A bank has $3$ counter desks and a very large waiting lounge $($assume infinite queue$).$ Customers

arrive with a mean of $20$ per hour and each desk serves with mean $10$ customers per hour, where

both rates are exponential. Determine the following :

$($a$)$ Determine $\backslash$lambda n$,$n$,$ c$,$ and $\backslash$lambda ef f for n $=0,1,2,3....$

$($b$)$ The steady$-$state probabilities pn$,$ n $=0,1,2,3....$

$($c$)$ Calculate steady$-$state measures Ls$,$ Ws$,$ Lq$,$ Wq$,$ c$$ and utilization ratio.