Little's Law states that a relationship exists between

Question

BlackTom AI · Accepted Answer

Little's Law states L = λ × W, where L is the average number of customers in the system (line length), λ is the average arrival rate, and W is the average time a customer spends in the system (waiting time). This concise formula directly links the average line length to the average waiting time via the arrival rate.

Relevant concepts:
- L (line length): long-run time-average number of items/customers in the system or queue.
- λ (arrival rate): long-run average number of arrivals per unit time.
- W (waiting time): long-run average time an item/customer spends in the system (or in queue, if applied to queue only).

Step-by-step reasoning and a numerical example:
1. If λ = 5 customers/hour and average waiting time W = 0.2 hours/customer, apply Little's Law: L = λ × W.
2. Compute L = 5 × 0.2 = 1 customer on average in the line.
3. This shows that knowing λ and W produces the average line length, directly tying line length and waiting time together.

Why the chosen answer is correct:
- The option "line length and waiting time" captures the core of Little’s Law: average number in system (line length) equals arrival rate times average time in system (waiting time). Thus Little’s Law defines a relationship between those quantities.

Why the other options are incorrect:
- "waiting in queue and waiting in the system": Little’s Law does not state a direct equality between these two times; those are distinct metrics (time in queue vs. time in system) and Little’s Law relates counts to times via arrival rate.
- "multiple and single queues": Little’s Law is not about the number of queues or their configuration.
- "exponential time between arrivals and Poisson arrival rate": that describes specific stochastic arrival processes, not the L = λW relationship.

Conclusion: The correct choice is "line length and waiting time," which matches the provided answer.

Little's Law states that a relationship exists between单项选择题

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