DAnalysis of CSMA Let the state of the system be the number of backlogged nodes Let the state transition times be the end of idle slots Let t(n)= average amount of time between state transitions when the system is in state n T(n)=β+(1-e(1-q When gr is small (1-a)n-e-qn=>T(n)=B+(1-e-p-ngr) At the beginning of each epoch, each backlogged node transmits with probabilit lity gr New arrivals during the previous idle slot are also transmitted With backlog n, the number of packets that attempt transmission at the beginning of an epoch is approximately Poisson with rate gn)=β+nq�Analysis of CSMA • Let the state of the system be the number of backlogged nodes • Let the state transition times be the end of idle slots – Let T(n) = average amount of time between state transitions when the system is in state n T(n) = β + (1 - e-λβ (1-qr)n) When qr is small (1-qr)n ~ e-qrn => T(n) = β + (1 - e-λβ−nqr ) • At the beginning of each epoch, each backlogged node transmits with probability qr • New arrivals during the previous idle slot are also transmitted • With backlog n, the number of packets that attempt transmission at the beginning of an epoch is approximately Poisson with rate g(n) = λβ + nqr Eytan Modiano Slide 5