Dynamic video broadcast?

Question

Video broadcast

How can you implement an "endless" video stream?
1. We started broadcasting -> the client connected, but there is nothing in the stream "queue" yet, so the client watches the "splash screen" or just a black screen. The connection should not be interrupted, the stream is active.
2. Add a file/link/other stream to the queue or playlist - the client gets an image.
3. Remove everything from the queue / playlist - the client has a "splash screen"
I would like to implement this using vlc, but how should it look like?