Why is it that the other goods are faster than theirs?

Usually when you go to the supermarket, after you get the items you need to buy, when you go to the checkout counter, you always choose the counter with the fastest people. But then you quickly realize that you made the wrong choice when you see the goods next to those who have queued up after you but are paid and left before you. This happens very often. Why so?

According to Wired, when you have to choose between the queues at the supermarket, that choice often doesn't make you satisfied, most likely, the other party is actually faster. Mathematicians specializing in queuing behavior , also known as queuing theory , used numerical sequences to prove this phenomenon. Their model is also the basis for current problems, including traffic engineering, plant design, Internet infrastructure. At the same time, queuing theory also brings a fairer way when paying at the store. The only problem here is that many people don't like it.

Before going into the supermarket situation, let's go to a location, which is the telephone exchange in Copenhagen, Denmark. In the early 1900s, a young engineer named Agner Krarup Erlang sought to calculate the optimal phone lines for telephone exchanges in the city of Copenhagen. At that time, when you wanted to make a call, one had to plug the jack into an electrical circuit that led to the switchboard.

The delay may also be caused by a number of special customers or items that have problems.

In order to save labor and infrastructure, Erlang wants to know exactly the minimum number of lines needed for all calls to be connected. For small and inexpensive switchboards, one single line is only equipped and customers have to queue for a long time before their calls are connected. So a single line for thousands of people in the city cannot be a long-term way.

Take a simple example, if the Copenhagen switchboard has to handle an average of 2 calls per hour, you think that just 2 lines is enough. But this is completely different from the fact that at peak hours, a lot of people want to call at the same time. Suppose at the peak hour, the switchboard must receive at the same time 5 requests for connection but because there are only 2 lines for 2 requests, the remaining 3 requests will have to wait. And if those customers like to chat, the call may last 1 hour, meaning that more requests will be connected to the call, gradually making the whole system over download.

Therefore, Erlang devised an equation to calculate the average number of calls in a given hour and the average duration of each call. Applying that equation to the simple example above, the Copenhagen telephone switch knows they need to equip 7 lines so that 99% of calls will be immediately connected. In 1909, Erlang published his initiative and gave birth to a new aspect of mathematics called "Queuing Theory."

Today, Queue Theory is used in many places. For example, telephone exchanges often use this theory to handle all customer problems. The most common basics will be solved by the lower qualified employees that occupy the majority. More complex issues will be assigned to a handful of more properly trained employees. To determine the number of each employee type, the switchboard can use Erlang's equation or random number method.

Queue model.

Back in the supermarket situation where some people get paid and leave before you, the queuing theory explains why you can't seem to choose the fastest goods. Supermarkets try to equip enough cash registers to serve customers in the shortest time, but sometimes, on weekends, all checkout counters are overloaded and additional construction Cashier counters are an impossible option. At the same time, delays can also be caused by some special customers or items that have problems . All of which cause waiting for those who are queuing behind.

If a supermarket has 3 payment counters, delays may occur randomly at each different counter. Think about the probability of a delay at each counter. The probability that the item you choose to charge is the fastest one is 1/3. This means that you have two thirds of opportunities that are not ranked in the fastest line. Therefore, the likelihood of you choosing the wrong product may be higher. In other words, it's not just your feelings but really, you can't choose the fastest.

The theory of queuing will give you the best solution to this problem: Just all customers stand in a kink and the first person in the line will be served by a cashier. So if we have 3 cashiers, this method will be 3 times faster than the traditional independent 3-row method. This is a method commonly used in some hospitals, large play centers, banks, fast food outlets. With a folded row , a delay in a cash register will not affect other people waiting in the line and only slow down a row.

So why don't almost every place use the folding method? Here, the problem depends on the psychological factors of customers. Human psychology often thinks that each person must be in control of his own life and if there is an opportunity, they can break the principle. In addition, the researchers have shown that there will be cases where people in the row are likely to hinder making queuing time longer than traditional.

Not just your feeling but really, you can hardly choose the fastest goods.

Today, queuing theory has grown beyond a mathematical model and incorporates psychological aspects to ease the wait of queuing. This is also the reason why outside some elevators often have mirrors extending from the floor to the ceiling to reduce boredom while waiting for the next turn. Queuing at game parks like Disneyland can enjoy some kind of entertainment such as changing the background, video projection screen, performing tasks when crossing rooms, making visitors feel less difficult. I had to wait 2 hours to play a roller coaster for 5 minutes. Currently, the waiting issue is also partly solved by mobile devices. People can kill time by reading news, playing games, surfing facebook, etc. while waiting.

To prove that the most sensible choice is not always the best choice , Dr. Richard Larson of the Massachusetts Institute of Technology (MIT) has a very interesting example. During a seminar, Dr. Larson said that the corridor at a hotel was congested due to the use of queuing theory for customers booking rooms. Mathematicians have used their knowledge and proposed a solution to create a folded queue to handle customers.

However, Dr. Larson said: "The corridor is not designed to line up and if that happens, it will create a very chaotic scene. In addition, the hotel manager will not In this case, we should put it into 6 rows as traditional, though somewhat unfair, but it will look better and less messy. "