A data multiplexing network is described which multiplexes a plurality of asynchronous data channels with an asynchronous data stream representing compressed voice signals and/or facsimile signals onto a single synchronous data packet stream. The single synchronous data packet stream is then transmitted by a high speed statistical multiplexer over a composite link to a second site using a modified high-level synchronous data link control protocol with an overlay of a priority statistical multiplexing algorithm. The asynchronous data channels and the compressed voice channel and/or facsimile signals are demultiplexed and reconstructed for sending to other asynchronous computer terminals and to a standard telephone or facsimile analog port at the second site, respectively. PBX trunk interfaces are also provided to allow PBX's to share the composite link between sites. Communication between the first site by voice or facsimile and the second site is transparent to the users. The multiplexer efficiently allocated the bandwidth of the composite link by detecting silence periods in the voice signals and suppressing the sending of the voice information to preserve bandwidth. The transmission of facsimile information is performed by decoding the fax transmissions, sending only the facsimile image packets over the multiplexed composite link and reassembling, with carrier, the facsimile signals at the remote site for transmission over an analog telephone line to a remote facsimile machine.