Scaling behavior of an airplane-boarding model.

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.