research
Pursuit of Happiness Is anybody ever truly happy while driving?
Most commuters suspect not, and a team of Mudd mathematicians has created a model to back them up. Joel Ornstein ’14, Sarah Scheffler ’15 and Ben Lowenstein ’16 offered a “Happiness Corollary” in their solution paper for this year’s Mathematical Contest in Modeling, an international competition that focuses on ingenuity, collaboration and justification of findings. The trio earned a Meritorious result for a model that uses a “driver happiness” metric to gauge the efficiency of the keep-right-except-to-pass traffic rule. They also got some laughs in the process. Unlike most other MCM teams, Ornstein, Scheffler and Lowenstein were only able to collaborate for about half of the allotted four-day window, working around other scholastic obligations when time permitted. This limitation required a novel approach. “We wanted it to be fun more than anything,” says Ornstein. Even with the time crunch, they managed to finish in the top 15 percent of over 6,700 MCM teams. Mathematically speaking, the team defines driver happiness as an average of current speeds minus the desired, or target, speeds for all cars, divided by the number of cars on the road. Since the dividend will always be negative or zero at best—cars will never surpass their target speeds—the quotient will typically be negative, and never more than zero. Meaning? “Happiness can never be positive,” says Lowenstein with a grin. The model works fairly simply. Cars approach a certain target speed, accelerating until reaching this speed or being obstructed by slower vehicles. At this point, any given car moves left one lane if there is room, passes, returns right one lane and continues approaching target speed until slowed again by another vehicle. Sound familiar? “The most you can ask for is to drive the speed you want to,” says Ornstein. “We wanted a metric we could actually have meaningful comparisons between. This measurement was consistent across both sparse and dense traffic.” Data from heavy and light traffic amid two- and three-lane simulations supported conclusive, if unsurprising, results: • Greater speed limits improve driver happiness. • Lower traffic densities improve driver happiness. • Increasing the number of lanes only improves driver happiness in dense traffic flow. One major challenge, says Scheffler, was setting
experimental parameters amid a laundry list of potential variables, including car volume and speed, road conditions, lane numbers and presence of on- or off-ramps. “We immediately thought of a ton of stuff that could affect this,” says Scheffler. Ideally more variables could have been accounted for, she admits. Given time constraints, the team had to make some less-than-realistic assumptions to move forward. Among them: cars accelerate and stop infinitely quickly; roads are straight; car-following distance is never violated. “The assumption was really that cars can never crash,” says Scheffler. Despite this fantasy, says Lowenstein, real-world drivers should take note: Data showed no appreciable evidence that closer car-following distance affected
driver happiness positively or negatively—suggesting tailgating does little, if anything, to enhance the driving experience. “Those results were not statistically significant,” says Lowenstein. He reflects a moment, then laughs. “Probably.” —Eric Feezell
SUMMER 2014
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