An advanced time-dependent queueing model for airport delay analysis

Abstract

Introduction: In the past several years many attempts have been made to model the probabilistic nature of airport runway operations using a queueing-theoretic approach to runway modeling. Early studies were limited by computational considerations to examination of systems only once they reached "steady state". These models were unable to reflect the characteristic hourly "rises" and "falls" of demand for runway use at major airports. Koopman was the first to include time-varying demand in a queueing model of a runway. He examined simple M(t)/M/l and M(t)/D/1 models with planes awaiting landing or takeoff placed in a single common queue. By using advanced numerical techniques he showed that the airport system equations can be solved recursively through the computer to exhibit the system behavior as a function of time. A later study by Hengsbach and Odoni extended these models to include the case of k independent runways. This study also resulted in a set of computer programs which increased tremendously the computational efficiency of this approach. In this report we explore, for the first time, time-dependent queueing-theoretic models in which landing and departing aircraft are kept in separate queues. This allows explicit acknowledgement of various sequencing strategies by air traffic controllers and computation of separate statistics for delays to landings and to takeoffs. The report is organized into several basic sections. Expanding on an idea introduced by Koopman, we begin with the development of a basic two-queue runway model under time-varying demand. We then present an extended model which more realistically reflects actual airport runway situations. Third, results from an experimental investigation with these models are presented, including comparisons with the earlier single-queue model. Section 4 is a discussion of the expected delay to aircraft in these two-queue systems. Finally, we mention some simple extensions and suggest directions for further study.