Dynamic usage of capacity for arrivals and departures in queue minimization

To analyse and solve air traffic problems of an airport in the time scope of, for instance, 24 hours we have to control traffic flows of aggregated flights rather than individual flights. Hence, queue arising from flow management is the unique physical value characterising it. Key performance indicators such as throughput, delay, etc. in some way or another depend on occurrence and behavior of arrival and departure queues. Therefore, we study and investigate properties of weighted queues sum as a function of capacity allocation. It results in straightforward and effective O(N²) algorithms giving integer solution for the problems of weighted queues sum minimization at the end of a time period and total weighted queues sum minimization over a time period with arbitrary number of considered time intervals. These integer problems have been solved earlier with linear programming methods which have the best complexity of O(N^3.5L). Here two initial solutions depending on the weight of corresponding queues are given. It is also shown which intervals are the key intervals for reallocation of capacity in order to reach desired flow variation. Moreover, the minimal finite solution set, which contains an optimal flow for each weight value in the mentioned problems, can be easily constructed. The developed algorithms find optimal solutions in “interval-to-interval” techniques. The obtained solution method gives us the tool for controlling and managing of flow construction and queue outcome depending on strategies we follow. It gives in maximal 0.1 seconds an optimal solution of considered problems for the whole day with interval length from 5 to 15 minutes.