Methods to achieve bounded router buffer sizes and Quality of Service guarantees for traffic flows in a packet-switched network are described. The network can be an Internet Protocol (IP) network, a Differentiated Services network, an MPLS network, wireless mesh network or an optical network. The routers can use input queueing, possibly in combination with crosspoint queueing and/or output queueing. Routers may schedule QoS-enabled traffic flows to ensure a bounded normalized service lead/lag. Each QoS-enabled traffic flow will buffer O(K) packets per router, where K is an integer bound on the normalized service lead/lag. Three flow-scheduling methods are analysed. Non-work-conserving flow-scheduling methods can guarantee a bound on the normalized service lead/lag, while work-conserving flow-scheduling methods typically cannot guarantee the same small bound. The amount of buffering required in a router can be reduced significantly, the network links can operate near peak capacity, and strict QoS guarantees can be achieved.