A media muxer node (10) of a local network (7) is configured to time-shift a live media stream, by storing the stream on a local network storage (3) during a pause, and providing the stored and time-shifted stream to a local network-UE (5) after the pause. The pausing and the resuming of the media stream can be initiated from an external network-connected UE (1) outside the local network, or directly from the local network UE (7). The system also comprises a media aggregating node (2) for authentication of the external network—connected UE (1), which are both connected to a virtual control node (4). If a pause in the replay is discovered, the media muxer node (10) sees to the storage of the media in a local network storage (3) until the discovery of a restart command.