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Queue inference from periodic reporting data
Operations Research Letters
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This article presents the first models developed specifically for understanding the infiltration and interdiction of ongoing terror plots by undercover intelligence agents, and does so via novel application of ideas from queueing theory and Markov population processes. The resulting “terror queue” models predict the number of undetected terror threats in an area from agent activity/utilization data, and also estimate the rate with which such threats can be detected and interdicted. The models treat terror plots as customers and intelligence agents as servers. Agents spend all of their time either detecting and infiltrating new terror plots (in which case they are “available”), or interdicting already detected terror plots (in which case they are “busy”). Initially we examine a Markov model assuming that intelligence agents, while unable to detect all plots, never err by falsely detecting fake plots. While this model can be solved numerically, a simpler Ornstein-Uhlenbeck diffusion approximation yields some results in closed form while providing nearly identical numerical performance. The transient behavior of the terror queue model is discussed briefly along with a sample sensitivity analysis to study how model predictions compare to simulated results when using estimated versus known terror plot arrival rates. The diffusion model is then extended to allow for the false detection of fake plots. Such false detection is a real feature of counterterror intelligence given that intelligence agents or informants can make mistakes, as well as the proclivity of terrorists to deliberately broadcast false information. The false detection model is illustrated using suicide bombing data from Israel.