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Problem1 - At UW Medical Center, blood samples collected from patients at the hospital are sent...

Problem1 -

At UW Medical Center, blood samples collected from patients at the hospital are sent to a lab room for a test. Specimens arrive at the lab room at the rate of 20 an hour (Poisson). Currently there is only one technician who spends on average 2.4 minutes to process one specimen (Exponential). If a specimen cannot be processed immediately when it arrives, it will be stored in a temperature-controlled container inside the lab room. For simplicity assume that the container has unlimited storage capacity.

Part A. What is this queuing model? How many specimens, on average, would you expect to have inside the lab room?

Part B. What is the average time a specimen spends inside the lab room?

Part C. What is the probability of having a queue?

Part D. Suppose that an additional technician (also spends on average 2.4 minutes to process one specimen) is hired. The two technicians work independently. What is this model? What is probability that both technicians are busy at the same time?

Part E. Assuming that it costs $20 an hour to hire a lab technician, and it costs $30 for every hour a specimen spent in the lab, calculate the optimal number of lab technicians to have for this lab.

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