Finding a continuous-time Markov chain via sparse stochastic matrices in manpower systems

We consider a manpower system with finite discrete non-overlapping states where recruitment is done to replace wastage and to achieve the desired growth. The states of the system are defined in terms of the ranks. Data for the evolution of manpower structure in the system may be obtained at any choice of time instants. The empirical stochastic matrix resulting from the evolution of the system at each time instant is sparse. We propose a transition model for the system where the multi-step empirical stochastic matrix is expressed as the exponential of a Markov generator. We give illustrations using academic staff data in a university setting.