Today, large telecommunications customers are increasingly using virtual private networks to link geographically dispersed sites. A virtual private network is provided by provision-ing a set of permanent (long term) virtual circuits between customer endpoints on a large backbone network. This paper considers the problem of routing a set of permanent virtual circuit requests over a backbone network. Several factors make this routing problem complicated. Routing decisions must be made on-line without any knowledge of future request sets. Furthermore, frequent rerouting to correct ineeciencies that can result from the on-line routing decisions are not possible since rerouting creates a service disruption for the customer. Finally, the forward and reverse bandwidth of a virtual circuit must be routed over the same single path. Using an extensive set of simulations, this paper evaluates several diierent strategies for on-line permanent virtual circuit routing. We nd that a strategy based on recent results in competitive analysis and ideas from combinatorial optimization consistently provides the best performance. The problem of admission control is closely related to the problem of routing. This paper also provides a theoretical lower bound which suggests that non-greedy admission control is a fundamental component of an eecient on-line permanent virtual circuit routing algorithm.