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mean waiting time of pockets

Hey guys !
I need some help about a mathematical proof because i dont quite understand it. its the proof of the waiting time of packets in M/M/1 and M/M/C. The conclusion is W=R/1-ρ but i can not understand how it got there. Thank you!!!!!!!
Original post by christinechi
Hey guys !
I need some help about a mathematical proof because i dont quite understand it. its the proof of the waiting time of packets in M/M/1 and M/M/C. The conclusion is W=R/1-ρ but i can not understand how it got there. Thank you!!!!!!!


You're going to have to post the proof, and tell us what bits you don't understand. Include any necessary background/assumptions.

And do have a look at the guidelines at the top of the forum - fourth sticky post currently.
(edited 6 years ago)
Reply 2
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christinechi
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20793189_781054845410070_233789055_n.jpg
Reply 3
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christinechi
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This is the proof of what i am asking. I dont understand the part from 11 to 12
Original post by christinechi
This is the proof of what i am asking. I dont understand the part from 11 to 12
Haven't they just taken expectations and used linearity of the expectation operator? (I don't know a lot about this topic, but it seems very clear that's what they've done on the RHS).
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christinechi
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yes i know that but i can not understand why the Sl after the lim gets as Nq
Original post by christinechi
yes i know that but i can not understand why the Sl after the lim gets as Nq


You said 11 to 12, and I was in the middle of a rather horrendously LaTex'd response.

Are you now saying it's just the NqN_q that's causing the problem, in 12 to 13? If so, it's defined two lines further down Nq=E{Ni}N_q=E\{N_i\}
Original post by christinechi
yes i know that but i can not understand why the Sl after the lim gets as Nq
I'm going to confess some exasperation here: you said "I don't understand the part from 11 to 12". I've tried to explain that, and your response is "yes I know that, but I don't understand {something completely unrelated with parts 11 + 12}".

Regarding the parts about taking the limit, I believe that everything following is basically "by definition", but it is impossible for me to be sure, because despite requests to include any necessary background or assumptions, you've simply posted one page from your text book.

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