Queueing Theory and Terrorism

I found this nice case study of Queueing Theory applied to the problems of terrorism.  In general, the problems of terrorism can be summed-up as a constraint problem, where there is more demand for a thing than there is suppy to meet it.  Couple that dynamic with the fact that people’s lives are at stake, and there are common phenomena present such as wait time, arrival rates, service times, etc.  Queueing Theory is really a fascinating subject, with so many applications.  Yet, many businesses and organizations still don’t understand it or use it.   But, the U.S. government was wise enough to apply Queueing Theory as a response to terrorism.

This article was originally published in Fortune, September 4, 2006.

What if the way we think about homeland security–phone taps, color-coded threat levels, and screeners–is myopic? What if the government could prevent attacks and bolster its disaster-response planning by emulating companies with expertise in flipping burgers or serving their customers faster? Good old-fashioned detective work in Britain recently thwarted planned attacks on airlines. But we can’t stop thinking about ways to prevent or respond to terrorism. By looking at security threats as large operations problems, Lawrence Wein, a professor of management at the Stanford School of Business, thinks we could save thousands of lives.

“Just like McDonald’s has to get hamburgers out in a rapid and defect-free manner, so too does the U.S. government have to get vaccines and antibiotics out or screen the borders for nuclear weapons and terrorists,” says Wein, a soft-spoken 49-year-old academic who until recently specialized in health care and manufacturing. Hearing Wein, an unlikely security wonk, spin out scenarios can be frightening. Whether it’s a few grams of botulinum toxin dropped into an unlocked milk tank or a couple of pounds of anthrax scattered above a crowded metropolis, Wein has spent the past five years developing models that pinpoint with precision the expected number of casualties.

Wein’s work began receiving wide notice in 2003 after he co-wrote a paper detailing the consequences of a large-scale anthrax attack on a big U.S. city. Its conclusions were alarming: Unless government officials drew up far better response plans, some 123,000 people would die.

The results were based on a scenario in which two pounds of weapons-grade anthrax were dropped from 300 feet; they included a series of mathematical models to map the dispersion of the spores, the likely rate of infection, and the progression of the disease in those infected. The series calculated the expected death toll based on a Centers for Disease Control plan to get enough antibiotics to treat the entire affected population into neighborhood centers within four days. There were two obstacles to reducing casualties: Not enough people would be available to distribute antibiotics, and not enough medical personnel would be on hand to treat those who got sick.

Wein says the bottlenecks were classic problems of queueing theory, the mathematical analysis of waiting lines, and a core subject in business school operations classes. They occurred because there were too many customers and not enough people to serve them. Wein found that a 7½-fold increase in distribution capacity would eliminate waiting lines for medicine, which would halve the death toll. So he recommended that the government scrap its distribution plan for antibiotics and use a network that serves every home in America: the U.S. Postal Service. Following publication of the paper, the Postal Service announced plans to distribute antibiotics in Washington, D.C., in case of an anthrax attack there. Wein also found that a further 90% cut in the death toll could be achieved by flying in 8,500 additional doctors and nurses or using military personnel to reduce waiting lines at hospitals.

Wein’s work hasn’t always sat well with officials in Washington. In 2004, Wein presented research to Congress that was sharply critical of the biometric screening process used by the US-VISIT program: a two-fingerprint scan of visitors entering the country to match them against a terrorist watch list. The probability of correctly identifying someone on the watch list with that system was a mere 53%, but with a ten-fingerprint scan, the probability of a match climbed to over 95%. Ensuing criticism from congressional Democrats put the Department of Homeland Security on the defensive. Jim Williams, the director of US-VISIT, says there were flaws in Wein’s work and denies that it influenced the policy. But less than ten months after Wein’s testimony, Homeland Security Secretary Michael Chertoff announced that the program would change to a ten-fingerprint system.