The paper considers the combined problem of QoS partitioning and routing (problem OPQR-G - optimal QoS partition and routing in general topology networks) for a QoS framework in which a performance dependent cost function is associated with each network element and the QoS metric is additive (e.g., delay, jitter). This problem has been addressed in the context of unicast and multicast only. Here we consider the problem for a more general case of an arbitrary topology network. Also, it is considered that the performance dependent cost functions are of a general integer type. The goal is to determine primary paths between the OD pairs and QoS partitions on the links so that the overall cost in the network is minimized while all OD (origin and destination) pair QoS requirements are satisfied. As the problem is NP complete, we concentrate on development of an efficient heuristic algorithm. In addition, two LP-based algorithms were developed, that use the optimization tool ILOG/spl trade/ CPLEX 7.1 LP for solving the problem OPQR-G. The results obtained for various network scenarios are very close to the optimal. The problem we address provides the basis for the solution of many interesting and practical engineering problems, such as dimensioning and admission control/resource reservation in multiservice IP networks.