Question: Problem 2: Queuing theory - 12 marks Suppose you have been tasked with setting up a COVID-19 testing site in a large urban area. You

Problem 2: Queuing theory - 12 marks Suppose you have been tasked with setting up a COVID-19 testing site in a large urban area. You estimate that your site will see 43 patients each hour. It takes approximately 12 minutes to test a patient. You are able to setup multiple parallel testing tracks. Assume you can model this system as an M/M/c queue. 1. How many tracks do you need to ensure the queue will reach steady-state? (2 marks) 2. Using the number of tracks from Q1, how long, on average, does a patient wait to be tested? (2 marks) 3. You decide that want the probability that no track is immediately available to be less than 0.1. How many tracks do you need? (2 marks) 4. Using the number of tracks from Q3, how long, on average, does a patient spend in the system? (2 marks) 5. Using the number of tracks from Q3, what is the probability that there are 12 patients in the system? (2 marks) 6. If there are an average of 12 patients in the system, what is the average waiting time per patient in minutes)? (2 marks) Problem 2: Queuing theory - 12 marks Suppose you have been tasked with setting up a COVID-19 testing site in a large urban area. You estimate that your site will see 43 patients each hour. It takes approximately 12 minutes to test a patient. You are able to setup multiple parallel testing tracks. Assume you can model this system as an M/M/c queue. 1. How many tracks do you need to ensure the queue will reach steady-state? (2 marks) 2. Using the number of tracks from Q1, how long, on average, does a patient wait to be tested? (2 marks) 3. You decide that want the probability that no track is immediately available to be less than 0.1. How many tracks do you need? (2 marks) 4. Using the number of tracks from Q3, how long, on average, does a patient spend in the system? (2 marks) 5. Using the number of tracks from Q3, what is the probability that there are 12 patients in the system? (2 marks) 6. If there are an average of 12 patients in the system, what is the average waiting time per patient in minutes)? (2 marks)

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