PerkState Happenings HW 5: Battling the Queue Mariel's Perk State has been more successful that than she had planned. 1. During the morning rush, students arrive at a rate of 48 per hour (poisson distribution) and a single server can serve 10 per hour (exponentially distributed). Mariel now has three servers, but is thinking on adding a fourth. What would be the average time for people to wait to get their coffees (wait in line and be served) with 5, 6, and 7 servers? What would be the average number of people in line with 5, 6, or 7 servers? 2. Later in the day, the arrival rate drops to 8 per hour. If she had one server, what is the average number of customers waiting in lane and how long do they wait to be served on average? 3. Mariel is thinking of installing an automatic espresso machine that runs at a fixed service time. If customers arrive at the rate of one every 6 minutes on average and the machine takes 4 minutes to make a cup, What would be the average time for customers to wait in line and receive their cup of espresso?

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