Packing of nodes in a circle

Question

This is in a scenario of packing wireless transmitters in a circle with interference constraints. We would like to place $N$ nodes, transmitting at a fixed power $P_{T}$ in a circle of radius $R$. Each encounters interference from the $N-1$ others as per the power law: $$ P_{Int,i} = \sum_{j \neq i} P_{T}d_{ij}^{-\alpha} $$ where $d_{ij}$ is the distance between nodes $i$ and $j$. $\alpha$ is the path-loss exponent (usually between 2 and 4). What is the maximum number of nodes that can be placed in the circle, while obeying the interference constraint: $$ P_{Int,i} \leq P_{Thresh} $$ or, if there are any closed-form bounds on the answer.

Answer 1

I doubt very much that there is a closed-form solution. Packing problems tend to be hard. You might be able to get upper and lower bounds.