Analysis of Airplane Boarding Times

Bachmat, Eitan; Berend, Daniel; Sapir, Luba; Skiena, Steven; Stolyarov, N

doi:10.1287/opre.1080.0630

Cited by 76 publications

(58 citation statements)

References 10 publications

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“…For reasons of comparability to the past and current airline boarding operations, all measured boarding times were linearly extrapolated (based an average of 76%) to a reference seat load factor of 90%. This approach contradicts the fact that the impact of seat load factor for the block boarding strategies (including back-to-front) shows a nonlinear behavior [7,20,33]. To allow a reliable comparison of the field trials with the simulation results, two approaches are used.…”

Section: Airline Trialsmentioning

confidence: 99%

Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Schultz

2018

Aerospace

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Efficient boarding procedures have to consider both operational constraints and the individual passenger behavior. In contrast to the aircraft handling processes of fueling, catering and cleaning, the boarding process is more driven by passengers than by airport or airline operators. This paper delivers a comprehensive set of operational data including classification of boarding times, passenger arrival times, times to store hand luggage, and passenger interactions in the aircraft cabin as a reliable basis for calibrating models for aircraft boarding. In this paper, a microscopic approach is used to model the passenger behavior, where the passenger movement is defined as a one-dimensional, stochastic, and time/space discrete transition process. This model is used to compare measurements from field trials of boarding procedures with simulation results and demonstrates a deviation smaller than 5%.

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Section: Airline Trialsmentioning

confidence: 99%

Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Schultz

2018

Aerospace

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“…Further work on patience sorting was undertaken by Burstein and Lankham [33], [34], [35]. Connections between patience sorting and airplane boarding times were found by Bachmat et al [12], [13] and between patience sorting and disk scheduling by Bachmat [11].…”

Section: Introductionmentioning

confidence: 99%

Increasing and decreasing subsequences and their variants

Stanley¹

2007

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006

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Abstract. We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behavior of the expected value of the length is(w) of the longest increasing subsequence of a permutation w of 1, 2, . . . , n was obtained by Vershik-Kerov and (almost) by Logan-Shepp. The entire limiting distribution of is(w) was then determined by Baik, Deift, and Johansson. These techniques can be applied to other classes of permutations, such as involutions, and are related to the distribution of eigenvalues of elements of the classical groups. A number of generalizations and variations of increasing/decreasing subsequences are discussed, including the theory of pattern avoidance, unimodal and alternating subsequences, and crossings and nestings of matchings and set partitions. Mathematics Subject Classification (2000). Primary 05A05, 05A06; Secondary 60C05.

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“…This causes significantly greater variations in boarding time and makes the error term ∆ D,n much larger, [4]. Nonetheless, rather miraculously the ranking of boarding policies which is produced by the estimate ℓ(C) √ n nearly coincides with the rankings given by very detailed computer simulations of the boarding process, [5,50]. The methods above led to a detailed understanding of back-tofront policies as practiced by many airlines.…”

Section: Problem Solutionsmentioning

confidence: 98%

Discrete spacetime and its applications

Bachmat¹

2008

Contemporary Mathematics

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A discrete spacetime is a random partially ordered set. It is obtained by sampling n points from a compact domain in a spacetime manifold w.r.t. the volume form. The partial order is given by restricting the causal structure on the domain to the sampled points. These objects were introduced by physicists in an attempt to reconcile gravity with quantum mechanics, [40,45,19]. They received very little direct attention in the mathematics literature.Recently, discrete spacetimes have appeared in very diverse applications which are very far removed from their original motivation. In this self-contained survey we will present some results and numerical calculations regarding the asymptotic behavior of these objects. Some of the more basic results are stated as theorems since they are particularly useful in the applications. Numerical calculations are presented with the hope that they will incite some theoretical work, aimed at proving some related assertions. We then present a few of the applications by shamelessly following the pattern of the recent survey paper [21], which describes some related material. We will present a short list of seemingly unrelated problems and show how they fit into the discrete spacetime formalism. While this is a survey paper, it does contain some new material, namely, the statement of theorem 1.3, the (simple) solution to the dimension reconstruction problem, the numerical calculations of figure 2, the connect-the-dots application and the relation between discrete spacetime and the literature on maximal layers. A more comprehensive and extensive treatment of the subject along with full proofs of the basic results will be presented in a forthcoming publication.Our own research relating to discrete spacetime owes much to the constant encouragement which was provided by Percy Deift and it is our sincere pleasure to dedicate this paper to him on the occasion of his 60th birthday.

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Analysis of Airplane Boarding Times

Cited by 76 publications

References 10 publications

Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Field Trial Measurements to Validate a Stochastic Aircraft Boarding Model

Increasing and decreasing subsequences and their variants

Discrete spacetime and its applications

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