1. A packet network comprising: a set of packet-switching nodes interconnected by communication links; a plurality of media switches (MSWs); and at least first and second connection resource managers (CRMs) that overlay a logical circuit-switched network onto at least a subset of the set of packet-switching nodes and corresponding communication links, which logical circuit-switched network provides transport for quality-of-service (QoS)-sensitive demands within the packet network, wherein: the logical circuit-switched network provides a guaranteed QoS to demands it carries; the logical circuit-switched network comprises a plurality of input virtual trunk groups (VTGs) and a plurality of output VTGs; each MSW is operatively coupled between two or more input VTGs and two or more output VTGs; the first CRM manages resources associated with at least one input VTG; the second CRM manages resources associated with at least one output VTG; each MSW multiplexes demands from two or more input VTGs to one or more output VTGs; and at least one MSW is operatively coupled to at least a first and a second input VTG and at least one output VTG and the at least one MSW multiplexes demands from the first and second input VTGs into the output VTG, wherein: the first input VTG couples a first media gateway (MGW) to the MSW; the second input VTG couples a second MGW to the MSW; and the output VTG couples the MSW to one other MSW in the packet network.