Runway Scheduling Using Generalized Dynamic Programming

ly, the runway scheduling problem (RSP) can be thought of as a job shop scheduling problem [11] with precedence and release time constraints, where the objective is to sequence a set of jobs (aircraft) in a particular order to be processed by a processor (runway) so that some cost function is minimized. For the runway scheduling problem, one wants to find an efficient schedule for aircraft to use the runway. The output, then, to the runway scheduling problem is a time for each aircraft to begin using the runway, which will be referred to as a runway schedule. The runway scheduling problem is formally described as follows: Given an ordered set of departure aircraft Qd for each departure queue d, a set of departure aircraft Gg for each gate g of cardinality 1, an ordered set of aircraft Cc for each runway crossing queue c, a set of aircraft Pi that must not use the runway before aircraft i, an earliest time α(i) for aircraft i to reach the runway, and various timing constraints (described below), find the set of non-dominating runway schedule(s) with respect to both delay and throughput. A diagram of a typical problem is shown below in Figure 1. This diagram shows an example airport with one departure runway, a ramp area, and a network of taxiways. Each aircraft on the airport surface waits to use the runway in chain like structures called queues. For this diagram, departure aircraft located within the ramp area are at their gates or gate queues, and departure aircraft near the top left entrance of the departure runway are waiting in departure queues. Finally, there is one taxiway that crosses the runway with a chain of two aircraft waiting cross. These aircraft waiting to cross the runway are said to be waiting in their crossing queue. To be exact, an aircraft aj is indexed by its queue j and with its position denoted by i. The position count starts at 0 from the back of the queue and successively increases for aircraft closer to the front of the queue. In particular, this figure has two departure queues near the top of the runway, with 2 departure aircraft, a0 and a 1 1, in departure queue 1, and 1 departure aircraft, a0, in the departure queue 2. The figure also has 3 departure aircraft, a 3 0, a 4 0, and a0, waiting at their gates (in the ramp area), and 2 aircraft, a 6 0 and a 6 1, waiting to cross the runway. Because aircraft in the same queue cannot simply pull in front of an aircraft waiting ahead of it, there will be precedence constraints between departure aircraft waiting in the same queues. To the same degree, departure aircraft located at the gates must wait to depart until their path is clear. Also since each aircraft i has only one α(i), it is assumed a single path to the runway is provided. Figure 1. Problem Description Based upon the various aircraft moving on the airport surface, a tower controller must figure out how to sequence the aircraft to best utilize the runway. Complicated timing constraints, however, make the task difficult. aA set of non-dominating sequences with respect to throughput and delay are those that are either better at throughput or delay but not both. A formal understanding of this concept is given in section III.D.