When local area networks are interconnected by high speed backbone network, there is a significant problem in local area networks. It is the speed mismatch between the high speed backbone network and the lower speed LANs which are connected to it. Packet loss can occur at the receive buffer of interconnected chain such as bridge, router, and gateway when transmitting packets simultaneously by many stations in the direction from the backbone to the LANs. In this paper, we describe a buffer control scheme for packet loss reduction and congestion prevention by using upper bound(ub) and lower bound(lb) of the destination buffer capacity which can be controlled appropriately, and a simple Markov chain model for the proper selection of ub and lb that can result in enhancement of the packet loss performance without serious degradation in throughput-delay characteristics. RBO(Risc of Buffer Overflow) defined is a certain threshold(e.g. 90% of entire buffer capacity) indicates that buffer overflow can occur immediately. Choke packet is an information packet transmitted by the destination gateway for notifying the congestion possibility. This paper presents a buffer control scheme for packet loss reduction and congestion prevention with using upper bound(ub) and lower bound(lb) of buffer capacity at destination bridge, router, or gateway, and a Markov chain model for the proper selection of ub and lb with the result of enhancement in packet loss reduction, but without serious degradation in throughput-delay performance. ub and lb are used to control the transmission speed of the source station according to the destination buffer condition. The ub is used to inform the possibility of congestion at the destination station so that the source station could reduce transmission rate, and the lb is used to improve efficiency in destination buffer utilization at receiving station by increasing transmission rate. Section 2 contains traffic model and station model, and section 3 performs mathematical analysis for obtaining proper ub and lb of buffer capacity for controlling the transmission speed. In section 4, numerical examples are presented, and in section 5, we make conclusions.