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 ser- vice 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 with a coefficient of variation of 1. 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. How many security officers are, on average, available to satisfy a new request?
b. 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? For the next two questions, consider the following scenario. During the period of final exams, the number of requests for escort services increases to 19.2 per hour (one request every 3.125 minutes). The coefficient of variation of the time between successive requests equals 1. However, if a student requesting an escort finds out from the dispatcher that her/ his request would have to be put in the queue (i.e., all security officers are busy walking other students), the student cancels the request and proceeds to walk on her/his own.
c. How many students per hour who called to request an escort end up canceling their request and go walking on their own?
d. University security regulations require that at least 80 percent of the students' calls to request walking escorts have to be satisfied. What is the minimum number of security officers that are needed in order to comply with this regulation?