# CU-Boulder Students Solve Tollbooth Question To Place Among Top Winners In Math Modeling Competition

April 7, 2005

A team of three CU-Boulder undergraduate students won a place among the "Outstanding Winners" in the prestigious Mathematical Contest in Modeling by devising a solution to a real-world problem in congested cities -- how many tollbooths does it take to minimize lines and avoid traffic jams?

University of Colorado applied mathematics majors Brad Klingenberg and Pascal Getreuer, with math and physics major Brian Camley, comprised the CU-Boulder team. The team has won the contest two years in a row, making the win CU-Boulder's sixth outstanding paper for the contest in six years.

The international contest is sponsored by the Consortium for Mathematics and its Applications. About 800 teams entered the contest, held in February, and winners were announced last week.

Klingenberg said the team modeled the traffic near a toll plaza with a combination of queuing theory, which predicts the distribution of cars as they form multiple lines, and "cellular automata," or the basic rules used by individual motorists in traffic, to determine the optimum number of toll booths for a given highway.

Their answer: "In the case of a two-lane highway, the optimal number of booths is four; for a three-lane highway, the optimal number is six. For larger numbers of lanes, the result depends on the arrival rate of the traffic."

According to Klingenberg, increasing the number of tollbooths beyond the numbers indicated by the model does nothing to improve traffic flow because motorists will lose time having to merge with additional lanes of traffic as they reenter the highway.

This year's Mathematical Contest in Modeling was held during a 96-hour "marathon" held Feb. 3 through Feb. 7, during which teams worked on one of three open-ended, applied problems. Teams formulated a mathematical model to analyze the problem, drew conclusions and submitted a written report.

Six other student teams -- from Harvard University, Massachusetts Institute of Technology, University of California at Berkeley, Duke University and Rensselaer Polytechnic Institute -- also solved the tollbooth question and were named "Outstanding Winners" in the contest.

A total of 14 Outstanding Winners were named for the three problems, out of about 800 teams that entered the contest.

The CU-Boulder team also was one of two CU-Boulder teams named "Outstanding Winners" in the 2004 contest, after they developed and analyzed a model that assessed the probability that fingerprints are unique. Klingenberg said the team was considered a "dark horse" in that competition because two of the team's three members were freshmen.

"We're absolutely thrilled about winning a second year in a row," Klingenberg said.

Two other CU-Boulder teams received recognition in the 2005 competition. Thomas Josephson, Edmund Lewis and Laura Waterbury received a "Meritorious" designation, while Rachel Danson, Kristopher Tucker and Brandon Booth received an "Honorable Mention."

Faculty adviser Anne Dougherty said CU's strong showing in the contest is a reflection of the strong curriculum offered at CU-Boulder. "We attract excellent students and give them the best possible education," she said.