The goal of this webpage is to explain the Statistic multiplexing (Variable bit rate) versus the constant bitrate.
A Satellite or a DTT mux can handle many TV channels. All these channels need to use the total bandwith of the mux. The providers take the choice to give the same amount of bandwith for each channel or to give the freedom of each channel to take a variable bandwith. In this case, the summing of channels bitrate cannot exceed the max bandwoth of the mux.
To explain the statistic multiplexing, we are going to take a SAT mux with French channels.

1) Fin the max bitrate of the mux :
The mux has a symbol rate of 19636, and a Fec of 2/3
The max bitrate of this mux is : 19636 x 2 x 2/3 x 188/204 = 24,127 Mb/s
The 188/204 is linked to the use of Reed Solomon corrector code.

2) Number of services boradcasted in this mux:
6 services : France2, France3, France4, France5, Arte, LCP.
In these services, we find 7 audios channels at 192kb/s (1 audio per TV , only Arte has 2 audios).
The bitrate taken by all audios channels is 7 x 192 kb/s = 1.344 Mb/s
There is also around 700 kb/s of datas (DVB tables , EPG ...) sent in the mux.
For all the video bitrate, it remains : 24.1 - 1.3 - 0.7 = around 22 Mb/s

3) Video bitrate measurment of each Tv channel at the same time:
This was done the evening between 19h58 and 20h04.

France2
France3
France4
France5
Arte
LCP

4) All bitrates linked in one mux:

We can see that the summing of all video bitrates is around 22Mb/s. France2 during it's breaking news tv show has it's bitrate decreasing, other channels are taking this bitrate availabilty for their proper use. France3 stays at constant bitrate. It was done to allow switch for other France3 with same bitrate in each area (local channels).
To allow statistic multiplexing, the mpeg compression is done in 2 steps : first step is analysing each channel to know what bitrate is requested to compress with good quality each channel, the results are taken to see if the summing is more than the total available in the mux, and in function of priority done on channel between each over, the 2nd step (mpeg compressor) compress the channel with the new computed bitrate. After all the streams are linked in the same stream (transport stream).

4) Conclusion:
the statistic multiplexing allow the provider to put more channels in one mux than constant bitrate. In statistic, the average bitrate of each channel is used to know how many channels can be put in one mux. If one channel is requested more bitrate due to detailed picture (france in mpeg2 is requested 8Mb/s), there is probability that other channels can surely have their bitrate decreased in the same time.

In CBR (Constant Bit rate), the bitrate needs to be the max allowed to the channel. 6Mb/s in MPEG2 CBR is a good broadcast. If more is allowed, the number of channels in a mux has to be decreased.

Today, a lot of provider are using statistic multiplexing in MPEG2 and MPEG4. When CBR is used, it is due to the fact that all channels are compressed in an other place than the link of transport stream. This do not allow 2 steps compression and bitrate comparison.