$(25$ points$)$ Consider a Jackson network with two service facilities having the parameter values shown below.

$\backslash$table$[[$Facility $j,Sj,j,qj,j,],[j=1,1,20,9,0,0\mathrm{.}45],[j=2,1,15,3,0\mathrm{.}60,0]]$

a$)$ Find the total arrival rate of customers at each of the facilities. $($Hint: there is a template for that.$)$

b$)$ Find the expected total number of customers in the system.

c$)$ Find the probability that there are no customers in the system.