Stability of spatially distributed, intersecting aircraft flows under sequential conflict resolution schemes

This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random flow geometry is considered to determine airspace stability in a more random airspace, where aircraft flows are spread over a given positive width. The use of this aircraft flow model generalizes the orthogonal flow geometry for arbitrary flow width. A set of upper bounds on the maximal aircraft deviation during conflict resolution is derived. Also with this flow geometry it is proven that these bounds are not symmetric, unlike the symmetric bounds derived in previous papers for simpler flow configurations (i.e. orthogonal flow geometry). Stability is preserved under sequential conflict resolution algorithms for all flow geometries discussed in this paper.

I. Introduction

The current use of centralized air traffic control to ensure aircraft separation is a safe option that has been proven over the years. The process of control is typically through the use of surveillance radars, voice radio systems, limited computer support systems, and numerous complex procedures [1]. With current air traffic control techniques, increasing air traffic volume steadily increases complexity [2] and produces drawbacks such as: system bottlenecks, indirect routing, and lack of navigation freedom for airlines [3], [4], not to mention the increased workload of the ground controllers [5]. The Federal Aviation Administration (FAA) and airlines have proposed the concept of “Free Flight” [6] to eliminate restrictions imposed by the current system and allow for more navigation freedom as well as direct routing. The US is further developing NextGen (Next Generation Air Transportation System) to address the challenges of increasing air traffic volume as well as limitations on operational flexibility [1], [7]. Europe is also further developing SESAR (Single European Sky Air-traffic-management Research program) to address growing problems with their current air traffic operations [8].