Little's Law for simulation
Use L = λW to connect average work in process, flow rate, and time in system.
For a stable system observed over a suitable period, the average number of items in the system equals the average arrival or throughput rate multiplied by the average time each item spends in the system.
- L: average number of items in the chosen system boundary.
- λ: average flow rate through that boundary.
- W: average time an item spends inside that boundary.
L = λW
If a stable process completes 12 jobs per hour and jobs spend 30 minutes in the process on average, the average work in process is 6 jobs.
12 jobs/hour × 0.5 hour = 6 jobs
If L counts only the queue, W must be queue waiting time and λ must be the flow through that queue. If L counts queue plus service, W must include both waiting and service time.
Mixing boundaries is one of the easiest ways to get a plausible-looking but wrong check.
Little's Law is valuable for checking long-run averages and for quick capacity reasoning. A simulation is still useful when you need distributions, transient behavior, priorities, schedules, blocking, failures, or other details that the average relationship does not describe.