Part II$.$ The jobs arrive according to a Poisson process with rate $.$

Hint. Consider an $($artificial$)$ exponential server with rate $$ to process the available fixtures. Let

$n_f$ be the state variable defined for this $($artificial$)$ server. When $n_f$ takes a positive value, it denotes

the number of available fixtures to be processed by the artificial server. When $n_f$ takes a negative

value, $|n_f|$ denotes the number of bacordered jobs waiting for an available fixture.

Q$1.$ There is only one manufacturing stage $($server$)$ and its exponential service rate is $(>).$

a$)$ Draw the state$-$transition diagram for $K=2.$

b$)$ What is the steady$-$state distribution for the state description you give?

c$)$ Give the Kendall$-$Lee notation for the queueing system you analyze in parts $($a$)$ and $($b$).$