1. (5 points) In queuing theory... a. The arrival rate is almost always greater than the service rate. b. Arrivals tend to occur in waves, with long periods of idle time and short periods of intense activity. c. Multiple servers are not considered. d. None of the above are true. 2. (5 points) Consider an espresso stand with a single barista. Customers arrive at the rate of 20 per hour according to a Poisson distribution. Service times are exponentially distributed with a mean service time of 2 minutes per customer. What is the service rate for the espresso stand? a. 15 customers/hour. b. 10 customers/hour. c. 30 customers/hour. d. 40 customers/hour. The following scenario applies only to problems #3 - #5. Consider an espresso stand with a single barista. Customers arrive at the stand at the rate of 28 per hour according to a Poisson distribution. Service times are exponentially distributed with a service rate of 35 customers per hour. 3. (10 points) The average number of minutes a customer spends waiting in line for service is: a. 0.114 minute. b. 0.143 minute. c. 6.85 minutes. d. 8.57 minutes. 4. (5 points) What is the probability that a customer will have to wait before being served by the barista? (Choose one answer - do not calculate the probability.) a. The probability that the system is busy: P b. The probability that no customers are in the system: Po c. The probability that one customer is in the system: P1 d. The probability that fewer than two customers are in the system: Po + P1 5. (10 points) The average number of customers in the system (i.e., waiting and being served) is: a. 4.0 b. 3.8 c. 3.2 d. 2.0