B-ISDNs are required to support a variety of services such as audio, data, and video, so that the guarantee of Quality-of-Service (QoS) has become an increasingly important problem. An effective fair scheduling algorithm permits high-speed switches do divide link bandwidth fairly among competing connections. Together with the connection admission control, it can guarantee the QoS of connections. In this paper, we propose a novel fair scheduling algorithm, Virtual-Time-based Round Robin (VTRR). Our scheme maps the priorities of packets into classes and provides service to the first non-empty class in each round, and it uses an estimation method of the virtual time necessary to this service discipline. To find the first non-empty class, VTRR adopts a priority queuing system using a bitvector which decreases the number of instructions that are needed to be carried out in one packet transmission time segment. These policies help VTRR implementation in software, which presents flexibility for upgrade. Our analysis has demonstrated that VTRR provides bounded unfairness and its performance is close to that of Weighted Fair Queuing. Therefore, VTRR gives a good performance and is simple as well, and hence is suitable for B-ISDN. (C) 1999 Elsevier Science B.V. Al rights reserved.