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A university offers a walking escort service to increase security around campus. The system consists of specially trained, uniformed professional security officers accompanying 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 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 to pick up a student and take 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 takeon averagefrom the moment a student calls for an escort to the moment the student arrives at her/his destination? Give your answer in minutes.

c)What is the probability that a customer needs to wait before being served?

d)What is the average time a student spends in the queue? Give your answer in minutes.

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).

e)University security regulations require that the average waiting time not to exceed 1 minute. What is the minimum number of security officers that are needed in order to comply with this regulation?

f)University security regulations require that probability of waiting for a student not to exceed 30%. What is the minimum number of security officers that are needed in order to com-ply with this regulation?

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