# Question

a. λ = 3 customers/hour

μ = 5 customers/hour

M = 1

1) What is the system utilization?

2) What is the average number of customers waiting for service?

3) What is the average time customers wait in line for service?

b. Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day (assume Poisson). Determine:

1) The average number of customers awaiting repairs.

2) System utilization.

3) The amount of time during an eight- hour day that the repairman is not out on a call.

4) The probability of two or more customers in the system.

c. An average of 18 customers arrive at a service center each hour. There are two servers on duty, and each server can process 12 customers per hour.

1) What is the system utilization?

2) What is the average number of customers in the system (waiting plus being served)?

3) What is the average time customers wait in line for service?

4) What is the average waiting time for customers who actually have to wait?

μ = 5 customers/hour

M = 1

1) What is the system utilization?

2) What is the average number of customers waiting for service?

3) What is the average time customers wait in line for service?

b. Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day (assume Poisson). Determine:

1) The average number of customers awaiting repairs.

2) System utilization.

3) The amount of time during an eight- hour day that the repairman is not out on a call.

4) The probability of two or more customers in the system.

c. An average of 18 customers arrive at a service center each hour. There are two servers on duty, and each server can process 12 customers per hour.

1) What is the system utilization?

2) What is the average number of customers in the system (waiting plus being served)?

3) What is the average time customers wait in line for service?

4) What is the average waiting time for customers who actually have to wait?

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