How Long Does It Take to Board an Airplane?
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 \(N \lesssim 500\) and find a good agreement.
The airplane-boarding problem has been discussed by E. Bachmat, S. Erland, V. Frette, J. Kaupužs, and S. Neumann during a meeting at Technical College of Haugesund in August 2016. This work has been completed at Rostock University in October 2017. The authors acknowledge the use of resources provided by the Latvian Grid Infrastructure and High Performance Computing center of Riga Technical University.
- 10.Kaupužs, J., Mahnke, R., Weber, H.: Boarding of finite-size passengers to an airplane. In: Knoop, V.L., Daamen, W. (eds) Traffic and Granular Flow ’15, pp. 597–604, Springer, Cham (2016)Google Scholar
- 11.Mahnke, R., Kaupužs, J., Brics, M.: Air traffic, boarding and scaling exponents. In: Chraibi, M. Boltes, M., Schadschneider, A., Seyfried, A. (eds.) Traffic and Granular Flow ’13, pp. 305–314, Springer, Cham (2015)Google Scholar
- 12.Vershik, A.M., Kerov, C.V.: Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tables. Dokl. Acad. Nauk SSSR 233, 1024 (1977) [Sov. Math. Dokl. 18, 527 (1977)]Google Scholar