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Bounds on the end-to-end delay, jitter and service lead/lag for all statically-provisioned multimedia traffic flows routed through any network of input-queued (IQ) switches are presented. A recursive fair stochastic matrix decomposition (RFSMD) algorithm is used to determine near-optimal transmission schedules for each switch, where the jitter and service lead/lag of all flows are simultaneously bounded by K middot IIDT time-slots for small constant K, where IIDT denotes the ideal inter-departure time for each flow. It is established that: (a) the number of buffered cells per flow per switch is near-minimal and bounded by O(K) cells, (b) the end-to-end queueing delay along an H-hop path is near-minimal and bounded by O(KH middot IIDT ) time-slots, (c) the end-to-end jitter and service lead/lag are near-minimal and bounded by O(K middot IIDT ) time-slots (the jitter is not cumulative), and (d) all network-introduced jitter can be provably removed using small playback buffers with O(K) cells. It follows that all statically-provisioned traffic flows, including VOIP, IPTV and Video-on-Demand traffic, can be delivered with essentially-perfect QoS even at 100% loads, thereby achieving the optimal statistical multiplexing gain. The bounds also apply when the crossbar switches use a combination of IQs and crosspoint queues. These theories explain several exhaustive results which have recently been presented in the literature.