Everything rests on processors and channels. The number of servers is directly proportional to the number of listeners. The number of listeners is limited by the bandwidth of the channel, both in terms of speed and the number of packets per second.
Soft:
Content Delivery Servers:
nginx-rtmp is a great plugin for nginx. Author's article about him
icecast2 - can give WebM, it means that it works with mobile browsers
Transcoders:
ffmpeg
gstreamer
Browser Players:
Flowplayer is good for supporting a bunch of formats.
Technological chain:
transcoder - recoil servers - player.
A transcoder can be one; it must generate several video formats, which can then be sent to the output servers using a multicast stream.