Hierarchical virtual partitioning facilitates sharing of a resource, such as a link, by multiple customers, each with multiple service classes. Calls of each service class have distinctive bandwidth requirements, arrival rates and mean holding times. The quality of service is in terms of call blocking probabilities. The algorithms allow the desired mix of fairness, robustness and multiplexing efficiency at each of two levels, namely, customers and the various services of each customer. The scheme relies on nominal allocations of capacities to each customer and service, and priorities in the call admission process, which are implemented by dynamic trunk reservations. An approximate method of analysis based on fixed point equations is given. A reward/penalty paradigm is devised to reflect the issues in virtual private networking and the performance of our algorithm compared to the optimal solution. The results show that the scheme is fair, efficient and robust.