Jobs arrive at a central controller from two different sources, each generating Poisson arrivals with rate lambda $=2$ jobs$/$min$.$ The central controller routes $20\%$ of the jobs to the upper floor office which serves customers with an exponential service times with rate mu $=2$ customer per min. The rest of the jobs are served by the first floor office with an exponential service times with rate mu $=4$ customers per min. After being serviced by either office, $50\%$ of the customer leave the building, while $50\%$ from each serviced floor, request an additional job service at the third floor office, which serves customers with an exponential service times with rate mu $=4$ customers per min.

$1)$ draw the system of queues

$2)$ is the system stable?

$3)$ Find the average time in system for the customers