Stability Analysis of Hybrid ALOHA
Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
EURASIP Journal on Wireless Communications and Networking 2010, 2010:753931 doi:10.1155/2010/753931Published: 9 August 2010
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 () has been conducted in our previous work. In this paper, we study the stability region of hybrid ALOHA for the general N-user () 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 the case. In this particular situation, the results are derived by solving a nonhomogeneous Riemann-Hilbert problem. Potentially, the mathematical tools used in this paper can be exploited for obtaining closed-form results in stability analysis of wireless networks.