Geometrical Analysis of the Stability of Markov Chains in $R_+^n$ and Its Application to Throughput Evaluation of the Adaptive Random Multiple Access Algorithm

The method of stochastic Lyapunov functions is applied to derive sufficient conditions of recurrence and nonrecurrence of Markov chains with values in a many-dimensional Euclidean space. In the two-dimensional case, the stability conditions are stated in terms of the limit mean drift vector function. The results are applied to evaluate the throughput of an adaptive random multiple access algorithm for packets in a broadcasting channel with feedback.