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Scaling behavior of an airplane-boarding model
Martins Brics1, Jevgenijs Kaupužs, Reinhard Mahnke
1Institute of Physics, Rostock University, D-18051 Rostock, Germany. martins.brics2@uni-rostock.de
Summary
This study precisely determines the asymptotic power-law scaling behavior of airplane boarding time using Monte Carlo simulations. The mean boarding time scales with the number of passengers N as N(1/2), correcting previous findings.
Area of Science:
- Statistical Physics
- Complex Systems Modeling
- Computational Physics
Background:
- The airplane-boarding model by Frette and Hemmer (2012) describes passenger flow and seating.
- Previous studies suggested a different power-law scaling for boarding time.
- Understanding asymptotic behavior is crucial for optimizing boarding processes.
Purpose of the Study:
- To precisely determine the asymptotic power-law scaling behavior of the airplane-boarding model.
- To analyze the mean boarding time
- To investigate the influence of corrections to scaling on the observed exponents.
Main Methods:
- Extensive Monte Carlo simulations were performed for system sizes up to N=65536.
- Numerical analysis of simulation data focused on scaling behavior and power-law exponents.
- Scaling Ansätze, including leading terms and power-law corrections, were applied, analogous to critical phenomena.
Main Results:
- The mean boarding time
- This precise value of α=1/2 significantly deviates from the previously reported α≈0.69.
- Corrections to scaling, with a leading exponent θ≈1/3, explain the variation of effective exponents at smaller N.
Conclusions:
- The study confirms the convergence of the effective exponent to 1/2 for large N.
- The findings provide a precise understanding of the asymptotic dynamics of the airplane-boarding model.
- This research offers valuable insights for optimizing passenger flow and reducing boarding times in real-world scenarios.
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