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

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.