ATM network must be designed to accommodate all types of traffic with their various characteristics and QOS demands. The degree of service quality is determined by cell loss rate and delay on the whole. Many studies have been concerned on only one of these two elements by adopting selective cell discarding for loss control and priority discipline or buffer size variation for delay control. But these traffic control do not guarantee the desired level for the other element of QOS. In this paper, we consider four types of traffic. First, delay sensitive and delay insensitive cells are separately queued in two buffers, to give high priority to sensitive ones in transmission. Each buffer is controlled by partial buffer sharing scheme to protect the loss sensitive cells. We \ model \ this system \ in discrete time queueing system \ as \\ $MMPP_1, MMPP_2 /D /1 /K~~$ and obtain the cell loss probabilities for each type of traffic and waiting time distribution for two buffers analytically. Numerical examples show that the buffer control proposed in this paper is very effective in guaranteeing the various QOS for all types of traffic.