Abstract: Traffic engineering vector operations that are capable of being independently solved can provide near-linear scalability through the exploitation of massively parallel processing. Optimization can be performed simultaneously on different paths in a data plane, as well as on different links within the same path (or within the same set of paths). In some embodiments, the traffic engineering vector operations include an adjustable alpha-fairness variable that allows managers to achieve different levels of fairness/throughput. Hence, embodiment alpha fairness techniques provide flexible policy execution, while maintaining excellent scalability for large network implementations.