When performing analytical math on random graphs and point processes we usually tend to assume infinite sets, that is in order to enhance the tractability. However in practical systems and simulations we do not have an “infinite” space. A suggested workaround is to use Toroidal distances that convolves the flat simulation map similar to the famous “snakes” game.
Can Toriodal distance measure enhance the simulation accuracy of random graphs?
Is there any other method for counter-effect the edge problem ?
Toroidal distance reference in the Appendix of:
C. Bettstetter, "On the minimum node degree and connectivity of a wireless multihop network," in Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing, 2002, pp. 80-91.
Well, the answer is that it depends on the kind of simulation. For instance, if you consider a point on the origin (center of the simulation area) and you want to measure the outage probability, it won't enhance your results because the toroidal distance measure will always provide the points inside the simulation area. Hence, you will not see any difference.
However, if you want to measure e.g. the interference or the nearest neighbor of a random point (not necessarily on the origin), then it will eliminate the border effects and it will increase vastly the accuracy of your simulation results.
Thanks for you answer Prodromos, you are correct. The purpose here is a distributed measure rather than a single point centered at the origin.
Edge effect, which refers to the points which lie at the border of ur finite deployment area, can bias the results especially as mentioned for interference, number of neighbors, and transmitted power. I would highly recommend using the Toroidal distance to by-pass the edge effects.
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