Registration at State University proceeds as follows: Upon entering the registration hall, the students first wait in line to register for classes. A single clerk handles registration for classes, and it takes the clerk an average of 2 minutes to handle a studentĂ˘â‚¬â„˘s registration. Next, the student must wait in line to pay fees. A single clerk handles the payment of fees. The clerk takes an average of 2 minutes to process a studentĂ˘â‚¬â„˘s fees. Then the student leaves the registration building. An average of 15 students per hour arrive at the registration hall.
a If interarrival and service times are exponential, what is the expected time a student spends in the registration hall?
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b What is the probability that during the next 5 minutes, exactly 2 students will enter the registration hall?
c Without any further information, what is the probability that during the next 3 minutes, no student will arrive at the fee clerkĂ˘â‚¬â„˘s desk?
d Suppose the registration system is changed so that a student can register for classes and pay fees at the same station. If the service time at this single station follows an Erlang distribution with rate parameter 1.5 per minute and shape parameter 2, what is the expected time a student spends waiting in line?