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A theoretical application of transient queueing analysis is provided for military air traffic control. The exact distribution of the nth arriving or departing flight's sojourn time in an M/M/s queue with k flights initially present is reviewed. Algorithms previously developed for computing the covariance between sojourn times for an M/M/1 queue with k ≥ 0 flights present at time zero are provided and utilized. Maple computer code is utilized for practical applications in air traffic control of transient queue analysis for many system measures of performance without regard to traffic intensity (i.e., the system may be unstable with traffic intensity greater than one), thus negating the need for simulation.