Содержание
- 2. The problem in general
- 3. D2D connection between moving devices
- 4. The main steps of modeling 1. Construction of the Fokker-Planck equation, based on the empirical data
- 5. Generation of non-stationary trajectories of random walk
- 6. Kinetic approach Let the distribution function density f(x,t) of the trajectories coordinates at a given moment
- 7. Correctness of Fokker-Planck Equation for Empirical Distribution Sample averages (mean value and dispersion) for time-series are
- 8. Explicit scheme for t with right pattern for the second derivative over x is unstable: So
- 9. Typical example of drift u(x,t) This drift velocity is not a velocity of any physical body
- 10. Probability Density Evolution Model The density is treated to be symmetrical with respect to arguments (i.e.
- 11. Example of trajectories ensemble simulation
- 12. For any given set volume N we construct the distribution function G of distances between distribution
- 13. Correctness of ensemble generation Initially we have s uniformly distributed time series with sample length N
- 14. SIR Indicator Trajectory
- 15. SIR value in a continuous media From the previous step we have N random trajectories i=1,2,…,N
- 16. Example of 10 trajectories in square with reflection boundary conditions
- 17. Let us derive the evolution equation for average SIR value where f(r,t) is satisfied to the
- 18. Final Evolution Equation for Average SIR
- 19. SIR dispersion evolution equation – 1 Let us consider a SIR variance Then we obtain And
- 20. SIR dispersion evolution equation – 2 So we see, that it is very complex non-linear with
- 21. Stability D2D connection indicator If q(t)>1, the connection can be treated as a stable one, even
- 22. SIR Indicator Distribution Function
- 23. Typical SIR trajectory and SIR distribution
- 24. SIR DFD vs diffusion for zero drift
- 25. SIR DFD vs drift for zero diffusion
- 26. Analysis of D2D connection stability
- 27. The SIR standard deviation We consider two cases, i.e. two ensembles of trajectories: s(t) 1 (for
- 28. Indicator of stability We consider two cases, i.e. two ensembles of trajectories: s(t) 1 (for this
- 29. The SIR Simulation The first case (q>1) is more stable, than the second one (q
- 30. Distribution Function of the first break down moment
- 31. Simulation of empirical distribution function of the first break down moment Distribution functions of the first
- 32. Classical result for Brownian motion If the SIR behavior can be approximated by a standard Wiener
- 33. Simulation DFD for non-stationary random walk of subscribers The asymptotical bechaviour of DFD for large time
- 34. Analysis of cashing effects
- 35. Simulation results for DFD first break down with cashing T=1 T=2 On the horizontal axe –
- 36. Empirical dependence of the maximum continuity period on the cashing value
- 37. The type of normalized DFD
- 38. Conclusions Numerical simulation the SIR trajectory for an arbitrary pare of abonents, based on the random
- 39. The main references 1. Orlov Yu.N., Fedorov S.L. 2016. Modelirovanie raspredelenij funkcionalov na ansamble traektorij nestatsionarnogo
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