Problem
A university offers a walking escort service to increase security around campus. The system consists of specially trained uniformed professional security officers that accompany students from one campus location to another. The service is operated 24 hours a day, seven days a week. Students request a walking escort by phone. Requests for escorts are received, on average, every 5 minutes. After receiving a request, the dispatcher contacts an available escort (via a mobile phone), who immediately proceeds to pick up the student and walk her/him to her/ his destination. If there are no escorts available (that is, they are all either walking a student to her/his destination or walking to pick up a student), the dispatcher puts the request in a queue until an escort becomes available. An escort takes, on average, 25 minutes for picking up a student and taking her/him to her/his desired location (the coefficient of variation of this time is also 1). Currently, the university has 8 security officers who work as walking escorts.
A. What is the average time a student spends in queue? Give your answer in minutes.
B. What is the probability that a customer needs to wait before being serve?
C. How much time does it take-on average-from the moment a student calls for an escort to the moment the student arrives at her/his destination? Give your answer in minutes.
D. How many security officers are, on average, available to satisfy a new request?