Debra Bishop's cabinet-making shop, in Des Moines, has five tools that automate the drilling of holes for the installation of hinges. Each machine needs an average of 3 "resettings" every 8-hour day, following the Poisson distribution. There is a single technician for setting these machines. Her service times are negative exponential, averaging 2 hours each.
a) What is the probability this system is empty?
b) What is the average number of machines in the system (i.e., being reset or waiting to be reset)?
c) What is the average waiting time in the queue?