Response to the following problem:
The telephone system at WAVY Radio has 6 incoming phone lines and 2 operators to take listener requests for music. If both operators are busy, a customer is normally placed on hold. If all 6 phone lines are busy, however, callers will get a busy signal and probably not call back. Customer calls to WAVY can be modeled by a Poisson process, with a mean rate of 50 per hour. The service times follow an exponential distribution, with a mean of 90 seconds.
a. What is the probability that a caller will be placed on hold?
b. On the average, how many callers are on hold?
c. If a caller does not get a busy signal, what is the average total time spent waiting on hold and speaking to an operator?
d. What is the probability that there is exactly one caller on hold?