Team 2053 differently, but also to make well-informed and theoretically-justified recommen- dations to our industry patrons We approached the problem by first mathematically analyzing different factors that contribute to delays in airplane boarding. Mathematical analysis of blocks which prohibit smooth flow was carried out using techniques from stochastic processes We also developed a computer simulation which modeled the airplane boarding process while accounting for different boarding methods and individual variation of passengers. We also used our simulation to learn an ideal boarding proce- dure, which we refer to as Parabola for the parabola-like zone assignments that it uses. We then pitted our boarding scheme against other standard boarding schemes to see how it fared 3 Conventions This section defines the basic terms used in this paper 3.1 Terminology Passenger: A passenger is an individual traveling on the plane who is not part of the crew Boarding Scheme: a boarding scheme refers to an assignments of zones or groups according to which passengers board the plane. Depending on the modeling options, it could be exactly deterministic or the general assignment before random mixings Interference An interference is an in which a passenger cannot progress towards their seat because ther passenger blocking their way. Variables efine the following variables here as they are used widely throughout Additional variables may be defined later, but will be confined to particular section C refers to the number of columns in the plane which is also the number of seats in a row R refers to the number of rows in the plane. For the most part we ignore or treat in a different manner distinctions between classes. for details see section 4Team 2053 4 of 30 differently, but also to make well-informed and theoretically-justified recommen￾dations to our industry patrons. We approached the problem by first mathematically analyzing different factors that contribute to delays in airplane boarding. Mathematical analysis of blocks which prohibit smooth flow was carried out using techniques from stochastic processes. We also developed a computer simulation which modeled the airplane boarding process while accounting for different boarding methods and individual variation of passengers. We also used our simulation to learn an ideal boarding proce￾dure, which we refer to as Parabola for the parabola-like zone assignments that it uses. We then pitted our boarding scheme against other standard boarding schemes to see how it fared. 3 Conventions This section defines the basic terms used in this paper. 3.1 Terminology • Passenger: A passenger is an individual traveling on the plane who is not part of the crew. • Boarding Scheme: A boarding scheme refers to an assignments of zones or groups according to which passengers board the plane. Depending on the modeling assumptions, it could be exactly deterministic or the general assignment before random mixings. • Interference: An interference is an event in which a passenger cannot progress towards their seat because of another passenger blocking their way. 3.2 Variables We will define the following variables here as they are used widely throughout our paper. Additional variables may be defined later, but will be confined to a particular section. • C refers to the number of columns in the plane which is also the number of seats in a row. • R refers to the number of rows in the plane. For the most part we ignore or treat in a different manner distinctions between classes, for details see section 4. 4