Simplified demonstration of Littles Law

Simplified demonstration of Little’s Law:

1874_little law.jpg

• a(t): the number of arrivals up to time t
• d(t): the number of departures up to t
• l(t) = a(t) –d(t) ≥ 0, the number of units in the system at time
• H(t): the area enclosed between the curves a(t) & d(t). represents the accumulated time in system during that interval measured in request-seconds (or request-minutes, etc.)

Simplified demonstration:

L ≡ H/T

R ≡ H/C

X ≡ C/T

H/T ≡ (C/T) (H/C);

L = X/R

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