The scenario is always the same: you enter the shop, choose the things you want to buy and stop in front of the cashiers, preferably in a point where you have a wider view. You have a quick look at the length of the lines and the shopping carts. If possible, you try to also to calculate the speed with which the cashier passes the objects on the optical drive. Then you choose the line that seems faster. But just in the queue, you realize that you have chosen badly, other lines seem to flow faster. It’s not right! Why does it happens always this?
Why the line you choose is always the slowest?
If you always think that you have chosen the slower line, there are only two possible explanations: the universe conspires against you or is there a psychological prejudice, that is, a misperception.
Our ability to think in terms of cause and effect plays an important role. In fact, it is an ancestral heritage, our ancestors had to learn to distinguish quickly a particular malicious food or clouds arranged in a certain way announcing a thunderstorm, in order to survive. Therefore, it is normal that sometimes we take the decisions automatically without thinking. We decide basing on experience and intuition. This is an excellent strategy when you don’t have enough time to think and make the proper calculations, but often these decisions have a side effect: lead us to make incorrect predictions.
One of these errors is called “illusory correlation”, a phenomenon by what two things seem to be associated, when in fact they are not. In many cases, our stereotypes or expectations are what lead us to make those connections. In the case of cashiers’ lines, the problem lies in the egocentric perspective that we take; that is, when our row flows we ignore that we are advancing, but when it stops, we look immediately at other lane and we complain about our bad luck.
Therefore, even if sometimes it is true that other lines are moving faster, it is statistically impossible that our is always the slowest, it is simply a perception based on our tendency to remember negative events (the other times we stuck in the queue), obviating the positive facts (whn our line was faster).
Nevertheless, mathematics has good news for all those who want to choose the fastest line.
The thorny question of lines
To understand the mechanism of the lines, we must go back in time, in Copenhagen in the early 1900. At that time, a young engineer named Agner Krarup Erlang was trying to find the optimal number of telephone lines for the switchboard of the city, since then operators were people connecting telephone calls by inserting a connector into a circuit.
To save manpower and infrastructure, Erlang wanted to determine what was the minimum number of lines required to ensure that all calls could be connected. For example, if the distribution board in Copenhagen had to handle an average of two calls per hour two lines were enough, but the problem was that there were times when calls were more and other times where less.
Therefore, during peak hours, the switchboard could receive five requests for connections, which would have meant having always three customers waiting. In addition, if the first two people spent much time on the phone the other should have wait very long.
Thus, Erlang created an equation in which not only took into account the average number of calls per hour, but also the average time of duration of the same. Then came to light what is known as the “queuing theory”.
Today his equation still applies, even in stores. Supermarkets calculate the optimum number of active cashiers to offer the fastest possible service. However, on certain days and at certain hours, the system becomes saturated.
A good solution is to use unique lines, so that customers are distributed for each of the cashier, as it happens in airports. However, these queues have two problems: first, they need more space and secondly, have a strong psychological impact because a row of these dimensions can stop from buying.
The faster queue is the one with the most filled shopping carts
The mathematician Dan Meyer took seriously the problem of queues and analyzed deeply the issue. There he found that in a large supermarket, each cashier takes on average 41 seconds with each customer, while each product purchased takes about 3 seconds.
These researchers suggest that the number of products is a “variable component”, while the “fixed component” are social interactions, the time that the cashier dedicated to every person, which includes the time of payment and greeting, as well as to free up the space.
For example, a person with 100 articles requires an average of 6 minutes. But if you are in a row of 4 people and each one has 20 items, it will take an average of seven minutes to reach the cashier.
This is because when you choose a row in which there are many people with few items, the “fixed component” increases considerably, which results in a longer waiting time. Conversely, if you choose a row in which there are few people with full carts, you can move faster as the “fixed component” is less and each of the “variable components” require less time. In fact, these are often same ítems that tend to pass faster through cashier. A cashier will require more time to pass six bottles of different beverages rather than a package of the same drink.