I M/G/C Queue Theory: Proving Results & Finding Sources

[mertcan]

hi, initially when I saw these statements , I got really amazed, and now I endeavor to find the proofs of these statements, bu I would like assure you of the fact that there are very very very few sources which evaluate M/G/K or M/G/infinite queue, mostly sources prefer to handle the subject of M/G/1 queue. Therefore, I am really asking you: Could you prove how these statements are possible to me using some mathematical demonstrations? Is there a proof of results above?

 

[mertcan]

@Ray Vickson and other respectable forum members, Is there a incomprehensible, complex situation in my question? Why can't I get any support from you? I am absolutely aware that most of you are very capable of overcoming my question easily. Why don't you prefer to help me?