Modeling Precheck Parallel Screening Process in the Face of Strategic Applicants with Incomplete Information and Screening Errors

In security check systems, tighter screening processes increase the security level, but also cause more congestion, which could cause longer wait times. Having to deal with more congestion in lines could also cause issues for the screeners. The Transportation Security Administration (TSA) Precheck Program was introduced to create fast lanes in airports with the goal of expediting passengers who the TSA does not deem to be threats. In this lane, the TSA allows passengers to enjoy fewer restrictions in order to speed up the screening time. Motivated by the TSA Precheck Program, we study parallel queueing imperfect screening systems, where the potential normal and adversary participants/applicants decide whether to apply to the Precheck Program or not. The approved participants would be assigned to a faster screening channel based on a screening policy determined by an approver, who balances the concerns of safety of the passengers and congestion of the lines. There exist three types of optimal normal applicant's application strategy, which depend on whether the marginal payoff is negative or positive, or whether the marginal benefit equals the marginal cost. An adversary applicant would not apply when the screening policy is sufficiently large or the number of utilized benefits is sufficiently small. The basic model is extended by considering (1) applicants' parameters to follow different distributions and (2) applicants to have risk levels, where the approver determines the threshold value needed to qualify for Precheck. This article integrates game theory and queueing theory to study the optimal screening policy and provides some insights to imperfect parallel queueing screening systems.