Nonstationary Queuing Probabilities for Landing Congestion of Aircraft

Abstract

Illustration is made, with reference to a case study of airport landing congestion in the New York area, of how numerical solutions may be easily obtained for the transient behavior of nonstationary waiting lines characterized by Poisson arrivals, constant holding time, and service in order of arrival. In the case study only the mean arrival rate varies as a given function of time, but the methods used as easily provide for variation also of servicing rate and of number of servers. Exact numerical values are sought and obtained only at intervals of the servicing time. While these times were short in the case study, so that little information is sacrificed, the method may be adapted to yield more frequent values in the case of long servicing times. Subject to this restriction, the entire probability distribution of the queue is calculated as the main numerical routine, from which the distribution of waiting time is directly obtained. Use of a stored-program computer is simple, cheap, and especially effective under saturating arrival rates.

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