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Find the proportion of time rabii is busy

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Rabii and his daughter manages a coffee shop on the university campus ULS. Although Rabii can service on average 30 customers per hour, he only gets 20 customers per hour. Since Rabii is expecting to get 50% more customers than actually, it doesn't make sense to him that he should have any waiting lines. The cost of waiting per customer is 10 cents per minute. Rabii is not considering any cost for his work and is working 12 hours per day.

Rabii hires you to examine the situation and to determine some characteristics of his queue. After looking into the problem, you find this to be an M/M/1 system.

1. Find the proportion of time Rabii is busy.

2. Find the proportion of time Rabii is idle.

3. Find the number of customers in the coffee shop.

4. Find the number of customers in the queue

5. Find the average time, customers stay in the coffee shop

6. Find the average time, customers wait in line.

7. What is the total waiting cost for the customers per day

Later on, Rabii agreed on the calculated findings, which seemed to represent his approximate business situation.
You tell Rabii that he could probably save some of the total customer's waiting cost per day if he hires an assistant to him. Rabii agrees to provide you with all the coffee and food you can get during for a full week in exchange for your analysis of having two persons servicing the customers. For this purpose, he suggested his daughter as the second server as she too won't get paid for that.
Assuming that Rabii hires his daughter as an additional server whose service rate equals Rabii's rate

8. Find the probability that checkpoints would be inactive

9. Find the number of customers in the newly organized system

10. Find the average time, customers stay in the coffee shop given the newly organized system

11. Find the number of customers in the queue given the newly organized system

12. Find the average time, customers wait in line given the newly organized system

13. Find the proportion of time the checkpoints will be busy

14. What is the total waiting cost for the customers per day given the newly organized system?

15. What can you conclude?

Reference no: EM132909588

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