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We present a general framework for the problem of quality-of-service (QoS) routing with resource allocation for data networks. The framework represents the QoS parameters as functions rather than static metrics. The formulation incorporates the hardware/software implementation and its relation to the allocated resources into a single framework. The proposed formulation allows intelligent adaptation of QoS parameters and allocated resources during a path search, rather than decoupling the path search process from resource allocation. We present a dynamic programming algorithm that, under certain conditions, finds an optimal path between a source and destination node and computes the amount of resources needed at each node so that the end-to-end QoS requirements are satisfied. We present jitter and data droppage analyzes of various rate-based service disciplines and use the dynamic programming algorithm to solve the problem of QoS routing with resource allocation for networks that employ these service disciplines.