Question: In an M/M/1 queueing system, customers arrive at a mean rate of 7 customers per hour and each service can be completed in 5 minutes

In an M/M/1 queueing system, customers arrive at a mean rate of 7 customers per hour and each service can be completed in 5 minutes on average. Using the template, input values for , and s to answer the following questions. Round probability answers to 3 decimal places. Otherwise round answers to the nearest tenth, if needed.

1. What is the probability that the server will be idle?

2. What is the probability of having more than 5 customers in the system?

3. What is the probability of having 3 or fewer customers in the system?

4. What percentage of time is the server busy serving customers? %

5. What is the expected number of customers in the system?

6. How many minutes can the customer expect to wait in the system?

7. What is the expected number of customers in the queue?

8. How many minutes can the customer expect to wait in line before being served?

9. What is the probability that the customer will have to wait in line more than 5 minutes before getting served?

10. What is the probability that the customer will be in the system longer than 10 minutes?

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