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In queueing theory, a discipline within the mathematical theory of probability, Little's result, theorem, lemma, law or formula is a theorem by John Little which states: :The long-term average number of customers in a stable system ''L'' is equal to the long-term average effective arrival rate, ''λ'', multiplied by the (Palm‑)average time a customer spends in the system, ''W''; or expressed algebraically: ''L'' = ''λW''. Although it looks intuitively reasonable, it is quite a remarkable result, as the relationship is "not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else." The result applies to any system, and particularly, it applies to systems within systems. So in a bank, 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 only requirements are that the system is stable and non-preemptive; this rules out transition states such as initial startup or shutdown. In some cases it is possible to mathematically relate not only the ''average'' number in the system to the ''average'' wait but relate the entire ''probability distribution'' (and moments) of the number in the system to the wait. ==History== In a 1954 paper Little's law was assumed true and used without proof. The form L = λW was first published by Philip M. Morse where he challenged readers to find a situation where the relationship did not hold.〔 Little published in 1961 his proof of the law, showing that no such situation existed. Little's proof was followed by a simpler version by Jewell and another by Eilon. Shaler Stidham published a different and more intuitive proof in 1972. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Little's law」の詳細全文を読む スポンサード リンク
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