Team 2053 7of30 Side of plane: left side of plane has priority over right side Row number: Rows in back have priority over those in front After ordering passengers in this manner the following algorithm could be ap- plied to board the plane optimally: While the ideal boarding algorithm may 吕吕吕日吕日吕日日日日 目目目目日目E目目 卣口 □ 2* Began walk i 品日日日日日日日日 。。。□ □ Hayate 4a Begin Walk In Figure 1: This figure demonstrates the operation of the ideal airplane boarding algorithm. Each group of R people is represented by a number corresponding to the order that group ter. Each group proceeds down the aisle until each person reaches their row(since people are in order they all reach their row simultaneously ). They step into the first seat in their row and then begin storing their carry-on baggage. During this time the next group commences walking down the aisle (they won't be getting married though). Notice the only time when a 2 in which case every ait in the aisle for B-2- seconds. This accounts for the additional term in the second part eem an enticing solution to the passenger boarding problem it is far from prad tical as it is unreasonable to expect people to perfectly order themselves and llow strict commands on what actions to perform in the plane(unless of course ou're boarding a company of United State Marines). Instead we will utilize the the ideal boarding algorithm to place a lower bound on the minimum amount of time required to board an airplane of a given size and shape. The formulaTeam 2053 7 of 30 • Side of plane: left side of plane has priority over right side • Row number: Rows in back have priority over those in front After ordering passengers in this manner the following algorithm could be ap￾plied to board the plane optimally: While the ideal boarding algorithm may 1 2 3 4 5 6 7 8 9 n−2 n−1 n 1 1 1 1 Time=0 1 1 1 1 1 1’s Begin Walk In 1 2 3 4 5 6 7 8 9 n−2 n−1 n 1 1 1 1 1 1 1 1 1 1 1 1 Time=R/v 2 2 2 2 2 2 2 2 2 1’s Move Into First Seat, Begin Storing Baggage 2’s Begin Walk In 1 2 3 4 5 6 7 8 9 n−2 n−1 n 1 1 1 1 1 1 1 1 1 1 1 1 T=2R/v 2’s Move In First Seat, Begin 3 3 3 3 3 3 3 3 3 Storing Baggage 2 2 2 2 2 2 2 2 2 2 2 2 3’s Begin Walk In 1 2 3 4 5 6 7 8 9 n−2 n−1 n 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3 T=3R/v or 2R/v+B whichever is longer 1’s Sit Down 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 3’s Move In First Seat, Begin Storing Baggage 4’s Begin Walk In Figure 1: This figure demonstrates the operation of the ideal airplane boarding algorithm. Each group of R people is represented by a number corresponding to the order that groups enter. Each group proceeds down the aisle until each person reaches their row (since people are in order they all reach their row simultaneously). They step into the first seat in their row and then begin storing their carry-on baggage. During this time the next group commences walking down the aisle (they won’t be getting married though). Notice the only time when a group might stall in the aisle is if B is larger than 2R v in which case every other group must wait in the aisle for B-2R seconds. This accounts for the additional term in the second part v of equation (5.1). seem an enticing solution to the passenger boarding problem it is far from prac￾tical as it is unreasonable to expect people to perfectly order themselves and follow strict commands on what actions to perform in the plane (unless of course you’re boarding a company of United State Marines). Instead we will utilize the the ideal boarding algorithm to place a lower bound on the minimum amount of time required to board an airplane of a given size and shape. The formula 7