The Recruitment Trajectory Corresponding to Particular Stock Sequences in Markovian Person-Flow Models

Preston (Preston, S. H. 1970. The birth trajectory corresponding to particular population sequences. Theoret. Population Biol.1 346–351.) treats the following problem: Given an exponential or linear sequence of population numbers, and assuming constant mortality and zero net migration, what birth sequence is required? In the following paper this question is investigated for more general person-flow models, namely for Markovian manpower models in the sense of Young & Almond (see Bartholomew [Bartholomew, D. J. 1973. Stochastic Models for Social Processes. Wiley, London.]). Considering the linear population-dynamic (Leslie) model as a special case, most of the results obtained by Preston may be derived. The general problem “what sequence of recruitment numbers is capable of generating a desired stock trajectory” is analyzed by means of inhomogeneous Markov chains. This technique yields also a new approach to the limiting behaviour of some manpower systems.