Degree distributions in AB random geometric graphs

In this paper, we provide degree distributions for $AB$ random geometric graphs, in which points of type $A$ connect to the closest $k$ $B$. The motivating example derive such is 5G wireless networks with multi-connectivity, where users their base stations. It important know how many a particular station serves, gives that station. To obtain these distributions, investigate distribution area sizes $k-$th order Voronoi cells $B$-points. Assuming $A$-points are Poisson distributed, amount connected certain $B$-point, equal point. simple case $B$-points placed an hexagonal grid, show all $k$-th areas and thus degrees follow distribution. However, observation does not hold distributed $B$-points, follows compound Poisson-Erlang 1-dimensional case. We then approximate 2-dimensional Poisson-Gamma one-parameter fit performs well different values $k$. Moreover, increasing $k$, become more concentrated around mean. This means $k$-connected graphs balance loads $B$-type nodes evenly as increases. Finally, study on real data little shadowing distances between stations, capture data, especially $k>1$. under strong shadowing, our approximations perform quite good even non-Poissonian location data.