Service Management: Operations, Strategy, Information Technology 8th Edition by James Fitzsimmons,Mona Fitzsimmons,Sanjeev Bordoloi

Exercise 8

On average, 4 customers per hour use the public telephone in the sheriff's detention area, and this use has a Poisson distribution. The length of a phone call varies according to a negative exponential distribution, with a mean of 5 minutes. The sheriff will install a second telephone booth when an arrival can expect to wait 3 minutes or longer for the phone.
a. By how much must the arrival rate per hour increase to justify a second telephone booth?
b. Suppose the criterion for justifying a second booth is changed to the following: install a second booth when the probability of having to wait at all exceeds 0.6. Under this criterion, by how much must the arrival rate per hour increase to justify a second booth?