OPTIMAL TRAFFIC MANAGEMENT FOR AIRCRAFT APPROACHING THE AERODROME LANDING AREA - I. B. Ivenin; A. S. Kurilenok (Научный вестник МГТУ ГА, 2018)
The research proposes a mathematical optimization approach of arriving aircraft traffic at the aerodrome zone. The airfield having two parallel runways, capable of operating independently of each other, is modeled. The incoming traffic of aircraft is described by a Poisson flow of random events. The arriving aircraft are distributed by the air traffic controller between two runways. There is one approach flight path for each runway. Both approach paths have a common starting point. Each approach path has a different length. The approach trajectories do not overlap. For each of the two approach procedures, the air traffic controller sets the average speed of the aircraft. The given model of airfield and airfield zone is considered as the two-channel system of mass service with refusals in service. Each of the two servicing units includes an approach trajectory, a glide path and a runway. The servicing unit can be in one of two states – free and busy. The probabilities of the states of the servicing units are described by the Kolmogorov system of differential equations. The number of refusals in service on the simulated time interval is used as criterion for assessment of mass service system quality of functioning. This quality of functioning criterion is described by an integral functional. The functions describing the distribution of aircraft flows between the runways, as well as the functions describing the average speed of the aircraft, are control parameters. The optimization problem consists in finding such values of the control parameters for which the value of the criterion functional is minimal. To solve the formulated optimization problem, the L.S. Pontryagin maximum principle is applied. The form of the Hamiltonian function and the conjugate system of differential equations is given. The structure of optimal control has been studied for two different cases of restrictions on the control of the distribution of incoming aircraft traffic. The regularities of the control parameters influence on the value of the functional criterion are revealed.