Mathematically speaking: wait don’t walk

William Atkins
Thursday, 31 January 2008 18:49

Science - Health

According to three U.S. mathematicians, if you are waiting for something, like a ride on a bus, and its late, keep on waiting rather than walk to the next bus stop.         

Scott D. Kominers, a mathematician at Harvard University (Cambridge, Massachusetts, United States) and his two colleagues, Justin G. Chen and Robert W. Sinnott, decided to find out the age-old question: If I am waiting for something, do I continue to wait or try something different?

In another example, how many times have you been in a slow-moving checkout line at a supermarket or retail store, and wondered whether you should move into another line or stay where you are?

Well, these three mathematicians state that you should take the lazy way out: stay where you are.

They developed a mathematical formula that tells you how long you should wait before trying something different. They found that when both options seem reasonable, you should stay where you are and do nothing but continue waiting.

In fact, the mathematicians state that even if it is frustrating to continue waiting, you are better off doing so.

However, the researchers did find that in extreme cases, their formula breaks down.

For instance, they describe when a bus is over one hour later and two bus stops are only 0.6 mile (one kilometer away) then you are better off walking to the next bus stop as soon as you find that the bus is late. You may reach your destination later the bus, but it will be a lot less frustrating than waiting an hour and then watch the bus pass you as you are walking to the next bus stop.

Their paper, submitted January 1, 2008 but last revised on January 27, “Walk versus Wait: The Lazy Mathematician Wins,” is found at: http://arxiv.org/abs/0801.0297.

Their abstract states, “In this recreational mathematics note, we address a simple, yet instructive question: Justin has to travel a distance of d miles along a bus route. Along this route, there are n bus stops i, each spaced at a distance of d_i from the starting point. At each bus stop, Justin is faced with a choice: to walk or to wait. If he walks on, he can still catch a bus at the next bus stop--but if a bus passes him while he walks, he is almost assured a longer wait.”

They further write, “We model Justin's decision constraint and completely solve the model in a special case. The answer is intuitive: the optimal strategy is the laziest.”