There have been many debates about the feasibility of providing guaranteed Quality of Service (QoS) when network traffic travels beyond the enterprise domain and into the vast unknown of the Internet. Many mechanisms have been proposed to bring QoS to TCP/IP and the Internet (RSVP, DiffServ, 802.1p). However, until these techniques and the equipment to support them become ubiquitous, most enterprises will rely on local prioritization of the traffic to obtain the best performance for mission critical and time sensitive applications. This work explores prioritizing critical TCP/IP traffic using a multi-queue buffer management strategy that becomes biased against random low priority flows and remains biased while congestion exists in the network. This biasing implies a degree of unfairness but proves to be more advantageous to the overall throughput of the network than strategies that attempt to be fair. Only two classes of services are considered where TCP connections are assigned to th...