On the Stability of Hybrid ALOHA

Abstract

In this paper, we investigate the stability of a general N-user hybrid ALOHA system. Based on the multipacket reception model, the hybrid ALOHA protocol was proposed and the stability region in the case of N = 2 was presented. Utilizing the result for N = 2, in this paper, by means of stochastic dominance and mathematical induction, we find out the sufficient condition for the stability of the more general N > 2 system. In particular, the N = 3 case is closely studied. It is shown that the stability inner bound of the N = 3 system can be obtained by solving a general Riemann-Hilbert problem.