The IP networks are faced today with difficult task of satisfying the needs of connections requiring different QoS by sharing the same physical resources, e.g. bandwidth and buffers. Buffers are a key component of packet-switched network, as they absorb burst arrivals of packets and hence reduce losses. Larger buffers can absorb larger bursts but they tend to build up high load and increase queueing delays. The traditional technique for managing delay is to set a maximum length for each buffer queue, accept packets in the queue until the maximum length is reached. Distributed computational grids depend on TCP to ensure reliable end-to-end communication between nodes across the wide area network (WAN). In the core of network (routers), it is believed that RED will alleviate problems related to synchronization of flows and also provide some notion of QoS by intelligent dropping. In this paper, we develop simple Markovian model for the RED buffer management schemes, and use these models to quantify the benefits brought about by RED. In particular, we examine the impact of RED on the loss rate and the mean delay. We analyse the transient and stationary states, using Markovian model. We show that the loss probability is the same for TCP and UDP traffics if RED algorithm is used. This loss rate of a flow going through a RED router does not depend of the burstiness of this flow, but only on the load it generates.