Statement of Research Problem on Aviation Security

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  • Topic: Probability density function, Access control, Dynamic programming
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A Stochastic Approach to Modeling Aviation Security Problems Using the KNAPSACK Problem

Amy E. Simms

Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Master of Science in Operations Research

Dr. Sheldon H. Jacobson, Co-Chair Dr. John E. Kobza, Co-Chair Dr. C. Patrick Koelling

June 20, 1997 Blacksburg, Virginia

Keywords: Access Control, Airport Security, Knapsack Problem, Probability Theory Copyright 1997, Amy E. Simms

A Stochastic Approach to Modeling Aviation Security Problems Using the KNAPSACK Problem

Amy E. Simms

(ABSTRACT)

Designers, operators, and users of multiple-device, access control security systems are challenged by the false alarm, false clear tradeoff. Given a particular access control security system, and a prespecified false clear standard, there is an optimal (minimal) false alarm rate that can be achieved. The objective of this research is to develop methods that can be used to determine this false alarm rate. Meeting this objective requires knowledge of the joint conditional probability density functions for the security device responses. Two sampling procedures, the static grid estimation procedure and the dynamic grid estimation procedure, are proposed to estimate these functions. The concept of a system response function is introduced and the problem of determining the optimal system response function that minimizes the false alarm rate, while meeting the false clear standard, is formulated as a decision problem and proven to be NP-complete. Two heuristic procedures, the Greedy algorithm and the Dynamic Programming algorithm, are formulated to address this problem. Computational results using simulated security data are reported. These results are compared to analytical results, obtained for a prespecified system response function form. Suggestions for future research are also included.

This research is done as part of the FAA National Center for Excellence in Aviation Operations Research at Virginia Tech. The computational results were obtained with support from the Simulation and Optimization Laboratory in the Department of Industrial and Systems Engineering at Virginia Tech.

ACKNOWLEDGEMENTS I would like to thank Ray Easterling for his infinite patience and unending support. I would have never made it through the past two years without his help. I would also like to thank my parents, Al and Lois Simms and Jim and Jane Sthreshley, for believing in me and for believing that I would graduate someday! I thank my advisors, Dr. Sheldon Jacobson and Dr. John Kobza, for giving me the opportunity to work on this exciting project. I also thank them for the many helpful insights and suggestions that they provided. Additionally, I wish to thank Dr. Patrick Koelling for taking the time to serve on my committee. I thank Ms. Lovedia Cole for her help throughout my tenure in the Industrial and Systems Engineering Department – she is definitely the backbone of this department! Finally, I would like to thank all of the friends that I have made in the ISE department, especially Kelly Sullivan. I will miss our long talks when we were supposed to be working! I will never forget all of the great times that I have had at Virginia Tech.

Contents

1 Introduction 2 Literature Review 2.1 Airport Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 2.1.2 2.1.3 Perimeter Security . . . . . . . . . . . . . . . . . . . . . . . . . . . Access Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detection and Estimation Theory . . . . . . . . . . . . . . . . . . .

1 3 3 3 4 6 7 8 9 13 13 14 14 15 17

2.2 The KNAPSACK Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 2.2.2 Variations of the KNAPSACK Problem . . . . . . . . . . . . . . . . Applications of the KNAPSACK Problem . . . . . . . . . . . . . .

3 Methodology 3.1 Problem...
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