Emphasize three points: wide application, super simplicity and mathematical law.
(1) Widely used: I don't know if the subject saw this little law by reading books on industrial engineering related websites. The "little rule" described by the terms "inventory", "output" and "process" can only be said to be the application of little rule in production inventory management (if you say that many problems in other fields can also be modeled as inventory management, it means that you have studied for a long time and I am worrying too much).
Little's law is a theory in queuing theory. As long as there is a queuing structure in real problems, we can consider applying Little's Law. The queues mentioned here don't have to conform to the rules of FIFO or FIFO, and the queues don't have to be in order. The key is to have a system (or space) that can accommodate individuals, as long as individuals enter and leave. for example
1. Products are queued for storage. Application of queuing theory in inventory management.
2. Customers go to department stores to buy goods. Department stores are systems and customers are individuals.
3. The netizen enters the Google website, and then clicks the link to leave. Google is a system and its screen name is Personal.
4. We reply to emails. The mailbox is the system, and the mail is the individual. When the mail is received, it means that the mail enters, and when we reply to the mail, it means that the mail leaves.
5. Pregnant women are hospitalized. Hospital is a system, pregnant women are individuals, ready to give birth to the hospital. Postpartum leave, rest and breastfeeding.
6. the intermediary sells the building. Intermediary is the system, the list of buildings to be sold enters the system, and if you don't sell the list, you can buy the building or leave.
There are many more, as long as the conditions are met anyway. What I'm talking about here is only a wide range of applications, and there is another level of application. I will talk about it in (2). )
A rule can be used in many places. What's better, it's concise, which is applicable not only to experts, but also to anyone who knows multiplication and division.
(2) Super concise.
How simple is it? If the preconditions are not mentioned, this law only needs four symbols: L = λW w W. It is tied with F=ma of Newton's second law, but sometimes it is better than Niu Er, which will be explained in the section of "Laws of Mathematics".
The complete Little's law is as follows: In the steady state of a queuing system, the average value L of the number of individuals in the system is equal to the average individual arrival rate λ (unit time) multiplied by the average individual residence time w.
This rule needs to pay attention to two points:
1. Steady state. It can be intuitively understood that the state of the system is average or does not change much at a certain point in time, the average number of individuals in each cycle does not fluctuate, the average arrival rate in each cycle does not fluctuate, and the average residence time does not fluctuate.
The average mentioned is the average over a long period of time. The average of the total number of individuals is the total number of individuals in a period of time divided by the length of this period.
Steady state ensures the existence of average value. All kinds of industrial systems are generally in a stable state.
This formula of L = λW can be used in the implementation of each queuing system. This means that, for example, we only need to study the passenger flow of a department store today, only need to look at the various averages today, and do not need to study the situation for several months. Every day is the realization of this system in department stores.
However, you may say that a formula needs to be stable, and God knows whether the system is stable or not. The number of people coming to the mall is different every time, so it looks unstable at all! In fact, instability can also be set! As long as two conditions are met:
1. The beginning and end of the system are empty.
2. Individuals don't just disappear.
Whether these two conditions are met easily or not. There are naturally no customers when shopping malls open and close, and customers will not evaporate for no reason.
The essence of a widely used law is that there are few preconditions. Little's law is only related to three average values, and you don't need to know it.
(3) Mathematical laws
Little's law is a mathematical theorem. As long as the precondition L = λW is satisfied, it must be correct, because every step is strictly mathematically reasoned. Newton's second law is also awesome, but it is not a mathematical law. Niuer is essentially a physical law and empirical formula. F=ma is tested by measuring f, m and a, and then verified by statistics. It's just that in the world we live in, the formula has a small error and can be used directly as an equation. In this sense, Little's law is better than "Niu Er".
Summarize the amazing things of Little's Law:
1. Widely used
2. The application conditions are simple, and most queuing systems can be used.
Step 3 simplex
reliable
Edited on 2017/09/25
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Thank you for your collection.
sky
Slag just turns to cs
Five people agree with the answer.
The first answer is very good, and then an example of intuitive understanding of Little's Law is added: We have to calculate the average number of students in universities, knowing that the enrollment rate is 0, and the average stay time of each person in universities is t (usually 4 years). Then when we calculate ourselves, we directly multiply the annual enrollment by four years, that is, n = t, that is, the average number of individuals in a system = the average individual arrival rate x the average individual stay time.