The Aircraft Queueing Problem

Background:

A common procedure at airports is to assign aircraft (A/C) to runways on a first-come-first-served basis. That is, as soon as an A/C is ready to leave the gate ("push back"), the pilot calls ground control and is added to the queue. Suppose that a control tower has access to a fast online database with the following information for each A/C:

• the time it is scheduled for pushback;
• the time it actually pushes back;
• the number of passengers on board;
• the number of passengers who are scheduled to make a connection at the next stop, as well as the time to make that connection;
• and the schedule time of arrival at its next stop.

Assume that there are seven types of A/C with passenger capacities varying from 100 to 400 in steps of 50. Develop and analyze a mathematical model that takes into account both the travelers' and airlines' satisfaction.