The Mathematics of Waiting in Line
From improvements in the efficiency of wait times at call centers, to the performance of personal computers, to the flow of traffic on local highway, Dr. Amber Puha’s research could make a difference in the lives of everyday people.
Puha, a professor of mathematics at California State University San Marcos, has secured a three-year, $180,000 National Science Foundation grant that involves investigating mathematical questions in queueing models, probabilistic models that involve waiting for service in networks affected by randomness. This randomness can include an especially lengthy call from a person on the line with an agent at a call center, or sometimes pronounced differences in the time between calls.
“If you’re trying to determine how much staff you’re going to need at a call center, you could just look at the average call times of customers, but averages don’t tell you the whole story,” Puha said. “With probabilistic modeling, you’re factoring in random events that can happen, allowing you to forecast your staffing needs with a much higher probability of accuracy.”
The same sort of probabilistic modeling is used in computing and traffic management.
Puha, whose research interest has long been in stochastic studies, is launching her latest efforts in a collaborative investigation with National Academy of Science Member Professor Ruth Williams at UCSD, and another with Professor Amy Ward at the USC Marshall School of Business.
“This project entails investigating some mathematical questions that emerge in the behavioral analysis of certain queueing models,” states a study abstract. “Queueing models are probabilistic models that capture the inherent randomness in a variety of modern networks, such as those that arise in customer service systems, computing and telecommunications, as well as transportation and hi-tech manufacturing.”
Ward said she and Puha have recently worked on issues that arise when customers are impatient and will only wait a certain amount of time for service.
“Amber is a very deep thinker,” Ward said. “I have very much valued her ability to go from an unexpected observation to the underlying phenomenon that is responsible. She ensures that there is perfect consistency between the fundamental assumptions that are made, and the conclusions that can eventually be deduced. For me, this is the beauty of math…and that beauty shines through Amber’s intelligence.”
Mathematics, Puha said, is a subject that has always captured her attention.
“I was always good at mathematics and I always enjoyed it,” she said. “In high school it was easy for me and I had fun with the subject.”
It was when she attended nearby MiraCosta College that the Carlsbad High School graduate found her calling.
“It’s where I really committed to becoming a math major,” Puha said.
Her decision to earn a doctorate in the subject came after transferring to UCSD and taking a probability course with Professor Ruth Williams, whom she worked with on a simulated annealing research project. Williams has been a mentor, collaborator and friend since.
Past and present students give her good grades.
“Dr. Puha is a brilliant educator,” said mathematics major Trevor Ryback, who is in the CSUSM Learning Assistant Program, which provides math and science majors with a structured introduction to teaching. “She always has positive energy and is passionate about the material which I believe results in a more enriching experience. She attends to the needs of the classroom as well as the individual. She’s always trying to get a sense of what her students are thinking and feeling which shows that she's empathetic. She tries to relate the mathematics to real life applications as much as she can and she's good at talking about the conceptual understanding in relation to the formulas.”
Besides leaving her mark as one of the top mathematics professors in the region, Puha also is leaving an impression as faculty advisor for the CSUSM surf team, which won the college national championship in 2009. She also won three National Scholastic Surfing Association Collegiate titles while a student earning her baccalaureate at UCSD and her doctorate at UCLA.
“I could have gone pro but I knew academics were more important,” Puha said in a 1997 article published in the Daily Bruin. “A career in academics is much more satisfying to me, but I will always surf.”
And despite being a prolific researcher, she will always teach, too.
“I very much love teaching and my involvement with students, and I see myself staying in the classroom my entire career. I really find it exciting to see how mathematics can make a positive difference in the lives my students.”