A scheme for routing packets of traffic to their destination after ensuring that they pass through one or more pre-determined intermediate nodes, thereby permitting all permissible traffic patterns to be handled without knowledge of the traffic matrix, subject to edge-link capacity constraints. In one embodiment, a request for a path with a service demand for routing data between the ingress point and the egress point is received. A set of two or more intermediate nodes between the ingress point and the egress point is selected. Based on a bandwidth of the network, respective fractions of the data to send from the ingress point to each node of the set of intermediate nodes are determined. The data is routed in the determined respective fractions from the ingress point to each node of the set of intermediate nodes, and routed from each node of the set of intermediate nodes to the egress point.