A multiplex or mux is a group of digital services (TV channels, Radio stations, teletext, signaling, etc.) that are mixed together for broadcast. For example, a TV channel has at least two services or streams. video and audio. Each DVB-T multiplex has capacity that depends on modulation and coding parameters (see possible bitrates). In principle there are two approaches used to combine digital services into multiplex: Constant Bit Rate (CBR) encoding and Variable Bit Rate (VBR) encoding.
We can have services that have constant bit rate. In this case they use fixed amount of the multiplex capacity. Since television video stream is compressed with either MPEG-2 or MPEG-4 (H.264) the amount of compressed data depends on the picture complexity. The more complex picture the more data is needed. Usually the picture changes rapidly and on average one MPEG compressed television video stream needs some fixed bitrate. Therefore it makes sense to allocate higher bit rate to the service when there is a need for it and to decrease bit rate when there is no need to transfer big amounts of data. The total multiplex capacity is still constant - it is dynamically shared between all services according to their current needs. This is called statistical multiplexing.
Basically, two different approaches can be distinguished for joint rate control: the feedback approach and the look-ahead approach. In the feedback approach, statistical measurements of video complexity are generated by the encoders as a by-product of the compression process. The statistics from all encoders are compared and used to control the bit allocation for the subsequent video. In the look-ahead approach, the complexity statistics are computed by preprocessing all video programs prior to encoding. These statistics are then used to more accurately predict the bit rate allocation needed for optimum compression of the video sources in the rate-distortion sense. Finding the best statistics to describe the complexity of a program is a challenging task. In the feedback approach, the statistics are limited primarily to coding-related parameters. The look-ahead approach provides more freedom of choice, but at the price of extra computational complexity and additional cost. In either case, the main feature of the statistical multiplexing system is that each encoder will produce a variable rate bitstream.
On the picture below you can see what percentage of the multiplex capacity has beed allocated to the individual service (TV channel) in particular time. If you see flat lines (i.e. constant bit rate available to each service) then there is no statistical multiplexing involved. The picture is dynamically created from the actual broadcasted MUX A received in Vrhnika (Slovenian Center allotment).