Operations research
Explainer
Little's Law: Linking Queue Length and Wait
One simple law connects how many wait with how long they wait.
Quick check · tap an answer to continue
Lesson notes
Key points
- Little's Law says the average number in a system equals arrival rate times average time spent there.
- Here L counts customers in the whole system, while Lq counts only those waiting, not being served.
- Suppose trucks reach a crusher at twelve per hour and each spends half an hour there, so six are present on average.
- The law holds for almost any stable queue, whatever the arrival or service distribution, which makes it widely useful.
Definitions
- Stable system
- A queue where long-run arrival rate is below service capacity, so averages settle down.
Takeaway: L = λW: know any two and you can find the third.
Quick check: With 4 arrivals per hour and 8 in the system, what is average time W?
- 32 hours
- 0.5 hours
- 2 hours
W = L/λ = 8/4 = 2 hours.
Little's LawL versus LqWorked exampleHolds broadly
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