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Little's Law


Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the average time that an item spends in the system. Algebraically, this can expressed as

 L=lambdaW,

where L denotes the average number of items in the queuing system, lambda is the average number of items arriving per unit time, and W is the average waiting time for an item within the system.

Due to its use of general language and its natural conditions with practically no extraneous assumptions, Little's law can be used to asymptotically describe conditions across a vast array of scenarios. For example, Little's law suggests that the average number of students attending a two-year college X which averages 6,000 first-year student admissions per year is simply 2×6,000=12,000.


See also

Asymptotic, Optimization Theory, Order of Magnitude

This entry contributed by Christopher Stover

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References

Little, J. D. C. and Graves, S. C. "Little's Law." In Building Intuition: Insights From Basic Operations Management Models and Principles (Ed. D. Chhajed, and T. J. Lowe). New York: Springer Science+Business Media LLC, pp. 81-100, 2008.Sigman, K. "Notes on Little's Law." 2009. http://www.columbia.edu/~ks20/stochastic-I/stochastic-I-LL.pdf.

Cite this as:

Stover, Christopher. "Little's Law." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LittlesLaw.html

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