Modeling Security-Check Queues

  • Authors:

  • Zhe George Zhang;Hsing Paul Luh;Chia-Hung Wang

  • Affiliations:

  • School of Management, Lanzhou University, Lanzhou, 730000 Gansu, People's Republic of China/ Beedie School of Business, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada/ and Coll ...;Department of Mathematical Sciences, National Chengchi University, Taipei, 11605 Taiwan, Republic of China;Department of Mathematical Sciences, National Chengchi University, Taipei, 11605 Taiwan, Republic of China

  • Venue:
  • Management Science
  • Year:
  • 2011

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Abstract

Motivated by the waiting lines between the U.S.--Canadian border crossings, we investigate a security-check system with both security and customer service goals. In such a system, every customer has to be inspected by the first-stage inspector, but only a proportion of customers need to go through the second stage for further inspection. This “further inspection proportion,” affecting both security screening and the system congestion, becomes a key decision variable for the security-check system. Using a stylized two-stage queueing model, we established the convexity of the expected waiting cost function. With such a property, the optimal further inspection proportion can be determined to achieve the balance of the two goals and the service capacities can be classified into “security-favorable,” “security-unfavorable,” or “security-infeasible” categories. A specific capacity category implies if the security and customer service goals are consistent or in conflict. In addition, we have verified that the properties discovered in the stylized model also hold approximately in a more general multiserver setting. Numerical results are presented to demonstrate the accuracy and robustness of the approximations and the practical value of the model. This paper was accepted by Assaf Zeevi, stochastic models and simulation.