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 of work in a system equals the long-term average effective arrival rate multiplied by the average time 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 ( is the queue time for an average job, number of jobs in a queue, average processing rate, is the system time for an average job, 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.
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 .