During the recent years, there has been a tremendous growth in the development and deployment of multimedia based networked applications such as video streaming, IP telephony, interactive games, among others. These applications, in contrast to elastic applications such as email and data sharing, are delay and delay jitter sensitive but can tolerate certain level of packet loss. A vital element of end-to-end delay and delay jitter is the random queueing delays in network switches and routers. Analysis of robust mechanisms for buffer management at network routers needs to be carried out in order to reduce end-to-end delay for traffic generated by multimedia applications. In this context, a threshold based buffer management scheme for accommodating multiple class multimedia traffic in network routers has been analysed. This technique effectively controls the allocation of buffer to various traffic classes according to their delay constraints. The forms of the joint state probabilities, as well as basic performance measures such as blocking probabilities are analytically established at equilibrium. Typical numerical experiments are included to illustrate the credibility of the proposed mechanism in the context of different quality of service (QoS) grades for various network traffic classes. This model, therefore, can be used as a powerful tool to provide a required grade of service to a particular class of multimedia based web traffic in any heterogeneous network.