Focusing on routing in broadband networks based on MPLS (Multiprotocol Label Switching) and ATM (Asynchronous Transfer Mode), this text shows the issue of performance optimization and scalability with respect to dynamic routing of logical connections in broadband networks. The routing methods are based on the theory of Markov decision processes which forms a very accurate framework for on-line route optimization. The methods used are applicable to routing virtual path connections (VPC) and virtual channel connections (VCC) in ATM networks as well as label switched paths (LSP) in MPLS networks. Simulation results and a performance comparison with reference routing are given for the different schemes.