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Probabilistic Properties of Near-Optimal Trajectories of an Agent Moving Over a Lattice

Author

Listed:
  • Alexander Kuznetsov

    (Voronezh State University)

  • Elina Shishkina

    (Voronezh State University)

  • Sergey Sitnik

    (Belgorod National Research University)

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.

Suggested Citation

  • Alexander Kuznetsov & Elina Shishkina & Sergey Sitnik, 2019. "Probabilistic Properties of Near-Optimal Trajectories of an Agent Moving Over a Lattice," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 768-784, August.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-1374-6
    DOI: 10.1007/s10957-018-1374-6
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    References listed on IDEAS

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    1. Ellery, Adam J. & Baker, Ruth E. & McCue, Scott W. & Simpson, Matthew J., 2016. "Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 74-84.
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