The design of aviation security systems has become increasingly important over the past decade. Passenger screening is a critical aspect of aviation security systems that employs trained personnel to operate screening devices that are designed to detect various threat objects. Several security classes can be defined with each class containing a subset of these screening devices, and in which each passenger is assigned to exactly one security class based on their perceived risk level. This paper introduces a real-time sequential binary passenger assignment model as a discrete-time difference equation. The stochastic value of the binary passenger assignment is replaced by a deterministic value capturing a fractional class assignment of each passenger. Through a probabilistic analysis, a closed-loop policy is presented to achieve desired security class occupancies for a finite set of passengers anticipated to undergo screening during a given time period, while maximizing the overall system security. The same closed-loop policy is also shown by applying feedback linearization to the fractional passenger assignment model. Closed-loop stability and convergence properties are discussed for a time-variant state feedback design. Simulation results are reported to illustrate sensitivity to parameter variation, and to demonstrate the effectiveness of control theory as an approximation to an otherwise computationally intractable dynamic programming problem. The key contribution is that passenger assignments to security classes can be performed in real time using the methodology introduced.