Stability and Instability Conditions for Slotted Aloha with Exponential Backoff

TL;DR

This paper analyzes the stability conditions of slotted Aloha with exponential backoff, providing precise criteria for ergodicity, null recurrence, and transience based on system parameters and buffer states.

Contribution

It establishes exact stability and instability conditions for slotted Aloha with exponential backoff in saturated buffers, extending understanding of system behavior under various parameters.

Findings

System is ergodic for i_0 > 1

System is null recurrent for 0 < i_0 ≤ 1

System is transient for i_0 = 0

Abstract

This paper provides stability and instability conditions for slotted Aloha under the exponential backoff (EB) model with geometric law $i\mapsto b^{-i-i_0}$, when transmission buffers are in saturation, i.e., always full. In particular, 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 and Poisson arrivals, the system is shown to be stable whenever EB in saturation is stable with throughput $\lambda_0$ and the system input rate is upper-bounded as $\lambda<\lambda_0$.