Question: Problem 1. Queueing Models Suppose that each SKU arrives at your machine every 12 minutes following Exponential Distribution, and that the service time is Exponential

Problem 1. Queueing Models Suppose that each SKU

Problem 1. Queueing Models Suppose that each SKU arrives at your machine every 12 minutes following Exponential Distribution, and that the service time is Exponential at a rate of one service per 8 minutes. You have now two identical machines, so each SKU can be served either of two machines. Moreover, two machines have a shared queue, which can hold 2 SKUs at most. If a new SKU arrives, when there are 2 SKUs in the queue, it will be returned immediately. SKUs will keep arriving in the system. a Q1-1. Please represent this system using Kendalls notation. Q1-2. Please represent this system using the rate diagram. Q1-3. Please develop all the balance equations in the rate diagram. Q1-4. What is the long-run probability that 2 number of SKUs are in the system (Indeed, find P2)? (Remark: In the final exam, I will give all the Pi values. I just wanted you to practice solving balance questions one time in this homework) Q1-5. What is the average number of SKUs in the system

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