Everyday Math. Calculating a Faster Checkout Line - wall street journal article (see images below)by: Eugenia Cheng1) Although the column does not explicitly mention economics concepts relevant to the evaluation of queuing systems, what economics concepts is the column describing?2) How does risk aversion with regard to wait times affect the preference for serpentine or separate line queuing system?3) How does a large penalty for queuing above a certain amount of time, say t, affect the preference for a serpentine or separate line queuing system? I love online grocery shopping-in part because I enjoy buying the same thing every week, in partbecause I don't drive, but mainly because I hate standing in line.When I do get stuck, I often find myself analyzing the way that checkout lines work. We are used to thestandard system of one line for each cashier. But what if there is just one big lane feeding multiplecashiers?How we think about the virtues of these two systems depends in part on psychology, but there's quite abit of mathematics in there too. The math of queuing theory turns out to be satisfyingly counterintuitive.Having one line feeding many checkouts is sometimes called the "serpentine" system: The single queueoften snakes around, as lines do at airport security checkpoints. Mathematical queuing theory says thatthe serpentine system should be faster than separate lines leading to separate cash registers, but onlywith a condition called "no jockeying"-the assumption that people in multiple lines won't hop over to adifferent line that has become free.But that isn't realistic, as we can all attest. If you allow jockeying in multiple lines, the serpentine systemis no faster on average. It might intuitively seem faster because you won't get stuck behind a singleperson taking a long time, but that same delay is just portioned out among more people, leaving theaverage wait time the same.I enjoy doing a small simulation by hand about one problematic customer, and I've found that under bothsystems, the mean wait time-the total of all wait times divided by the number of people-is the same.In a curious twist, one recent study showed that cashiers work faster when they are serving adedicated line.In practice, the average wait time is likely to be longer in the serpentine system. That is because of humandelays: reaction times, walking times, unloading times. In a curious twist, one recent study showed thatcashiers work faster when they are serving a dedicated line. Perhaps it instills a sense of pride orconnection with the customers waiting for one hardworking cashier.Summing up a situation in a single number is useful but crude. Averages are the most familiar way tosummarize data, but they come in different types. Instead of the mean, we could consider the median-the middle number in a list of customers' wait times-in which case multiple lines seem better than aserpentine line. A few people get through very slowly, but more people get through quickly.Still, averages omit information that might be key. For the serpentine lines, I care about a measure calledvariance, which assesses how far the numbers in the set vary from the mean. This can be far greater under the standard system, since an unlucky choice of line can lead to an extra-long wait. The serpentinesystem distributes that risk, which means that there is less variance.I often care more about the variance than any average because I prefer predictability to good averagesover time. That's why I prefer escalators to elevators: An elevator may be faster on average, but I dislikenot knowing how long l'l have to wait for it. Similarly, I like walking (within reason) even if it takes a bitlonger than waiting for a bus or a train.A different principle applies for meeting someone at the airport. I need neither the mean nor thevariance; I need just the minimum time it could take them to wait for their checked bags.When I'm walking to work, I need to know the maximum time my commute can take (if I hit a red light atevery crosswalk). If I'm in a car or a bus, my caleulation is more subtle. The maximum time the trip cantake is almost infinite, since a bad accident could mean a big delay.But that isn't very likely, so I'm more focused on something like the 95th percentile: If the mean journeytime is 30 minutes and the 95th percentile is 45 (that is, 95% of journeys take less time), I'llallow 45minutes to be 95% sure of arriving on time. But l'l add some time for luck, especially if I really need to bepunctual. Sometimes, the only way to be completely certain of being on time is arriving the day before.As for our grocery lines: Life isn't math. Human factors prevent us from knowing which line is the fastest.My best strategy is just not to be in a hurry. I once spent a few weeks trying to pick the slowest lines andused the time to memorize Wordsworth's "Intimations of Immortality." It not only helped me to pass thetime but actually made me want to stand in line longer.

Answer - Part 1 Answer - Need to find- Although the column does not explicitly mention economics…

Answered: Everyday Math. Calculating a Faster…

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC