Question 3: Waiting Time Analysis

Question 3 (9 points). Preceding Super Bowl 50 in Santa Clara, California, Jo, an enterprising Undergraduate Junior, plans to set up a stand just outside Levi's Stadium to give a 1-minute hug for $5. Demand is overwhelming, and "customers" arrive at an average rate of 50 per hour, (the arrivals tend to follow a Poisson process). Jo soon discovers that not every hug takes exactly 1 minute: instead, the "service time" is distributed exponentially, with an average of 1 minute per customer. What is the average time that a customer spends in the queue and in the system? After the first day, Jo started receiving complaints from impatient customers about the long waiting time. Fortunately, Jo's friend, Lo, was available to work at the stand, and could serve customers at the same rate as Jo. The only question was whether to have two separate queues (one each for Jo and Lo), or a single queue of customers. With two separate queues, the average arrival rate to each queue is half (25/60) and follows Poisson process. No jockeying between lines is permitted. Which system is better in terms of average waiting time