Bernstein Noam
Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 1):023101. doi: 10.1103/PhysRevE.86.023101. Epub 2012 Aug 10.
Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)] recently showed that for a simple model for the boarding of an airplane, the mean time to board scales as a power law with the number of passengers N and the exponent is less than 1. They note that this scaling leads to the prediction that the "back-to-front" strategy, where passengers are divided into groups from contiguous ranges of rows and each group is allowed to board in turn from back to front once the previous group has found their seats, has a longer boarding time than would a single group. Here I extend their results to a larger number of passengers using a sampling approach and explore a scenario where the queue is presorted into groups from back to front, but allowed to enter the plane as soon as they can. I show that the power law dependence on passenger numbers is different for large N and that there is a boarding time reduction for presorted groups, with a power law dependence on the number of presorted groups.
弗雷泰(Frette)和赫默(Hemmer)[《物理评论E》85, 011130 (2012)] 最近表明,对于一个简单的飞机登机模型,平均登机时间与乘客数量N呈幂律关系,且指数小于1。他们指出,这种标度关系导致这样的预测:“从后往前”策略(即乘客被分成连续排数范围的组,并且前一组找到座位后,每组依次从后往前登机)的登机时间比单个组的登机时间更长。在此,我使用抽样方法将他们的结果扩展到更多乘客,并探讨一种队列从后往前预先分组,但一旦可以就允许进入飞机的情况。我表明,对于大量乘客N,幂律对乘客数量的依赖关系有所不同,并且预先分组会使登机时间减少,且与预先分组的数量呈幂律关系。