By Laura Hancock
Media and publications writer
lhancock@eou.edu
La Grande, Oregon – What is the optimal number of tollbooths for a heavily traveled, multi-lane highway? If a dam is breached by a massive earthquake and a flood sweeps through an area, how much damage will occur?
Two teams from Eastern Oregon University joined students from across the globe in tackling these real-life questions for the annual Mathematical Contest in Modeling in February sponsored by the Consortium for Mathematics and its Applications (COMAP).
Dr. Anthony Tovar, associate professor of physics, and Dr. David Allen, professor of mathematics, served as advisors for the EOU teams.
“The COMAP competition is a tremendous resource that promotes undergraduate applied mathematics education throughout the entire world,” said Allen.
Once the math problems are posted to the COMAP web site, the competition begins. Every team starts at the same time, which means the contest begins at 3 a.m. for some, 5 p.m. for others. Both EOU teams chose to answer the tollbooth question. Allen and Tovar taught classes the previous term introducing students to the concepts of math modeling, which they said was a big help. Students put what they learned in class to work for them in the competition.
After ninety-hours of relentless research and hard work, the teams were ready to submit their answers for review by a panel of math professors who rank the solutions into five categories: Successful Participant, Honorable Mention, Meritorious and Outstanding. Each team came to a different conclusion.
EOU senior Jason Vielma, of the physics team, created a controlled computer simulation of a four-lane highway utilizing four tollbooths. After incorporating a random flow of traffic, Vielma and teammates Zach Goude and Vojislav Petrovic, concluded that eight tollbooths would be the optimal solution.
Dr. Tovar’s team received a Meritorious standing, placing the physics team in top 15 percent of the competition with schools like Duke University, the University of Washington, and Cornell University.
“The students had several models to work from. They started with the simplest model, and made it more and more advanced,” said Tovar. “I think this is why our team was so successful. Placing in the top 15 percent in the world is pretty good for a small university.”
Only 124 other teams received a meritorious standing for their participation. Tovar and his physics team are very proud of their accomplishment.
“We knew exactly what to expect, but there are always struggles” said physics team member Petrovic, a senior. “You can’t panic. What made a difference was the prep course. It let us into the minds of the judges.”
Petrovic and Vielma both took the mathematical modeling course, and learned how to simulate math problems that would be difficult to solve by hand.
Dr. Allen’s team was named a Successful Participant, ranking them below the top 44 percent of the competition with schools like Idaho State University, Lewis and Clark College and others. The experience was rewarding, but exhausting for all of the participants.
"It was really intense,” said math team member Ishane Bikri, a junior at EOU. Bikri and fellow team member Ivan Simeonov, a sophomore, ended up staying on campus for the majority of the four-day competition, working through the night.
“The tollbooth question could take over a year to solve for a real application. We had to solve it in 90-hours,” said Bikri.
Using the queuing theory, math team members Bikri, Simeonov, and Vincent Whitmore came to the following open-ended solution to the tollbooth question: If the arrival rate is less than the service rate of a tollbooth plaza, traffic congestion will not pose a problem. However, if the arrival rate exceeds the service rate, more tollbooths must be opened until the problem of the resulting congestion is equalized.
“This is a marathon!” said Allen. “There are many smart and hard working students at EOU, and hard work is 90 percent of success.”
The hardest part of the competition came on the final day when the teams were faced with writing an abstract summarizing their conclusion. The COMAP judges take one brief look at the abstract, and if it does not meet a specific standard, the entire entry gets tossed aside. Allen feels that his students worked well together as a team, and he is lookig forward to the competition next year.
“Sometimes lighting strikes,” said Allen, “and it did with Tony’s team.”
Eastern Oregon University
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