In this context, we would like to mention that the variation of broadcast capacity as a function of the number of nodes $N$ (located randomly inside a unit square) was studied in [@zheng06information-dissemination]; but the broadcast capacity in their paper increases with $N$ since they assume per-node power constraint.

As-You-Go Deployment of Relays on a Line of Unknown Length {#sec:mdp_total_power}
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Having developed the problem of placing a given number of relays over a line of fixed, given length, we now turn to the deploy-as-you-go problem. An agent walks along a line, starting from the source and heading towards the sink which is at an unknown distance from the source location, deploying relays as he goes, so as to achieve a multi-relay network when he encounters the sink location (and places the sink there). We model the distance from the source to sink as an exponentially distributed random variable with mean $\overline{L}=\frac{1}{\beta}$.[^6] The deployment objective is to achieve a high data rate from the source to the sink, subject to a total power constraint and a constraint on the expected number of relays placed (note that, the number of relay nodes, $N$, is a random variable here, due to the 