Answer each part below about the M$/$M$/1/$K queue with arrival rate $\backslash$lambda and service rate $.$ Assume

the system is in steady$-$state.

$($a$)$ Find the departure rate in customers per unit time in terms of $$ and pn for some n$.$ Hint: Notice

while the system is empty, the rate of departure from the system is $0$ customers per unit time.

$($b$)$ Show that your answer in part $($a$)$ equals $\backslash$lambda NB$,$ the effective arrival rate for non$-$balking customers,

and explain why that is to be expected.