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This paper provides stability and instability conditions for slotted Alohaunder the exponential backoff (EB) model with geometric law $i\mapstob^{-i-i_0}$, when transmission buffers are in saturation, i.e., always full. Inparticular, we prove that for any number of users and for $b>1$ the system is:(i) ergodic for $i_0 >1$, (ii) null recurrent for $0<i_0\le 1$, and (iii)transient for $i_0=0$. Furthermore, when referring to a system with queues andPoisson arrivals, the system is shown to be stable whenever EB in saturation isstable with throughput $\lambda_0$ and the system input rate is upper-boundedas $\lambda<\lambda_0$.

Stability and Instability Conditions for Slotted Aloha with Exponential Backoff