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4.  The airport security in Mobile Alabama has a single officer that checks ids and boarding passes. People arrive at random on average every 1 min to the security check up line. The officer is serving passengers according to an exponential distribution. a.  On average there are 30 people in the system. At what rate is the officer working? b.  The airport is considering adding another officer who will work at the same rate while maintaining a single queue for both officers.  By how much the average waiting time will change? c.  The airport is considering changing to the following PRIORITY policy:  there will be two queues, one for  business class and one for economy class while still having a single officer that serves both. Whenever the officer completes a service and the business queue is not empty, the officer will serve next the first passenger in the business queue and otherwise, the first passenger in the economy queue (if both queues are empty he will next serve the first arriving passenger). 10 percent of the passengers belong to business class. Comparing to the current system answer the following questions with a very brief explanation (a qualitative comparison is sufficient): i.  What will happen to the average waiting time of economy passengers? ii.  What will happen to the average waiting time of business class customers? iii.  Would the business class customers prefer to have a separate queue with their own server that serves them at the same rate or is the PRIORITYpolicy? iii.  What will happen to the average waiting time of all passengers?

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