Scaling behavior of an airplane-boarding model.
Scaling behavior of an airplane-boarding model.
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DOI：
10.1103/physreve.87.042117
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发表时间：
2013-04
期刊：
影响因子：
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通讯作者：
M. Brics;J. Kaupužs;R. Mahnke
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文献类型：
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作者：
M. Brics;J. Kaupužs;R. Mahnke
研究了Frette和Hemmer [Phys. Rev. E 85，011130（2012）]早期引入的飞机登机模型，目的是精确确定大量乘客N的渐近幂律标度行为。基于对N=2（16）=65536的超大型系统的Monte Carlo模拟数据，我们数值分析了平均登船时间等相关量的标度行为。与临界现象类似，我们使用了适当的缩放Ansätze，其中包括作为N的某个幂的主导项（例如，[比例]N（α）for），以及缩放的幂律修正。我们的结果清楚地表明，α=1/2保持非常高的数值精度（α=0.5001±0.0001）。该值基本上偏离了Frette和Hemmer早先从2≤N≤16范围内的数据获得的α=/~0.69。我们的结果证实了伯恩斯坦所观察到的在大N时有效指数α（eff）（N）收敛到1/2.我们的分析解释了这种效应。也就是说，有效指数α（eff）（N）从小系统尺寸的约0.7的值变化到N→∞时的真实渐近值1/2，对于大N，在N（-1/3）中几乎线性地变化。这意味着这种变化是由定标修正引起的，定标修正的前导指数是θ = 1/3。我们还估计了其他指数：在一个时间步内同时就座的乘客平均数为ν=1/2，t（B）的二阶矩为β=1，方差为γ = 1/3。
An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number of passengers N. Based on Monte Carlo simulation data for very large system sizes up to N=2(16)=65536, we have analyzed numerically the scaling behavior of the mean boarding time and other related quantities. In analogy with critical phenomena, we have used appropriate scaling Ansätze, which include the leading term as some power of N (e.g., [proportionality]N(α) for ), as well as power-law corrections to scaling. Our results clearly show that α=1/2 holds with a very high numerical accuracy (α=0.5001±0.0001). This value deviates essentially from α=/~0.69, obtained earlier by Frette and Hemmer from data within the range 2≤N≤16. Our results confirm the convergence of the effective exponent α(eff)(N) to 1/2 at large N as observed by Bernstein. Our analysis explains this effect. Namely, the effective exponent α(eff)(N) varies from values about 0.7 for small system sizes to the true asymptotic value 1/2 at N→∞ almost linearly in N(-1/3) for large N. This means that the variation is caused by corrections to scaling, the leading correction-to-scaling exponent being θ≈1/3. We have estimated also other exponents: ν=1/2 for the mean number of passengers taking seats simultaneously in one time step, β=1 for the second moment of t(b), and γ≈1/3 for its variance.