title: Scaling behavior of an airplane-boarding model.
abstract: 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 <t(b)> 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 <t(b)>), 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.
authors.affiliation: Institute of Physics, Rostock University, D-18051 Rostock, Germany. martins.brics2@uni-rostock.de
authors.forename: Martins
authors.initials: M
authors.lastname: Brics
authors.forename: Jevgenijs
authors.initials: J
authors.lastname: Kaupužs
authors.forename: Reinhard
authors.initials: R
authors.lastname: Mahnke