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How Long Does It Take to Board an Airplane?

In: Traffic and Granular Flow '17

Author

Listed:
  • Jevgenijs Kaupužs

    (Institute of Technical Physics, Riga Technical University, Faculty of Materials Science and Applied Chemistry
    University of Liepaja, Institute of Mathematical Sciences and Information Technologies)

  • Reinhard Mahnke

    (Rostock University, Institute of Physics)

  • Eitan Bachmat

    (Ben-Gurion University, Department of Computer Science)

  • Vidar Frette

    (Stord/Haugesund College, Department of Engineering)

Abstract

A simple airplane-boarding model, introduced earlier by Frette and Hemmer, is considered. In this model, N passengers have reserved seats, but enter the airplane in arbitrary order. We are looking for an analytical expression, which describes the mean boarding time depending on the total number of passengers N. For this purpose, we first determine precise values of the exponents and expansion coefficients in the asymptotic expression at N →∞. It is reached by mathematical calculations and fitting the Monte Carlo simulation data for very large N, up to N ∼ 6 ⋅ 108. Finally, we compare the obtained analytical approximation to the simulation data for a realistic number of passengers N ≲ 500 $$N \lesssim 500$$ and find a good agreement.

Suggested Citation

  • Jevgenijs Kaupužs & Reinhard Mahnke & Eitan Bachmat & Vidar Frette, 2019. "How Long Does It Take to Board an Airplane?," Springer Books, in: Samer H. Hamdar (ed.), Traffic and Granular Flow '17, pages 415-421, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-11440-4_45
    DOI: 10.1007/978-3-030-11440-4_45
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