CU Students Solve Tollbooth Question to Place Among Top Winners In Math Modeling Competition

A team of three CU-Boulder undergraduates has won a place among the “outstanding winners” in the prestigious Mathematical Contest in Modeling for the second consecutive year. The team devised 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, and math and physics major Brian Camley comprised the CU-Boulder team, which wrote CU-Boulder's sixth outstanding paper for the contest in six years.

Brad says 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 Brad, 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.

The 2005 Mathematical Contest in Modeling, sponsored by the Consortium for Mathematics and its Applications, was a 96-hour “marathon” from 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. A total of 14 papers were designated outstanding 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 in the 2004 contest, after developing and analyzing a model that assessed the probability that fingerprints are unique. Brad says 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,” he says.

For more information on the Mathematical Contest in Modeling, contact faculty advisor Anne Dougherty at Anne.Dougherty@colorado.edu or 303-492-4011.

Ashley Moore Aerospace Scholarship Jeff Lyng Building Systems/ Solar Decathlon Brad Klingenberg Applied Mathematics Contest Candace Vaughn Chemical Engineering Co-op Brian Stephens- Hotopp Environmental Engineering Maria Belmonte- Rivas Aerospace Engineering