Algorithm 2. Proposed Algorithm to obtain Average Normalized Throughput

Input: $\left(s_k,k\in N_j\right)$; Output: Average Normalized Throughput $Th\left(s^t\right)$

(1)Neighbors of node $j$ provide their target service rates. (2)Local optimization function (6) is solved using Newton’s method of optimization for node $j$ with its surrounding neighbors and the maximum achievable service rates is locally obtained for all feasible schedules of the neighborhood. (3)Node $j$ and each neighbor from $k\in N_j$ provide their locally maximum achievable service rates. (4)The average achievable service rate can be calculated for each node separately by averaging the service rates in each neighborhood contained in that node. (5) Calculate the approximate error between the achieved and the target service rates: $$e\left(s^t\right)=\frac{{{\displaystyle \sum }}_{i=1}^N\left|s_i^t-s_i^a\right|}{N},$$ (7) where $s^a={[s_i^a]}_{i=1}^N$ are the service rates that can be achieved and $s^t={[s_i^t]}_{i=1}^N$ is the given target service rate vector. (6) Compute the average normalized throughput: $$Th\left(s^t\right)=\frac{{{\displaystyle \sum }}_{i=1}^N{s}_i^t\left(1-e\left(s^t\right)\right)}{N},$$ (8) (7)Use Polynomial interpolation to form the average normalized throughput equations as a function of either—number of nodes and target service rates or SINR threshold and target service rates. Polynomial interpolation is also used to get the maximum normalized throughput as a function of the number of nodes.