Transcoding a live stream in real time requires lots of processing power. In the past when more processing power was needed it was just a simple process of adding a new server and you are ready to go. Adding physical servers is not easy and simple tasks. It would be a matter of loading operating systems adding the proper hardware like memory and storage. It would take hours to deploy. Now it there is something called the cloud. There are many cloud providers that allow you to create server instances almost instantly. You can select all of the resources you want and load a premade OS within minutes. Some of the large streaming providers use Amazons cloud to allow them to increase their processing power on the fly.
You can also have a streaming provider do the transcoding for you on their systems. You can see an example of a reputable streaming provider here. They offer custom packages for almost any level of service needed. Sometimes you can even save money going this route since they can offer better pricing on their existing resources. They would also provider you self service portals to have the ability to manage your services. Here at Next Wave New Media we have used their services for our annual conference. It was broadcasted live to thousands of viewers.