Southeast Airlines is a small commuter airline serving primarily the state of Florida. Their ticket counter at a certain airport is staffed by a single ticket agent. There are two separate lines—one for first-class passengers and one for coach-class passengers. When the ticket agent is ready for another customer, the next first-class passenger is served if there are any in line. If not, the next coach-class passenger is served. Service times have an exponential distribution with a mean of 3 minutes for both types of customers. During the 12 hours per day that the ticket counter is open, passengers arrive randomly at a mean rate of 2 per hour for first-class passengers and 10 per hour for coach class passengers.
(a) What kind of queueing model fits this queueing system?
(b) Find the main measures of performance—L, Lq, W, and Wq — for both first-class passengers and coach-class passengers.
(c) What is the expected waiting time before service begins for first-class customers as a fraction of this waiting time for coach-class customers?
(d) Determine the average number of hours per day that the ticket agent is busy.