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) = 65 536, 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 Ansatze, which include the leading term as some power of N (e.g., alpha N-alpha for < t(b)>), as well as power-law corrections to scaling. Our results clearly show that alpha = 1/2 holds with a very high numerical accuracy (alpha = 0.5001 +/- 0.0001). This value deviates essentially from alpha similar or equal to 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 alpha(eff) (N) to 1/2 at large N as observed by Bernstein. Our analysis explains this effect. Namely, the effective exponent alpha(eff) (N) varies from values about 0.7 for small system sizes to the true asymptotic value 1/2 at N -> infinity 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 theta approximate to 1/3. We have estimated also other exponents: nu = 1/2 for the mean number of passengers taking seats simultaneously in one time step, beta = 1 for the second moment of t(b), and gamma approximate to 1/3 for its variance. DOI: 10.1103/PhysRevE.87.042117