Instability of slotted aloha if backlog increases beyond unstable point (bad luck then it tends to increase without limit and the departure rate drops to o Aloha is inherently unstable and needs algorithm to keep it stable Drift in state n, D(n)is the expected change in backlog over one time slot Dn)=λ-P( success=λ-g(n)e9 negative drift Departure rate negative drift Arrival rate Stable Unstable G=0|G=1 G=λ+n Slide 10λ λ Instability of slotted aloha • if backlog increases beyond unstable point (bad luck) then it tends to increase without limit and the departure rate drops to 0 – Aloha is inherently unstable and needs algorithm to keep it stable • Drift in state n, D(n) is the expected change in backlog over one time slot – D(n) = λ - P(success) = λ - g(n)e-g(n) negative drift positive drift G=0 e G=1 Ge-G -1 λ Arrival rate Departure rate Stable Unstable negative drift positive drift Eytan Modiano G = λ + nqr Slide 10