Abstract
The paper considers probabilistic properties of the trajectory of a moving agent. The agent finds a route close to the optimal one on a lattice consisting of cells with different impassabilities. We study the distribution of the agent’s exit time to the end point for random landscapes of different types using a special sort of simulation. After that, we compare the obtained empirical probability density function with the probability density function derived from theoretical considerations. We also obtain the probability density function for the ratio of Rician and uniform random variables. Finally, the probability distribution of the agent’s residence in a given cell at a given moment of time for random landscapes of different types is analyzed.
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References
Kuznetsov, A.V.: A model of the joint motion of agents with a three-level hierarchy based on a cellular automaton. Comput. Math. Math. Phys. 57(2), 340–349 (2017)
Kuznetsov, A.V.: A simplified combat model based on a cellular automaton. J. Comput. Syst. Sci. Int. 56(3), 397–409 (2017)
Kuznetsov, A.V.: Cellular automata-based model of group motion of agents with memory and related continuous model. In: Sazhin, S., Shchepakina, E., Sobolev, V., Kudryashov, D. (eds.) Mathematical Modeling. Information Technology and Nanotechnology 2017, no. 1904 in CEUR Workshop Proceedings, Aachen, pp. 223–231 (2017)
Kuznetsov, A.V.: On the motion of agents across terrain with obstacles. Comput. Math. Math. Phys. 58(1), 137–151 (2018)
Kuznetsov, A.V.: Generation of a random landscape by given configuration entropy and total edge. Comput. Technol. 22(4), 4–10 (2017)
Ellery, A.J., Baker, R.E., McCue, S.W., Simpson, M.J.: Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes. Phys. A Stat. Mech. Appl. 449(Supplement C), 74–84 (2016)
Buchin, K., Sijben, S., van Loon, E.E., Sapir, N., Mercier, S., Marie Arseneau, T.J., Willems, E.P.: Deriving movement properties and the effect of the environment from the brownian bridge movement model in monkeys and birds. Mov. Ecol. 3(1), 18 (2015)
Adamatzky, A.I., De Lacy Costello, B.P., Melhuish, C., Ratcliffe, N.: Experimental reaction–diffusion chemical processors for robot path planning. J. Intell. Robot. Syst. 37(3), 233–249 (2003)
Adamatzky, A.I., De Lacy Costello, B.P.: Reaction–diffusion path planning in a hybrid chemical and cellular-automaton processor. Chaos Solitons Fractals 16(5), 727–736 (2003)
Schumann, A.: Proof-theoretic cellular automata as logic of unconventional computing. Int. J. Unconv. Comput. 8(3), 263–280 (2012)
Schumann, A.: Payoff cellular automata and reflexive games. J. Cell. Autom. 9(4), 287–313 (2014)
Schumann, A.: Towards context-based concurrent formal theories. Parallel Process. Lett. 25(01), 1540008 (2015)
Adamatzky, A.I.: Voronoi-like partition of lattice in cellular automata. Math. Comput. Model. 23(4), 51–66 (1996)
Gumbel, E.: Les valeurs extremes des distributions statistiques. Ann. Inst. Henri Poincaré 5, 115–158 (1935)
Acknowledgements
Work of S. M. Sitnik was supported by the State Contract of the Russian Ministry of Education and Science (Contract No. 1.7311.2017/8.9).
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Kuznetsov, A., Shishkina, E. & Sitnik, S. Probabilistic Properties of Near-Optimal Trajectories of an Agent Moving Over a Lattice. J Optim Theory Appl 182, 768–784 (2019). https://doi.org/10.1007/s10957-018-1374-6
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DOI: https://doi.org/10.1007/s10957-018-1374-6