Queueing Models for Trajectory-Based Aircraft Operations

This paper develops a queueing model for aircraft arrivals at a single server under trajectory-based flight operations, which are expected to prevail in the Next Generation Air Transportation System. Aircraft are assigned scheduled times of arrival at a server, which they meet with some normally distributed stochastic error. The Clark approximation method is employed to estimate expected queueing delays, and it is shown, through comparison with simulation, that the method yields very accurate estimates. Exact results are derived for a special case in which aircraft are metered into a capacity-constrained area with constant excess time separation between them. This allows analysis of the tradeoff between the "stochastic delay" that results from imperfect adherence to metered times of arrival and the additional "deterministic delay" from metering at a headway above the minimum required.