Geodesic
On the distribution of the time of the first communication release in wireless networks with caching
Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 131-142

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The function analyzes the time distribution of the first communication failure in D2D wireless networks as a function of the caching time, assuming that subscribers make a nonstationary random walk. This distribution function is constructed numerically on the basis of generation of an ensemble of nonstationary trajectories, a series of incremental increments of which is determined by solving the Fokker–Planck equation in the unit square in the plane with mirror reflection conditions from the boundaries. This method allows you to effectively solve the problems of stochastic control and analyze the conditions for the stability of connections in wireless networks.
Keywords: wireless connection, caching, kinetic equation, random walk modeling, time distribution of the first clipping. 
@article{MM_2018_30_8_a8,
     author = {Yu. N. Orlov and A. A. Russkov and Yu. V. Gaidamaka and K. E. Samouylov},
     title = {On the distribution of the time of the first communication release in wireless networks with caching},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {131--142},
     publisher = {mathdoc},
     volume = {30},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_8_a8/}
}
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Yu. N. Orlov; A. A. Russkov; Yu. V. Gaidamaka; K. E. Samouylov. On the distribution of the time of the first communication release in wireless networks with caching. Matematičeskoe modelirovanie, Tome 30 (2018) no. 8, pp. 131-142. http://geodesic.mathdoc.fr/item/MM_2018_30_8_a8/