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Service providers need very effective traffic engineering tools to obtain quantitative end-to-end QoS guarantees in DiffServ networks. For example, ISP has to check if the new SLA (service-level agreement) can be accepted because of limited capacity resources on the path. The basic condition is that predicted traffic demands must be satisfied at any moment. The problem is seen as an expansion problem of link capacity in given limits from the common source. For N quality of service levels, an efficient heuristic algorithm for end-to-end congestion control is being developed. Algorithm of BFH (backward-forward heuristic) type is applied to achieve QoS guarantees in the network with M links and M-1 interior routers. The heuristic algorithm is compared with an algorithm based on an exact approach, to show that the complexity of the optimization process can be reduced. In all numerical test-examples, the best possible result is achieved, but with significant computation savings.