Abstract: This paper studies a loss and delay queueing model under the restriction of N-policy for the situations where arrival and service of customers are correlated and follows a bivariate Poisson process. When there is no customer present in the system then the server goes on vacation and returns back in the system whenever the specified N (>1) or more customers are accumulated. The server may breakdown only if it is working and is immediately sent to a repair facility to restore its capability as before failure. For steady state various operational characteristics have been derived. Sensitivity analysis has also been made to examine the effect of different parameters so as to facilitate optimal control policy.