To increase Security on campus, USC is offering escort rides to students. The service is operated 24 hours a day. Requests for rides are received every 10 minutes, on average with a coefficient of variation of 4. Once a request is received, if there are no escorts available, the request will be placed in a queue. An escort ride takes on average 20 minutes for picking up the student and taking him/her to the destination. Assume that the Escort Ride time is exponentially distributed. Currently there are six security officers who fulfill the escort requests.

A. How much time does it take on average from the moment a student requests Escort Ride until the student arrives at the destination?

B. On the average how many security officers are available to fulfill a new request?

C. Suppose at the Goodwill cost (cost to the student of hers wash his waiting time) is $8 per hour. What is the total Goodwill cost per day?

D. Suppose that the average inter - arrival time for request remains 10 minutes but the inter - arrival times are exponentially distributed. How will this change the waiting time for a request? Does it increase or decrease? Justify your answer.

E. Due to an increase in DPS crime alerts in the neighborhood, suppose that the number of requests for Escort Ride increases to 35 per hour for the Escort Ride times remain on average at 20 minutes. The escort service changes its regulations in that if all the security officers are busy, then the new arriving request will be canceled instead of being put in a queue. Suppose that you will see requires at least 75% of her quest to be fulfilled. What is the minimum number of security officers needed in order to comply with this requirement? (hint it's a little laws problem)

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