MadeEasy Workbook: Computer Networks - Network Flow

Question

An upper layer packet is split into 10 frames each of which has an 80% chance of arriving undamaged.if no error control is done by the data link protocol ,how many times must the message be sent on average to get the entire thing through?

Answer 1

Probability (successful transmission of the message) = Probability (all the  frames arrive intact) = 0.8¹⁰=p

So, Probability (unsuccessful transmission) = 1−p=q

successful transmission may occur in 1st try, or 2nd try, or 3rd try,.........kth try etc.

Mean value of no of try = Expected value of k = ∑[k][P(k)]∑[k][P(k)] with k = 1 to inf

1p+2qp+3q²p+4q³p+5q⁴p+..........   

= p[1+2q+3q²+4q³+..........]   

= p*1/(1-Q)2

= 1p+2qp+3q²p+4q³p+5q⁴p+.......... 

  = p[1+2q+3q²+4q³+..........]  

 = p*1/(1-Q)²   = 1/p

 =9.31=9.31

So, Mean no of try will be 10