Stability and Throughput of Buffered Aloha with Backoff

TL;DR

This paper analyzes the stability and throughput of buffered Aloha networks employing K-exponential backoff algorithms, providing conditions for stability, maximum throughput, and implications for finite and infinite node networks.

Contribution

It introduces a unified analytical method for stability and throughput of K-exponential backoff, including finite and infinite node scenarios, and addresses stability issues at undesired points.

Findings

K-exponential backoff is stable with proper retransmission factors for finite networks.

Maximum stable throughput is derived for geometric and exponential backoff.

Geometric retransmission is unstable in infinite networks, while exponential backoff can achieve stability with potential delays.

Abstract

This paper studies the buffered Aloha with K-exponential backoff collision resolution algorithms. The buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the multi-queue system into independent first-in-first-out (FIFO) queues, which are hinged together by the probability of success of head-of-line (HOL) packets. A unified method is devised to tackle the stability and throughput problems of K-exponential backoff with any cutoff phase K. For networks with a finite number of nodes, we show that the K-exponential backoff is stable if the retransmission factor is properly chosen from the stable region. The maximum stable throughput is derived and demonstrated via examples of geometric retransmission (K=1) and exponential backoff (K=infinity). For networks with an infinite number of nodes, we show that geometric retransmission is unstable, and the stable network throughput of exponential backoff can only be achieved at the cost of potential unbounded delay in each input queue. Furthermore, we address the stability issue of the systems at the undesired stable point. All analytical results presented in this paper are verified and confirmed by simulations.