Find the frame length with derivative

[DODGEVIPER13]

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.

 

[jedishrfu]

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.

 

[DODGEVIPER13]

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.

 

[jedishrfu]

u = nf - n0 your numerator and v= (nf+B)^-1

 

[DODGEVIPER13]

 

[jedishrfu]

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.

 

[jedishrfu]

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.

 

[DODGEVIPER13]

Sorry if the post is a bit confusing and my slow responses.

 

[DODGEVIPER13]

Is my answer improved at all?

 

[jedishrfu]

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).

 

[DODGEVIPER13]

Posted this with my phone sorry if it is hard to read

 

[DODGEVIPER13]

So should this be simplified further?

 

[jedishrfu]

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