Air-Terminal Queues under Time-Dependent Conditions

The queues formed by aircraft in stacks awaiting landing clearance have usually been treated either by machine simulation, or analytically as stochastic processes with time-independent transition probabilities (possessing stationary solutions). In contrast to such methods, the present paper regards the queue-developing process in question as strongly time-dependent, often with a diurnal (24-hour) periodicity. The formulation and treatment are entirely analytic and make use of machines only to solve the equations for the probabilities, by economical deterministic steps, using the coefficients as given in tabular form. Time-varying Poisson arrivals are assumed, and also an upper limit to queue length. Two laws of servicing are used: Poisson and fixed service time; these extremes are found to lead to numerically close results in the realistic case. This situation contrasts with the much cruder approximation of deterministic flow models. The stochastic equations belong to well studied types of differential or...