Closing the gap in the multicast capacity of hybrid wireless networks

We study the <i>multicast capacity</i> of a random wireless network consisting of <i>n</i> randomly placed <i>ordinary wireless nodes</i> and <i>m</i> regularly placed <i>base stations</i> in a square region, known as a <i>hybrid network</i>. All ordinary wireless nodes have the uniform transmission range <i>r</i> and uniform interference range <i>R</i>=θ<i>(r)</i> and they can transmit/receive at <i>W<sub>a</sub></i>-bps. Each base station can communicate with adjacent base stations directly with a data rate <i>W<sub>B</sub></i>-bps and the data transmission rate between a base station and a wireless node is assumed to be <i>W<sub>c</sub></i>-bps. Assume that there is a random set of <i>n<sub>s</sub></i> ordinary wireless nodes that will serve as the source nodes of <i>n<sub>s</sub></i> multicast flows (each has randomly selected <i>k</i>-1 receivers). Each flow will have data rate λ<i><sub>i</sub></i> bps. We found that the minimum per-flow multicast capacity min <i>n</i> <i><sub>s</sub></i> over <i>i</i> = 1 λ<i><sub>i</sub></i> for hybrid networks has three regimes, and for each regime we derive matching asymptotic upper and lower bounds. Thus it closes the gap of previous results in the literature.

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