Suppose customers arrive according to Poisson process of rate $\backslash$lambda to a service

station with infinitely many servers. Immediately upon arrival a customer is forwarded

for service which takes Exponential$()$ time, and departs after receiving service. Let

X$($t$)$ be the number of customers being served at time t$.$

$($a$)$ Determine the generator of the process $($X$($t$),$ t $>=0).$ Is it a birth$-$death process? $[3]$

$($b$)$ What are the values of $\backslash$lambda and $$ that ensure existence of stationary distribution. $[7]$

Whenever stationary distribution exists find it explicitly.