Two models of time constrained target travel between two endpoints constructed by the application of Brownian motion and a random tour
Comstock, William Justin
Gaver, Donald P.
Eagle, James N.
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A target must chose a path between some origin and destination. The total travel times and the target speed are specified, and the target wishes to maximize the "randomness" of its track subject to the spatial and temporal constraints. Measures of effectiveness are developed against which the "randomness" of any path-producing method can reasonably be judged. Previous investigations into the scenario are reviewed and two models are developed, one using a random tour with drift and the other derived from Brownian motion. Statistics generated by Monte Carlo simulations for both models are compared. While the Brownian motion derived process is not always under perfect control of the constraints, if the timed arrival constraint may be slightly violated then that process performs better against the measures of effectiveness and is easier for a target to execute than is the random tour with drift.
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