A continuous-time population model with poisson recruitment

A continuous-time model of a multigrade system is developed, which includes Poisson arrivals, interaction between grades and a leaving process. It therefore constitutes a continuous-time analogue of Pollard's hierarchical population model with Poisson recruitment. An expression is found for the first and second moments of grade size at any time. A general formulation of the joint probability generating function of the numbers in each grade is given, and the limiting distribution of grade size is shown to be Poisson.