Multiple switch planes, each having meshed bufferless switch units, connect source nodes to sink nodes to form a communications network. Each directed pair of source and sink nodes has a first-order path traversing a single switch unit in a corresponding switch plane and multiple second-order paths each traversing two switch units in one of the remaining switch planes. To reduce processing effort and minimize requisite switching hardware, connectivity patterns of source nodes and sink nodes to the switch planes are selected so that each pair of source node and sink node connects only once to a common switch unit. Widely-varying flow rates may be allocated from each source node to the sink nodes. To handle frequent changes of flow-rate allocations, in order to follow variations of traffic distribution, a high-throughput scheduling system employing coordinated multiple scheduler units is provided in each switch plane.