OPTIMIZATION OF RUNWAY CAPACITY UTILIZATION IN THE CASE OF GENERAL PARETO CURVE

Abstract

This paper studies an essential application of Air Traffic Management investigating the runway capacity allocation with the aim of pretactical planning in the time scope of approximately 24 hours. For the prediction and solving of traffic problems for such planning horizon we have to control flows of aggregated flights rather than individual flights. Hence, the length of the queue arising from a capacity allocation decision is the main feature of flow management. Related standard key performance indicators such as throughput, delay, etc. depend on occurrence and behavior of arrival and departure queues. We study and investigate properties of weighted queues sum as a function of capacity allocation in the case of general Pareto curve. It results in straightforward and effective O(N2) algorithm giving integer solution for the problem of total weighted queues sum minimization over a time period with arbitrary number of considered time intervals. This integer problem has been solved earlier with the linear programming methods. However, the best complexity of such methods is O(N3.5L) and linear programming solvers based on them give a solution of the problem in a reasonable time for the limited number of considered intervals only. Furthermore, the algorithm developed in this paper constructs an "almost optimal" initial solution depending on the weight of corresponding queues. Significant feature of the initial solution is that it can be easily obtained by hand for an arbitrary number of considered intervals. It is also shown which intervals have to undergo reallocation of capacity in order to achieve an optimal flow. Moreover, the minimal finite solution set which contains an optimal flow for each weight value in the mentioned problem can be easily constructed. The developed algorithm finds 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 an optimal solution of considered problem for the whole day with interval length from 5 to 15 minutes on standard PC in maximal 0.1 seconds.