Frame relay is a fast packet switching technology that performs relaying and multiplexing frames with variable lengths over a wide area link at the T1 or E1 speed, by elminating error and flow control in the network. In frame relay networks, congestion control is typically performed through the rate enforcement with a discard eligibility (DE) bit, and the explicit negative feedback meachanisms using explicit congetion notification bits. In this paper, we consider the congestiong control scheme using the rate enforcement mechanism with DE bit for frame relay network. Assuming that each frame with exponentially distributed length arrives according to the Poission fashion, we can treat the frame relay switch as an M/M/1/K priority queueing system with pushout basis. We analyze and present the blocking probabilities and waiting time distributions of frames.