Problem 1: To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 15 people per hour request a test. Assuming that arrivals follow a Poisson distribution. Each blood pressure measurement takes a variable amount of time, which is assumed to follow an exponential distribution. On average it takes three minutes to check each person. Assume there is a single queue, and the queue length can be infinite with FCFS discipline. (Hint: use the excel template posted online for calculation)

(1) What's the utilization of the current queueing system? (10 points)

(2) What is the average number of people waiting in the line for blood pressure check? (10 points)

(3) What is the average time a person must spend in the queueing system in total? (10 points)

The Heart Association later decided to add one identical testing booth to the mall due to high demand. There are two options to arrange the two booths:

a. A two-channel operation with two booths in one location. New arrivals join one queue which feeds both booths.

b. Two separate queueing systems with one booth in front of Macy's and the other by Bloomingdales. Each booth has its own waiting line.