An airport concourse has a shoe shine station. During a typical weekday morning, customers arrive at a rate of 5 per hour (approximately one new customer arrives every 12 minutes), and the arrivals follow a Poisson distribution. The mean service rate for shining shoes follows an Exponential distribution, and is 8 customers per hour (it takes approximately 7.5 minutes to complete a shoe shine.)
a. What is the mean (average) time in minutes (note that there are 60 minutes in an hour) that a customer spends in the system (waiting in line at the shoe shine station, and then getting their shoes shined)?
b. The airport wants to know how crowded the area around the shoe shine station will be during a typical day. What is the mean number of customers that are in line, waiting to get their shoes shined?
c. What is the mean utilization percentage of the shoe shine station (the server in this system)?
d. Knowing that passengers in an airport are often impatient, the airport decides to add a second shoe shine station at the same location (there are now two “servers” in this expanded system). As a result, the waiting time should be shorter. On average, how long will a customer now have to wait in line to get their shoes shined?