Southeast Airlines is a small commuter airline serving primarily the state of Florida. Their ticket counter at the Orlando 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.
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