Happy Concert is a concert organizer. For a new concert, they need to evaluate the location of portable toilets. In particular, they are considering giving service to a part of the venue that is far away from the existing restrooms. There will be a single queue to access all portable toilets in this area. Only one person uses a toilet at a time. There are 2 arrivals per minute on average, the standard deviation of the time between arrivals is 15 seconds, and the average time a person spends in the toilet is 4 minutes (with standard deviation 1 minute). Suppose 10 portable toilets will be installed. HC1. What is the average utilization of the 10 toilets? HC2. What is the expected time a customer will have to wait? HC3. On average, how long will a toilet be empty during a 5?hour long concert? (This is the same as asking how long will a toilet be empty if it has an individual waiting line and it gets 1/10 of the demand. Recall that utilization of a pooled service is the same as independent services.) HC4. What is going to be the average number of people in the queue? (Your answer does NOT have to be an integer.) HC5. The firm does not want the average waiting time to be higher than 2 minutes. What is the minimum number of portable toilets that the firm will have to install to meet that goal? (Your answer should be an integer; they can install 2 toilets or 3 toilets but they cannot install 2.6 toilets. Keep in mind that our waiting line formula applies only when demand is smaller than capacity.)
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