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In this paper we define a non-deterministic dynamic neighborhood model. As a special case, a linear neighborhood model is considered. When a non-deterministic neighborhood model functions, it is possible to introduce a restriction on the number of active layers, which will allow the variation of the non-determinism of the model at each moment of time. We give the notion of the non-determinacy measure and prove that it has the properties of a probability measure. We formulate the problem of reachability with partially specified parameters, layer priorities, and the non-determinacy measure. An algorithm for solving the attainability problem for a neighborhood model with variable indeterminacy and layer priorities is presented. An example of its solution is shown, which shows that when the priorities are compared and the measure of non-determinism is used, the solution of the problem can be obtained more quickly than by a method that does not use priorities. [ABSTRACT FROM AUTHOR]