A new scheduling scheme, called earliest- virtual-deadline-first (EVDF), is proposed to improve resource utilization in a high-speed packet network. The proposed EVDF scheduling is a generalized form of the earliest-deadline-first (EDF) scheduling [D. Ferrari, D. Verma, A scheme for real-time channel establishment in wide-area networks, IEEE J. Select Areas Commun. 8 (3) (1990) 368-379], using the concept of virtual delay bounds and it gives us the flexibility of controlling the delay violation probabilities of traffic flows. As a result, the EVDF scheduler can provide the flows with the quality-of-service (QoS) guarantees that cannot be supported by the EDF scheduler. The performance of the EVDF scheduler is very sensitive to the choice of virtual delay bounds. An iterative algorithm is developed to obtain the virtual delay bounds that achieve ideal service fairness while satisfying the QoS requirements of the flows. Numerical results show that the EVDF scheduler can utilize network resources more efficiently than the EDF scheduler. (c) 2007 Elsevier B.V. All rights reserved.