According to Little's Law, which of the following equations correctly relates the average number of items (L) in a system, the average arrival rate (λ), and the average time an item spends in the system (W)?

• A. L = λ + W
• B. L = W/λ
• C. L = λ/W
• D. L = λW

Answer: (D)

Verified step by step guidance

1. Understand the context of Little's Law: It is a fundamental principle in queuing theory that relates the average number of items in a system (L), the average arrival rate (λ), and the average time an item spends in the system (W).
2. Recall the formula for Little's Law: L = λW. This equation states that the average number of items in the system is equal to the product of the average arrival rate and the average time an item spends in the system.
3. Analyze the given options: Compare each option to the correct formula L = λW. The first option, L = λ + W, is incorrect because it adds the arrival rate and time instead of multiplying them. The second option, L = W/λ, is also incorrect because it divides time by the arrival rate. The third option, L = λ/W, is incorrect because it divides the arrival rate by time.
4. Confirm the correct answer: The only equation that matches the correct formula of Little's Law is L = λW.
5. Conclude that the correct relationship between the variables is L = λW, as it aligns with the principles of Little's Law.