Transmission Control Protocol (TCP) has been recognized as the most important transport-layer protocol for the Internet. It is distinguished by its reliable transmission, flow control, and congestion control. However, the issue of fair bandwidth-sharing among competing flows was not properly addressed in TCP. As web-based applications and interactive applications grow more popular, the number of short-lived flows conveyed on the Internet continues to rise. With conventional TCP, short-lived flows will be unable to obtain a fair share of available bandwidth. As a result, short-lived flows will suffer from longer delays and a lower service rate. It is essential for the Internet to come up with an effective solution to this problem in order to accommodate the new traffic patterns. With a more equitable sharing of bottleneck bandwidth as its goal, two cross-layer stateless queue management schemes featuring Drop Maximum (DM) and Early Drop Maximum (EDM) are developed and presented in this dissertation. The fundamental idea is to drop packets from those flows having more than an equal share of bandwidth and retain low level of queue occupancy. The congestion window size of a TCP sender is carried in the options field on each packet. These proposed schemes will be exercised on routers and make its decision on packet dropping according to the congestion windows. In case of link congestion, the queued packet with the largest congestion window will be dropped from the queue. This will lower the sending rate of its sender and release part of the occupied bandwidth for the use of other competing flows. By so doing, the entire system will approach an equilibrium point with a rapid and fair distribution of bandwidth. As a stateless approach, these proposed schemes inherit numerous advantages in implementation and scalability. Extensive simulations were conducted to verify the feasibility and the effectiveness of the proposed schemes. For the simple proposed packet discard scheme, Drop Maximum outperforms the other two stateless buffer management schemes, i.e. Drop Tail and Random Early Drop, in the scenario of homogeneous flows. However, in heterogeneous flows, Random Early Drop gains superiority to packet discard schemes due to its additional buffer occupancy control mechanism. To overcome the lack of proper buffer occupancy control, Early Drop Maximum is thus proposed. As shown in the simulation results, this proposed scheme outperforms existing stateless techniques, including Drop Tail, Drop Maximum and Random Early Drop, in many respects, such as a fair sharing of available bandwidth and a short response time for short-lived flows.