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Little's Law


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

 L=lambdaW,

where L denotes the mean number of items in the queuing system, lambda is the mean number of items arriving per unit time, and W is the mean residence 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, in steady state, a college X with 6,000 student admissions per year and a mean student residence time of two years has a mean enrollment of 2×6,000=12,000.


See also

Asymptotic, Optimization Theory, Order of Magnitude

Portions of 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. https://www.columbia.edu/~ks20/stochastic-I/stochastic-I-LL.pdf.

Referenced on Wolfram|Alpha

Little's Law

Cite this as:

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

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