Consider a single$-$server facility where customers arrive according to a Poisson process with $\backslash$lambda $,$ and the service times are i$.$i$.$d$.$ exponential with rate $.$ The following

operating policy is applied: the server is turned off when the system is empty. It

remains turned off until there are N customers in the system. As soon as there are

N customers in the system the server is turned on$.$ Once the server is turned on it

stays on until the system becomes empty again. It costs $ A and $ B to turn$-$on and

turn$-$off the server, respectively. For each time unit that is spent by each customer

in the system, a cost of $ C is incurred. Model the system as a CTMC by providing

a clear state definition, state space and drawing the rate diagram. Assume that the

CTMC is positive recurrent and you are given the steady state distribution. Provide

expressions for the following: