Approximate model for CSMA/CD Simplified approximation for added insight Consider a slotted system with"mini-slots"of duration 2t minislots If a node starts transmission at the beginning of a mini-slot, by the end of the mini-slot either No collision occurred and the rest of the transmission will be uninterrupted A collision occurred but by the end of the mini-slot the channel would be idle again Hence a collision at most affects one mini-slot
Approximate model for CSMA/CD • Simplified approximation for added insight • Consider a slotted system with “mini-slots” of duration 2 τ −> 2τ <− <----------- 1 ----------------> packet minislots • If a node starts transmission at the beginning of a mini-slot, by the end of the mini-slot either – N o collision occurred and the rest of the transmission will be uninterrupted – A collision occurred, but by the end of the mini-slot t he channel would be idle again • Hence a collision at most affects one mini-slot Eytan Modiano Slide 11
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 PI( users attempt)=N)P(1-P- Plexactly 1 attempt)= P(success)=NP(1-P) To maximize P(success), NP(1-P)]=N(1-P)-N(N-1)P(1-P) p Average attempt rate of one per slot Notice the similarity to slotted aloha
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 N P(i users attempt) = i Pi(1− P)N −i 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 ⇒ Popt = N ⇒ Average attempt rate of one per slot ⇒ Notice the similarity to slotted Aloha Eytan Modiano Slide 12