To increase security on campus, UCLA 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 her/him to the destination. Assume that the escort ride time is exponentially distributed. Currently, there are 6 security officers who fulfill the escort requests.

a) Suppose that the goodwill cost (cost to the student of her/his waiting time) is $8 per hour. What is the total goodwill cost per day?

b) Suppose that the average inter-arrival time for requests remain 10 minutes but the inter-arrival times are exponentially distributed. How will this change the waiting time for requests? Does it increase or decrease? Justify your answer. (Note: You dont need to calculate the new waiting time.)

c) 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, but the escort ride times remain on average at 20 mins. The escort service changes its regulations in that if all the security officers are busy, then the new arriving requests will be cancelled instead of being put in the queue. Suppose that UCLA requires at least 75% of requests to be fulfilled. What is the minimum number of security officers needed in order to comply with this requirement? (Hint: this is a Littles law problem)