The present invention provides hierarchical structures of queues and schedulers for switches and routers with, preferably fully-connected, mesh fabrics, for efficiently and properly handling the quality or service requirements of multiple network services, such as ATM and IP, in switch or router. The switches of this invention provide, for example, fair allocation of bandwidths to different network services, to different QoS classes within network services, and to different resources within the switch by use of, preferably, weighted, fair scheduling methods. The switches and routers of this invention are particularly directed to multi-protocol, high-throughput communication application, but may have wide applicability in systems generally where data packets are switched or routed.