Geometric Ergodicity of the ALOHA-system and a Coupled Processors Model
F. M. Spieksma · Probability in the Engineering and Informational Sciences · 1991
μ-Geometric ergodicity of two-dimensional versions of the ALOHA and coupled processors models is verified by checking μ-geometric recurrence. Ergodicity and convergence of the Laplace-Stieltjes transforms in a neighborhood of 0 are necessary and sufficient conditions for the first model. The second model is exponential, for which ergodicity suffices to establish the required results.