Stability and Capacity of Wireless Networks with Probabilistic Receptions: Part I—General Topologies

We study the stability and the capacity problems in packetized wireless networks. Communication medium is modeled using probability density functions that determine the packet reception probabilities. The model subsumes several previous models as special cases, and it is suitable for networks with timevarying topology and channels. Our main result is a characterization of the stability and the capacity regions using network flows. We also introduce a class of control policies sufficient to achieve every rate inside these regions. In Part II, we apply the proposed policies and the flow analysis to regular networks. We obtain closed-form expressions for the capacity of Manhattan networks (two-dimensional grid) and ring networks (circular array of nodes). We analyze the performance loss due to suboptimal medium access and routing. We also investigate the impact of link fading, link state information, and variable connectivity on achievable rates in Manhattan networks.