||For the future boardband public network service, Asynchronous Transfer Mode (ATM) is proposed. It supports applications with different requirements of delay, cell loss, throughput or bandwidth allocation. The aim of our research is to improve the best effort service quality on ATM networks. We investigate and contribute in the area of fairness definition for ATM service and TCP on ATM networks. Extensive studies are performed on the ABR flow control algorithm. However, fair share allocation on residual bandwidth is the main concern for the design of ABR flow control algorithms but the definition for fair share is still not clear. In this thesis, a generalized fairness criterion referred to as the Generalized Weighted Fairness Criterion (GWFC) for flow control on ABR service is presented. Within the GWFC framework, a weight is assigned to each ABR connection and bandwidth is allocated to it in proportion to the corresponding weight. The GWFC can be used to provide prioritized services, and in particular, it also subsumes the Max-Min criterion as a uni-weight fairness criterion. Two weighted fairness sub-criteria are introduced and their performance on bandwidth allocation will be presented and compared with that of the Max-Min criterion. Transmission Control Protocol (TCP) has already been a widely used protocol in many networks. Recent studies show that the performance of TCP over ATM networks is severely degraded. In the second part of our thesis, we propose applying the buffer reservation technique on TCP traffic over ATM networks. We study the performance achieved by the Delayed Transmission (DT) and the Immediate Transmission (IT) buffer reservation schemes. Simulation results show that with the DT buffer reservation technique, TCP can achieve better throughput and delay performance compared with plain TCP and TCP with Early Packet Drop (EPD) scheme except in the LAN environment with short TCP packet length. In the situation, the IT scheme can achieve similar throughput performance but smaller delay compare with plain TCP and TCP with EPD.