Assume that a rock spends an average of 3 minutes in the buffer and an average of 5 minutes to be crushed. Furthermore, assume the entire process produces crushed rocks at a rate of 12 rocks per hour, on average. What is the average number of rocks in the process?

Note: Do not write the scientific unit. For example, if your answer is 10 rocks, then write 10.

Question

Assume that a rock spends an average of 3 minutes in the buffer and an average of 5 minutes to be crushed. Furthermore, assume the entire process produces crushed rocks at a rate of 12 rocks per hour, on average. What is the average number of rocks in the process?

Note: Do not write the scientific unit. For example, if your answer is 10 rocks, then write 10.

BlackTom AI · Accepted Answer

Little's Law states L = λW, so the average number in a stable system equals throughput rate times average time in system.

1) Relevant concepts
- Little's Law (queueing theory): average number in system L = arrival (or throughput) rate λ × average time in system W.
- Steady-state assumption: the process is stable and averages apply.
- Convert time units consistently.

2) Step-by-step reasoning and intermediate steps
- Total average time in the process W = time in buffer + time to be crushed = 3 minutes + 5 minutes = 8 minutes.
- Convert the throughput rate to the same time units or convert W to hours. Method A: convert rate to per-minute.
  - λ = 12 rocks per hour = 12/60 = 0.2 rocks per minute.
  - L = λ × W = 0.2 (rocks/min) × 8 (min) = 1.6.
- Method B (equivalent): convert W to hours.
  - W = 8 minutes = 8/60 hours = 2/15 hours.
  - L = 12 (rocks/hour) × 2/15 (hours) = 24/15 = 8/5 = 1.6.

3) Why this answer is correct
- Little's Law directly relates the given average throughput and average time in system to the average number of items in system. Using either consistent unit conversion yields the same exact result, 1.6. A fractional value is valid because it represents an expected (average) count.

4) Other options
- No multiple-choice options are provided here; any alternative numeric result would come from incorrect unit conversion or forgetting to sum the two time components.

Conclusion: The average number of rocks in the process is 1.6, which matches the provided answer.

类似问题

Little's Law states that a relationship exists between

The average total time in the system (including time to be served) is calculated using which of the following equations for an infinite queue model?

What is the name of the law that states that there is a long-term relationship between the inventory, throughput, and flow time of a production system in a steady state?

The long-term relationship between inventory, throughput, and flow time is mathematically related using 's law.

Little's law relates inventory, throughput rate, and flow time as which of the following formulas?

At Carver, it takes the average person 6 minutes to wait in line and get ice cream. They are able to serve 200 customers in an hour. The serving of 200 customers in an hour is an example of which component of Little's Law?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单