Research for Queuing Theory

This paper reports on some of the mathematical results that the author obtained while seeking to refine the Markov chain models used in air ASW tactical analyses in numerous studies done at CNA. In an effort to take into account the waiting time in each state prior to transition, a non-Markov process was postulated. Subsequent investigation showed the process to be a reformulation of a semi-Markov process.

Air traffic congestion at airports and along major jet routes are the primary sources of concern with the airspace system. This paper describes two related mathematical models to study these problems. The first model is a simulation of en route traffic. It defines a quantity called the congestion index and relates this to the level of air traffic and the level of investment in the airspace system. The second model is a queuing model used to study congestion and average flight delays at points of jet route intersections. The models consider only high altitude IFR flights but allow for parameterization of plane speeds, separation criteria, available jet routes, and airport operations capacity. The models do not look at holding and takeoff patterns around an airport. The intention of the author is to provide a tool that can be used for identifying major sources of air traffic congestion and for evaluating various ways of dealing with the congestion.