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Find the frame length with derivative

  1. Sep 20, 2014 #1
    Find the optimum frame length nf that maximizes transmission efficiency for a channel with random bit erros by taking the derivative and setting it to zero for the following protocols:
    (a) Stop-and-Wait ARQ
    (b) Go-Back-N ARQ
    (c) Selective Repeat ARQ

    My work has been uploaded I am a bit rusty on derivative, so I am pretty sure I made a mistake just unsure of where.
     

    Attached Files:

  2. jcsd
  3. Sep 20, 2014 #2

    jedishrfu

    Staff: Mentor

    The last factor with nf is wrong I think. I used the duv = u*dv + v*du rule with v= (nf+B)^-1 and got a different factor from yours so check it again and post your result.
     
  4. Sep 21, 2014 #3
    What did you use for u? I guess you did a u substitution to do this then so if I find u I can do the derivative.
     
  5. Sep 21, 2014 #4

    jedishrfu

    Staff: Mentor

    u = nf - n0 your numerator and v= (nf+B)^-1
     
  6. Sep 23, 2014 #5
    EPSON001.JPG
     
  7. Sep 23, 2014 #6

    jedishrfu

    Staff: Mentor

    My apologies, I must have done something wrong. Yours looks correct. How is the book answer different? That might tell you where the real error is.
     
  8. Sep 24, 2014 #7

    jedishrfu

    Staff: Mentor

    Okay I think I see your error. You differentiated the a^nf and multiplied it to the differentiated version of the second factor. Don't you have to apply the duv product rule here too?

    With u=a^nf and v= the rest.
     
  9. Sep 25, 2014 #8
    Sorry if the post is a bit confusing and my slow responses. EPSON002.JPG
     
  10. Sep 29, 2014 #9
    Is my answer improved at all?
     
  11. Sep 29, 2014 #10

    jedishrfu

    Staff: Mentor

    Yes, it looks right but you can do more by extracting out the a^nf factor and by finding a common denominator so you can combine numerator terms ie multiply the second term by (nf+B)/(nf+B).
     
  12. Oct 2, 2014 #11
    Posted this with my phone sorry if it is hard to read 1412268926261.jpg
     
  13. Oct 2, 2014 #12
    So should this be simplified further?
     
  14. Oct 2, 2014 #13

    jedishrfu

    Staff: Mentor

    I can't see anything further. Does this differ from some book answer you have? or were you expecting it to be much simpler?
     
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