In an integrated services network, resources are shared by multiple traffic classes. Service classes that deliver guaranteed Quality-ofService (QoS) to applications have priority over others that do not. In such a multi-service network, routing decisions for high priority QoS traffic will affect what resources are available for lower priority traffic: Poor route selection can result in congestion for, or even starvation of, lower priority traffic. Whereas many studies have focused on routing algorithms that optimize the network throughput for individual service classes, little effort has been devoted to routing algorithms that address inter-class resource sharing. In this paper, we propose a routing algorithm that allows dynamic sharing of link resources among multiple traffic classes. The algorithm is based on the concept of "virtual residual bandwidth," which is derived from the link residual bandwidth by taking the congestion condition of low priority traffic into account...