Motivated by the NEXUS program between the US-Canada border, we consider a security screening process where travelers such as cars and trucks are assigned to a selectee or nonselectee lane depending on whether their threat values exceed a threshold level. The goal is to design a two-tier system to maximize the probability of detecting a threat subject to the waiting time and operating cost constraints. We formulate the problem as an optimization program, in which the objective function and some variables can be estimated only by simulation. We then develop algorithms to compute the global optimum, within a proposed bounding region, for the Markovian and non-Markovian systems, respectively. The convergence analysis and extensive numerical results are provided to demonstrate the algorithms' promising performance.
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