A Matrix-Analytic Method for Evaluating Performance of Security-Check System with Two-Type Inspection Queues

the significant increasing of terrorist attacks, the homeland security has become more and more important, but the enhanced security-check process has caused serious impacts on the transportation delay and inconvenience for passengers. This paper studies two types of inspection channels in a security-check system, which is formulated as a queueing model with a state-dependent Quasi-Birth-and-Death (QBD) process. A matrix-analytic method is proposed in the paper to determine the steady-state probability for the studied security-check queueing system. We also develop a solving algorithm for computing the average queue length and waiting time by applying the embedded Markov chain. The presented computing method and queueing analysis could be applied in evaluating the system performance of security checkpoints.