Security checkpoints at airports across the United States are essential for preventing passengers with dangerous weapons, explosives, and other threats from boarding airplanes. However, the multiple screening technologies and speeds of passengers lead to unpredictable and sometimes long waiting times. Security agencies and airport managers must find ways to minimize screening times at checkpoints without compromising the security of aviation transportation. This paper introduces an analytic model that derives the distribution of completion times for passengers through a security checkpoint, given its architecture, passenger profiles, and expected service times at checkpoint components. By varying the model's parameters and checkpoint architecture, security agencies and airport managers can quickly understand how the end-to-end completion times of passengers are affected by policy changes and checkpoint reconfigurations. The model can also be used to forecast the performance of future checkpoint architectures that use new components and policies. The authors demonstrate the utility of the model by analyzing a prototypical security checkpoint.