Stability of Manpower Systems

Members of an organization belong to one of the grades (1, 2,... k), and movements between grades are governed by a substochastic matrix P. The model can be deterministic, stochastic, or partially stochastic; and we may or may not insist that the total size be restored to a fixed quantity each year. Various notions of the stability of a structure x = (x₁, x₂, … x _k ), where x _i represents the number, or proportion, in grade i are considered. Mainly, but not exclusively, the case when P is upper triangular is considered.