slotted aloha let g(n) be the attempt rate(the expected number of packets transmitted in a slot) in state n gn)=λ+nqr The number of attempted packets per slot in state n is approximately a poisson random variable of mean g(n) P(m attempts)=g(nme-9g(n)/m P(idle)= probability of no attempts in a slot =e g(n) p(success)= probability of one attempt in a slot g(n)e-g(n) P(collision = P(two or more attempts)=1-P(idle) -P(success)slotted aloha • let g(n) be the attempt rate (the expected number of packets transmitted in a slot) in state n g(n) = λ + nqr • The number of attempted packets per slot in state n is approximately a Poisson random variable of mean g(n) – P (m attempts) = g(n)me-g(n)/m! – P (idle) = probability of no attempts in a slot = e-g(n) – p (success) = probability of one attempt in a slot = g(n)e-g(n) – P (collision) = P (two or more attempts) = 1 - P(idle) - P(success) Eytan Modiano Slide 9