Question: 1. (20 points) a) The following parameters represent a system with a Poisson arrival rate and negative exponential service rate: 1 = 3 customer/hour, u

1. (20 points) a) The following parameters

1. (20 points) a) The following parameters represent a system with a Poisson arrival rate and negative exponential service rate: 1 = 3 customer/hour, u = 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? 4. How long is the average customer in the system? b) Repair calls are handled by one technician at a photocopy shop. Repair time (including transportation time) is exponentially distributed with a mean of two hours/call. Requests for copier repairs come in at a mean rate of 3 per eight hour day (assume Poisson). Determine the following: 1. Average number of customers awaiting repairs 2. System utilization 3. The amount of time during an eight hour day the technician 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 averages one customer every 5 minutes. Assume Poisson and negative exponential distributions for arrival and service rates. 1. What is the system utilization? 2. What is the average number of customers in the system? 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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