slotted aloha Let g be the attempt rate(the expected number of packets transmitted in a slot) The number of attempted packets per slot is approximately a poisson random variable of mean g=n+n*qr q e probability that a backlogged packet is retransmitted in a slot n= number of backlogged packets P(m attempts)=gme 9/m P(idle)= probability of no attempts in a slot=e 9 p(success)=probability of one attempt in a slot= ge9 P(collision)=P (two or more attempts)=1-P(idle)-P(success Eytan Modianoλ slotted aloha • Let g be the attempt rate (the expected number of packets transmitted in a slot) – The number of attempted packets per slot is approximately a Poisson random variable of mean g = λ + n*qr qr = probability that a backlogged packet is retransmitted in a slot n = number of backlogged packets – P (m attempts) = gme-g/m! – P (idle) = probability of no attempts in a slot = e-g – p (success) = probability of one attempt in a slot = ge-g – P (collision) = P (two or more attempts) = 1 - P(idle) - P(success) Eytan Modiano Slide 8