Suppose that the average input rate to the process is 30 cars per hour. What is the average rate at which cars enter the ‘Checkout’ activity?

Note: Answer in cars per hour. So, if your answer is 10 cars per hour, then input 10.

Question

Suppose that the average input rate to the process is 30 cars per hour. What is the average rate at which cars enter the ‘Checkout’ activity?

Note: Answer in cars per hour. So, if your answer is 10 cars per hour, then input 10.

BlackTom AI · Accepted Answer

Flow conservation (steady-state throughput) implies the average rate into a downstream activity equals the average rate into the system multiplied by the probability an arriving item visits that activity.

1. Relevant knowledge points and concepts
- Flow conservation / throughput: In steady state, the long-run average arrival rate to the system equals the long-run average rate at which items enter a non-blocking downstream activity that every arriving item must visit.
- Branching probability: If only a fraction p of arrivals go to a given activity, the activity’s arrival rate = system input rate × p.
- Little’s Law is not required here because no information about inventories or times is needed.

2. Complete reasoning process step by step
- Given: average input rate to the process = 30 cars/hour.
- Determine: average rate cars enter the “Checkout” activity.
- If every car that enters the process eventually goes through Checkout (i.e., Checkout is a required stage with p = 1), then the checkout arrival rate equals the system input rate.
- If there were branching and only a fraction p of cars visited Checkout, we would compute 30 × p. No such branching probability is provided, and the standard interpretation is that Checkout is the activity that follows for all arrivals.

3. Intermediate calculation steps
- λ_in = 30 cars/hour.
- p(visit Checkout) = 1 (implied).
- λ_checkout = λ_in × p = 30 × 1 = 30 cars/hour.

4. Why the correct answer is correct
Because the problem states the average input rate and asks for the average rate into a subsequent activity that all cars enter. By conservation of flow, that rate must equal the input rate when every arrival visits that activity.

5. Why other intuitive alternatives are incorrect
- Dividing the input among multiple activities would require explicit branching probabilities (not given).
- Any answer lower or higher (e.g., 15 or 60) would contradict conservation unless additional information (splitting, merging, losses) were specified.

6. Conclusion
Therefore the average rate at which cars enter the Checkout activity is 30 cars per hour, which matches the provided answer.

Suppose that the average input rate to the process is 30 cars per hour. What is the average rate at which cars enter the ‘Checkout’ activity? Note: Answer in cars per hour. So, if your answer is 10 cars per hour, then input 10.数值题

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