Application of the Queuing Theory in Characterizing and Optimizing the Passenger Flow at the Airport Security

Mengjiao Wang
2017 Journal of Applied Mathematics and Physics  
This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passengers waiting for going through the security. Then, the Poisson distribution is combined with a multiple M/M/s model. Following that, an arrival model (passengers' arriving at the checkpoints preparing for security examination and departure) with Gumbel extreme value estimation is
more » ... alue estimation is described that predicts the busiest time in the busiest airport. Real case data collected from several major airports worldwide is used for creating a hybrid Poisson model to generate the simulation of passenger volume. At last, Markov Chain theory is applied to the analysis to randomly simulate the flow of enplaned passengers again, and the results of these two simulations are compared and discussed, revealing that the hybrid Poisson model is the more accurate one. After successfully characterizing the passenger flow mathematically, two methods for optimizing the passenger flow are then provided in two different respects: one is bypassing passengers and creating an express pass; while the other one promotes Pre-Check service application. model is built to account for the fact that queues may be far away from each other and passenger are not informed to which queue is the shortest. Although Figure 5 shows an illustration of multiple asynchronous M/M/s queue with same queue length, in our simulation or real world, this rarely happens. Hence we choose to imitate passengers' behavior on random basis. We use multinomial distribution to model their decisions, meaning each queue is equally likely for each passenger to join. The multinomial distribution model will be discussed in more details in Section 4.
doi:10.4236/jamp.2017.59134 fatcat:nmry6wdmnzhvdbaespjca7fhzm