Question about queuing theory


Suppose that two types of customers arrive at a queueing system
according to independent Poisson process of rate λ/2 . Both types of customers require
exponentially distributed service times of rate μ. Type 1 customers are always accepted
into the system, but type 2 customers are turned away when the total number of customers
in the system exceeds K.
(a) Sketch the state transition diagram with total number of customers.
(b) Find the steady state PMF.