Stability Analysis of Hybrid ALOHA

We perform stability analysis of a recently proposed MAC protocol, hybrid ALOHA, based on the multipacket reception (MPR) model. Hybrid ALOHA distinguishes from conventional slotted ALOHA by allowing conditional collision-free channel estimation and simultaneous transmissions, and hence improves the MPR capability of the system. The stability analysis of the two-user case (N = 2) has been conducted in our previous work. In this paper, we study the stability region of hybrid ALOHA for the generalNuser (N > 2) system. By using the method of stochastic dominance and mathematical induction, we obtain the sufficient condition for the stability of hybrid ALOHA. As an illustration, we characterize the stability inner bounds for theN = 3 case. In this particular situation, the results are derived by solving a nonhomogeneous Riemann-Hilbert problem. Potentially, themathematical tools used in this paper can be exploited for obtaining closed-form results in stability analysis of wireless networks.