Lorentzian-geometry-based analysis of airplane boarding policies highlights "slow passengers first" as better
Lorentzian-geometry-based analysis of airplane boarding policies highlights "slow passengers first" as better
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DOI：
10.1103/physreve.100.062313
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发表时间：
2019-12-27
影响因子：
2.4
通讯作者：
Bachmat, Eitan
中科院分区：
文献类型：
--
作者：
Erland, Sveinung;Kaupuzs, Jevgenijs;Bachmat, Eitan
我们研究飞机登机的限制，大量的乘客使用几何光学在洛伦兹度量。登机问题自然地嵌入在具有平坦洛伦兹度量的（1 + 1）维时空中。登机过程的持续时间可以基于在二维时空图中试图到达座位的乘客的一维队列的表示来计算。一个乘客延迟其他乘客的能力取决于他们的排队位置和排指定。这相当于时空中两个事件之间的因果关系，而两个乘客是类时分离的，如果一个人挡住了另一个人，如果两个人可以同时坐下。这种几何中的测地线可以用来计算渐近登机时间，因为时空几何是飞机登机的多粒子（乘客）限制。我们的方法自然会导致引入有效折射率，从而能够分析计算具有不同通道清理时间分布的乘客组的平均登机时间。在过去，航空公司试图通过尝试登机政策来缩短登机时间，这些政策允许速度慢或速度快的乘客先登机。我们的分析计算，支持离散事件模拟，支持违反直觉的结果，总登机时间更短的慢乘客登机前快的乘客。这是一个通用的结果，适用于表征问题的任何参数组合：慢行乘客的百分比，快速和慢速组的过道清理时间之间的比率，以及过道上沿着的乘客密度。我们发现，与快速优先登机政策相比，最多可提高28%。我们的方法开辟了一个框架下统一众多基于模拟的案例研究的可能性。
We study airplane boarding in the limit of a large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a (1 + 1)-dimensional space-time with a flat Lorentzian metric. The duration of the boarding process can be calculated based on a representation of the one-dimensional queue of passengers attempting to reach their seats in a two-dimensional space-time diagram. The ability of a passenger to delay other passengers depends on their queue positions and row designations. This is equivalent to the causal relationship between two events in space-time, whereas two passengers are timelike separated if one is blocking the other and spacelike if both can be seated simultaneously. Geodesics in this geometry can be utilized to compute the asymptotic boarding time, since space-time geometry is the many-particle (passengers) limit of airplane boarding. Our approach naturally leads to the introduction of an effective refractive index that enables an analytical calculation of the average boarding time for groups of passengers with different aisle-clearing time distribution. In the past, airline companies attempted to shorten the boarding times by trying boarding policies that allow either slow or fast passengers to board first. Our analytical calculations, backed by discrete-event simulations, support the counterintuitive result that the total boarding time is shorter with the slow passengers boarding before the fast passengers. This is a universal result, valid for any combination of the parameters that characterize the problem: the percentage of slow passengers, the ratio between aisle-clearing times of the fast and the slow group, and the density of passengers along the aisle. We find an improvement of up to 28% compared with the fast-first boarding policy. Our approach opens up the possibility to unify numerous simulation-based case studies under one framework.