Stability of heterogeneous slotted ALOHA networks

I. Lee and J.A. Silvester (1982) previously presented an iterative model for the throughput/delay performance of slotted ALOHA networks. This work was refined and extended by J.A. Silvester et al. (1989). In that paper, the authors presented results for various configurations, including single- and multi-hop for homogeneous and heterogeneous traffic requirements and network parameters. The authors investigate the stability issues for these networks in more detail using both exact analysis and the approximate model described by Silvester et al. The exact stability behavior of infinite buffer, homogeneous fully connected and ring networks is analyzed. The conditions for these networks to be stable, unstable, or overloaded are found. Specifically, an unstable network has two equilibrium points where one is locally stable and the other is unstable. The utility of the approximate model for stability analysis of heterogeneous networks is also demonstrated