Consider an M/M/1 queueing system with parameters  and μ. At each of the arrival instants one new customer will enter the system with probability 1/2, or two new customers will enter simultaneously with probability 1/2.

(a) Draw the state-transition-rate diagram for this system.
(b) Write down the equilibrium equations for Pk.
(c) Find P(z) and also evaluate any constants in this expression so that P(z) is given in terms only of  and μ. If possible eliminate any common factors in the numerator and denominator of this expression (this makes life simpler for you in part (d)).
(d) From part (c) find the expected number of customers in the system.