Saturday, October 1, 2016

A Clue for Remembering Little's Law

During the Guerrilla Data Analysis class last week, alumnus Jeff P. came up with this novel mnemonic device for remembering all three forms of Little's law for a queue with mean arrival rate $\lambda$.

The right-hand side of each equation representing a version of Little's law is written vertically in the order $R, W, S$, which matches the expression $R=W+S$ for the mean residence time, viz., the sum of the mean waiting time ($W$) and the mean service time ($S$).

The letters on the left-hand side: $Q, L, U$ (reading vertically) respectively correspond to the queueing metrics: queue-length, waiting-line length, and utilization, which can be read as the word clue.

Incidentally, the middle formula is the version that appears in the title of John Little's original paper:

J. D. C. Little, ``A Proof for the Queuing Formula: L = λ W,''
Operations Research, 9 (3): 383—387 (1961)

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