Time-dependent Queuing Approaches for Airport Immigration

Standard queuing theory describes only the long-term behavior of a queue. The passenger arrivals at the airport immigration fluctuate significantly during the day. The standard queuing theory cannot be used in this case for predicting the queue lengths. Instead time-dependent queuing approaches need to be applied. The queues and arrivals at the incoming immigration of Narita airport were observed on a single day. The utilization ratios show that the immigration was overloaded during a large part of the observation period. This condition requires the use of queuing approaches that can cope with overload. In this paper a deterministic fluid approximation and an approach based on the numerical integration of the Kolmogorov differential equations are discussed. Both approaches produce similar results and these results are reasonable compared to the observed queues.