是最大限度地提高乘车服务供应商的长期平均收入，该收入定义为通过提供乘车服务获得的长期平均奖励与违背行程的旅客所遭受的长期平均罚款之间的差额。这个问题因其规模、旅行者的异质性（在出发地、目的地和旅行偏好方面）以及违背行为而变得复杂。为此，我们将乘车匹配问题表述为特定的马尔可夫决策过程，并提出了一种可扩展的乘车匹配策略，称为双变量指数 （BI） 策略。BI 策略根据旅行者的二元指数排名对旅行者进行优先级排序，我们证明，在特殊情况下，这会导致乘车匹配问题的宽松版本的最佳策略。对于一般情况，通过对具有实际差旅需求的系统进行广泛的数值模拟，表明 BI 策略的性能明显优于基线策略。