Multi-channel queue with Poison arrivals, Erlangian service time distributions in which the server breaks down according me to a Poisson process ( as mentioned in [2] ) with a limited waiting room, The system consists of servers of varying efficiency. This paper proposes easily -computed steady-state probabilities of such a system. A recursive solution technique was used for computing steady-state probabilities of such a system. We have obtained also some performance measures of the system, such as the expected waiting time per customer, the expected number of customers who arrive to a full system, the expected number of customers will also be calculated. Finally, an example will be introduced.