A semi-Markov model for a multigrade population with Poisson recruitment

Abstract

We consider a multigrade population with semi-Markov transitions between grades, Poisson arrivals to each grade, and departures from each grade. For this model the joint distribution of the numbers in each grade at any time is found, and the limiting distributions shown to be independently Poisson; this extends a previous result for a multigrade population with Markov transitions and Poisson recruitment.This model is particularly applicable to manpower planning. The inclusion of semi-Markov transitions allows us to take into account existing knowledge of the distribution of length of service until an individual leaves his firm.