Analysis of CSMA/CD, continued P(success)=NP(1-p)=(1 N s= limit(N>oo)P(success) et X Average number of slots per succesful transmission P(X=)=(1P)1 EⅨX e Once a mini-slot has been successfully captured, transmission continues without interruption New transmission attempts will begin at the next mini-slot after the end of the current packet transmission Eytan Modiano
Analysis of CSMA/CD, continued 1 P(success) =NP(1 - p)N-1 = (1− N) N −1 1 Ps = limit (N → ∞) P(success) = e Let X = Average number of slots per succesful transmission − P(X = i) = (1 - Ps )i 1 Ps 1 ⇒ E[X] = = e Ps • Once a mini-slot has been successfully captured, transmission continues without interruption • New transmission attempts will begin at the next mini-slot after the end of the current packet transmission Eytan Modiano Slide 6
Analysis of CSMA/CD, continued Let s average amount of time between successful packet transmissions s=(e-1)2τ+D+t t Ave time until start of next Mini-slot dle/collision Mini-slots Packet transmission time Efficiency =D /S= Dn / D +t+ 2i(e-1) °Let阝=tDn=> Efficiency=1(1+445)=≤11t24) Eytan Modiano
τ τ τ τ β τ ≈ β λ β Analysis of CSMA/CD, continued • Let S = Average amount of time between successful packet transmissions S = (e-1)2τ + DTp + τ Ave time until start of next Mini-slot Idle/collision Mini-slots Packet transmission time • Efficiency = DTp/S = DTp / (DTp + τ + 2τ(e-1)) • Let β = τ/ DTp => Efficiency ≈ 1/(1+4.4β) = λ < 1/(1+4.4β) Eytan Modiano Slide 7