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Little's law
Theorem in queueing theory
Little's law
In mathematical queueing theory, Little's law (also result, theorem, lemma, or formula) is a theorem by John Little which states that the long-term average number of customers (L) in a stationary system is equal to the long-term average effective arrival rate (λ) multiplied by the average time that a customer spends in the system (W). Expressed algebraically the law is L = λ W . {\displaystyle L=\lambda W.} The relationship is not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else. In most queuing systems, service time is the bottleneck that creates the queue. The result applies to any system, and particularly, it applies to systems within systems. For example in a bank branch, the customer line might be one subsystem, and each of the tellers another subsystem, and Little's result could be applied to each one, as well as the whole thing. The...
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