Little's Law

Notes

• The law states that average queue time will equal the average queue size divided by the average processing rate.

• It also states that the long-term average number $L$ of work in a system equals the long-term average effective arrival rate $\lambda$ multiplied by the average time $W$ that the work stays in the system.

• MIT professor John D. C. Little proved it in 1961.

• This formula is robust; it applies to virtually all queues disciplines, arrival rates, and departure processes ($W_Q$ is the queue time for an average job, $L_Q$ number of jobs in a queue, $\lambda$ average processing rate, $W_S$ is the system time for an average job, $L_S$ number of jobs in the system).

• You can use the formula for the whole system instead of just for a queue. This use is helpful when you have trouble distinguishing which items are in the queue and which ones are in service.

Examples

Assume customers arrive at a rate of 10 per hour in a store and stay 0.5 hours on average. The average number of customers in the store is $L = 10 * 0.5 = 5$.

References

• The Principles of Product Development Flow
• Wikipedia. Little's law

Backlinks

• The Principles of Product Development Flow
• Cycle Time
• Kanban Uses WIP Constraints to Control the Cycle Time