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July 04, 2022

Murphy's Law: Queuing

By John Trindle

We're always stuck in the slowest line. It's a truism, and it may be the truth. There are two factors to this almost universal human experience (as with any other phenomenon); The Perception, and the Reality. Let's take the Reality first.

We present for your approval a hypothetical grocery store, with three active checkouts run by Abel, Brenda, and Charlie. Abel can handle one customer per minute, Brenda one customer every two minutes, and Charlie (who is a trainee) takes three minutes for each customer.

In an ideal world, every six minutes Abel would process six people, Brenda three, and Charlie two. Will they? Can they? Which line would you get in?

Generally, we base our line selection decision on the physical length of the line. Let's say that, for whatever reason, there are now 6 people in Abel's line, 4 in Brenda's, and only three in Charlie's. You get to the front of the store. Which line do you chose?

Almost all of us would go to Charlie's line, unless we had prior experience with his particular talents (unlikely, he's a trainee) or he had a flashing light on his lane. A few of us, noticing a flashing light or the trainee badge, would chose Brenda's only slightly longer line. Almost none of us would chose Abel, unless we were intimately familiar with the threesome's relative skills.

However, if we do the math, we'll see there's an expected delay of 6 minutes in Abel's line, 8 in Brenda's, and 9 in Charlie's. We'll get waited on 3 minutes sooner if we pick the longest, instead of the shortest line. In fact, we'll leave the store after 7 minutes in Abel's line, and after 12 in Charlie's!

It gets worse, you know. Obviously things don't go smoothly for a cashier. Each customer has a different number of items, and can present special problems such as coupons or price checks. If the a cashier gets blocked, eventually his customers will get impatient and switch lines. This motivation exists whether the blocked cashier is, on average, fast or slow. We'll look around for a shorter line, and join it, tending to equalize the line lengths. We usually can't tell if a line is faster, versus physically shorter, by quick observation.

What if the lines are all equal, say 4 in each? We will randomly choose Abel, Brenda, or Charlie. If we chose Abel, we'll spend 4 minutes thinking about the fact we're in line; Brenda, 8 minutes, and Charlie; 12 minutes. Assuming we see this same situation every time we go to the store, and randomly pick a line each time, we're spending 50% of our time thinking about how awful it is to be in the slowest line!

Now on to Perception. Humans tend to notice certain things and not others. It's an outgrowth of our hardwired instincts that allowed us to quickly analyze predator/prey situations in the wild. In this example, we are far more likely to notice a line moving faster than ours (a desirable prey), than one moving slower. This draws our attention to the speed of the line in general.

If we randomly choose Abel's line, there are no lines moving faster than ours, and we are much less likely to notice the speed. We will sail through the line, oblivious, and continue with our day.

If we randomly choose Brenda's line, we may very well notice Abel's line moving faster, especially if there is someone attractive in that line. We will then pay attention to the fact that our line is slower than theirs. We may not, however, notice that Charlie's line is at a relative standstill. We are more likely to spend our 8 minutes thinking about our fate than be in the oblivious state likely in Abel's fast line. We may even arrive at the false perception that we are indeed in the slowest line.

If we randomly choose Charlie's line, you can see that we are sure to notice all the other lines are beating us out. In fact, we may notice we're waiting for four minutes after our counterparts in the other two lines have been served. We are definitely upset, and will remember the experience.

Admittedly, these numbers are contrived. It is likely that no cashier is more than twice as fast as the slowest one, on average. However, when you add the fact that we are more likely to remember the slow lines rather than the fast ones, it is no wonder that Murphy's Law of Queuing is nearly universally experienced.

Solution? There is no way to evaluate the speed of a line from a quick glance. If we had line delay readouts, perhaps we could make a more informed decision. This device would measure the number of people in the line, and the average processing time per over the last (say) 10 minutes. A nifty gadget, but....

You've probably seen the real solution, at the bank, or at the book store. A single queue is farmed out to multiple cashiers, so each customer has an approximately equal wait. The faster cashiers handle more customers automatically. Everybody's happy.

Sadly, this is prohibitively expensive in terms of floor space if each customer is also pushing a bulky cart. In addition, there's no place for the customer to load their merchandise for cashiering (like the conveyor belt in a conventional grocery checkout) prior to being served. The single queue solution is viable only for small numbers of small items, which can be comfortably held by the customer while in line.

The super stores such as Target and Wal-Mart have a compromise solution. A queue will be formed for a set of two or three registers, so that if one is blocked, customers can spill into the next. I was astonished the first time I saw such an arrangement, and continued to view it as excessive, until I shopped at Wal-Mart during the Christmas season. Then, it seemed inadequate.

Next time you are stalled in line at the grocery store, use the time to your best advantage. Look at the number of people in each line, and at the contents of their baskets, as you probably do already. This time, though, to make your experience more productive, look at the customers themselves, and at the cashiers. Note any clues which might slow or speed their interaction, such as grumpy attitude, checkbooks or coupons deployed versus pre-counted cash or a debit/credit card, trainee badges or inebriation. These clues may speed your future experiences in retail.

Article © John Trindle. All rights reserved.
Published on 2003-05-05
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