Stability Analysis of Hybrid ALOHA

  • Huahui Wang1 and

    Affiliated with

    • Tongtong Li1Email author

      Affiliated with

      EURASIP Journal on Wireless Communications and Networking20102010:753931

      DOI: 10.1155/2010/753931

      Received: 22 March 2010

      Accepted: 4 August 2010

      Published: 9 August 2010

      Abstract

      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 ( http://static-content.springer.com/image/art%3A10.1155%2F2010%2F753931/MediaObjects/13638_2010_Article_2020_IEq1_HTML.gif ) has been conducted in our previous work. In this paper, we study the stability region of hybrid ALOHA for the general N-user ( http://static-content.springer.com/image/art%3A10.1155%2F2010%2F753931/MediaObjects/13638_2010_Article_2020_IEq2_HTML.gif ) 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 http://static-content.springer.com/image/art%3A10.1155%2F2010%2F753931/MediaObjects/13638_2010_Article_2020_IEq3_HTML.gif 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.

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      Authors’ Affiliations

      (1)
      Department of Electrical and Computer Engineering, Michigan State University

      Copyright

      © Huahui Wang and Tongtong Li. 2010

      This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.