On the stochastic theory of compartments: The general time-dependent two-compartment reversible system with an application to manpower planning

In this paper a general time-dependent stochastic model for the analysis of the two-compartment reversible system with non-homogeneous Poisson inputs and arbitrary residence times in each of the compartments is presented. The transition probabilities are suitably modified in order to be useful for estimation purposes of the parameters of the model. Various results are derived in terms of the distributions of the residence times only are expressed in the form of convolution integrals which are readily evaluated by means of known computational algorithms. Finally, the theoretical results are applied to examples from the literature on manpower planning and some practical implications for the personnel and labour fields are considered.