标题： 闵可夫斯基空间中的透镜通过隐藏瓶颈单元来优化队列。 显示英文标题

标题： Lenses in Minkowski space optimize queues by hiding bottleneck units

摘要： 我们在闵可夫斯基空间中数学构造了正质量粒子的焦透镜。从点源发出的粒子，无论初始方向和速度如何，都会以同步的固有时间重新聚焦。闵可夫斯基空间为我们提供了飞机登机过程中形成的乘客队列表示。乘客之间的阻塞关系与时空中的过去-未来关系一致，并且登机时间由最长的阻塞链决定。如果根据闵可夫斯基空间中的透镜安排慢速乘客，则可以保持所有阻塞链长度相等。透镜的两种介质对应于快速和慢速乘客的分组，透镜指定了闸口排队中快速和慢速乘客的最佳位置。不仅登机时间被最小化，其方差也被最小化。 显示英文摘要

摘要： We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a useful representation of the passenger queue formed during airplane boarding. The blocking relations between passengers coincide with the past-future relation in spacetime, and the boarding time is determined by the longest blocking chain. All blocking chains can be kept equally long if slow passengers are placed according to a lens in Minkowski space. The two media of the lens correspond to a grouping of fast and slow passengers, and the lens specifies the optimal placement of fast and slow passengers in the queue at the gate. Not only the boarding time, but also its variance is minimized.