Analysis of CSMA/CD Assume n users and that each attempts transmission during a free"mini-slot with probability p P includes new arrivals and retransmissions P(i users attempt)=.P(1-P) Plexactly 1 attempt=P(success)=NP(1-P) To maximize P(success), NP(1-P)1]=N(1P)-N(N-1)P(1-P 3 Average attempt rate of one per slot Notice the similarity to slotted Aloha Eytan ModianoAnalysis of CSMA/CD • Assume N users and that each attempts transmission during a free “mini-slot” with probability p – P includes new arrivals and retransmissions  N i N −i P(i users attempt) =  i  P ( 1− P) P(exactly 1 attempt) = P(success) = NP(1 - P)N-1 To maximize P(success), d dp [NP(1 - P)N-1] = N(1 - P) N-1 − N(N − 1)P(1− P) N− 2 = 0 1 ⇒ P = opt N ⇒ Average attempt rate of one per slot ⇒ Notice the similarity to slotted Aloha Eytan Modiano Slide 5