Little's Law
Little's Law is a fundamental theorem in queueing theory that relates the average number of items in a queuing system (L), the average arrival rate of items (λ), and the average time an item spends in the system (W).
Where:
- L = Average number of items in the system (Work-in-Process)
- λ = Average arrival rate (Throughput)
- W = Average time an item spends in the system (Cycle Time)
Calculation Scenario
Select what you want to calculate:
Calculate Work-in-Process (L)
Calculate the average number of items in the system when you know the throughput and cycle time.
Result
Average Work-in-Process (L): items
Calculate Throughput (λ)
Calculate the average arrival rate when you know the work-in-process and cycle time.
Result
Average Throughput (λ): items per time unit
Calculate Cycle Time (W)
Calculate the average time an item spends in the system when you know the work-in-process and throughput.
Result
Average Cycle Time (W): time units
Practical Examples
Manufacturing Example
A factory produces 120 units per day (λ), and each unit spends an average of 5 days (W) in the production process. The average Work-in-Process (L) would be:
L = λ × W = 120 × 5 = 600 units
Service Industry Example
A call center has an average of 15 calls waiting (L) and handles 5 calls per hour (λ). The average Cycle Time (W) would be:
W = L / λ = 15 / 5 = 3 hours
Software Development Example
A development team has 10 tasks in progress (L) on average, and each task takes about 2 days (W) to complete. The Throughput (λ) would be:
λ = L / W = 10 / 2 = 5 tasks per day