We model and analyze the process of passengers boarding an airplane. We show how the model yields closed-form estimates for the expected boarding time in many cases of interest. Comparison of our computations with previous work, based on discrete event simulations, shows a high degree of agreement. Analysis of the model reveals a clear link between the efficiency of various airline boarding policies and a congestion parameter which is related to interior airplane design parameters, such as distance between rows. In particular, as congestion increases, random boarding becomes more attractive among row based policies.

We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. We then show how such models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental.Airplane boarding is a process experienced daily by millions of passengers worldwide. Airlines have developed various strategies in the hope of shortening boarding time, typically leading to announcements of the form "passengers from rows 40 and above are now welcome to board the plane", often heard around airport terminals. We will show how the airplane boarding process can be asymptotically modeled by spacetime geometry. The discrepancies between the asymptotic analysis and finite population results will be shown to be closely related to random matrix theory (RMT). Previously, airplane boarding has only been analyzed via discrete event simulations [1,2,3].We model the boarding process as follows: Passengers 1, ..., N are represented by coordinates X i = (q i , r i ), where q i is the index of the passenger along the boarding queue (1st, 2nd, 3rd and so on), and r is his/her assigned row number. We rescale (q, r) to [0, 1] × [0, 1]. It is assumed that the main cause of delay in airplane boarding is the time it takes passengers to organize their luggage and seat themselves once they have arrived at their assigned row. The input parameters for our model are:u -Average amount of aisle length occupied by a passenger.w -Distance between successive rows. b -Number of passengers per row. D -Amount of time (delay) it takes a passenger to clear the aisle, once he has arrived at his designated row. p(q, r) -The joint distribution of a passenger's row and queue joining time. p(q, r) is directly affected by the airline policy and the way passengers react to the policy.For the purposes of presentation, we shall assume that u, w, b, D are all fixed. The airplane boarding process produces a natural partial order relation of blocking among passengers. Passenger X blocks passenger Y if it is impossible for passenger Y to reach his assigned row before passenger X (and others blocked by X) has sat down and cleared the aisle. Airplane boarding functions as a peeling process for the partial order defined by the blocking relation. At first, passengers who are not blocked by others sit down; these passengers are the minimal elements under the blocking relation. In the second round, passengers who are not blocked by passengers other than those of the first round are seated, and so forth. Boarding time thus coincides with the size of the longest chain in the partial order.We assign to the boarding process with parameters u, b, w, D, p(q, r) a Lorentz metric defined on the (q, r) unit square bywhere k = bu/w and α(q, r) = 1 r p(q, z)dz. There are two properties of the metric which relate it to the boarding process:• The volume...

Abstract. Consider a committee of experts dealing with dichotomous choice problem, where the correctness probabilities are all greater than 1 2 . We prove that, if a random subcommittee of odd size m is selected randomly, and entrusted to make a decision by majority vote, its probability of deciding correctly increases with m. This includes a result of Ben-Yashar and Paroush (2000), who proved that a random subcommittee of size m ≥ 3 is preferable to a random single expert.

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