MATHEMATICAL AND LOGICAL MODEL OF AIRCRAFT TIMETABLES

Abstract

The article analyses the methods of forming the aircraft flight schedule based on the classical theory of schedules as a theory of multi-stage systems. It is shown that the timetable is a system without interruptions, since each specific flight at a certain point in time is carried out by only one aircraft. In accordance with the theory of schedules, the optimal distribution of a discrete finite set of requirements serviced by deterministic systems with one or more devices is analysed under various assumptions about the nature of their maintenance. It is shown that the weakest assumption regarding the abstract operator, which translates many requirements into many agreed and executed plans, is the monotonic and unimodal behaviour of the corresponding functional of the generated plans. The possibilities of applying the theory of multi-stage systems to create the optimal schedule for medium or large airlines are investigated. The basic requirements for constructing a schedule are advanced. Mathematical models of the schedule are constructed taking into account the basic data of the current movement of aircraft in the area of ​​the airport or air hub. It has been established that if the base airports change their purpose and act as terminal arrival airports, the corresponding matrix elements are inversely symmetric, and with a rarefied spatial distribution of airports, the matrix can tend to diagonally dominant. A comparative analysis of scheduling algorithms is performed (based on queuing models, based on lists with the distribution of flights over time, etc.). The most suitable indicators of the effectiveness of the formation of the optimal schedule and system of priorities were selected and justified, taking into account the advantages of the arrival and departure times of passenger flights. An expression is derived for the resulting functional schedule efficiency, with which you can get quantitative comparative assessments of the quality of the schedule.