Recently, efficient network resource management and quality-of-service (QoS) guarantee become more and more important for multimedia applications and services, especially when considering network delays. An optimal bandwidth allocation scheme is introduced. It achieves maximal utilization of the client buffer and minimal allocation of bandwidth for each client. The proposed scheme allocates bandwidth to multiple clients requesting services from a server by adjusting the transmission rates based on the client buffer occupancy, the playback requirements of the individual client and the network delays. Simulations for the single client and multiple client scenarios are conducted under different network congestion levels. The simulation results show that our approach performs better in comparison with the fixed rate allocation approach and the rate by playback requirement approach, since it avoids underflows and overflows efficiently and provides QoS for more clients with limited available bandwidth in the network.