| Abstract: | A continuous time Markov-renewal model is presented that generalizes the classical Young and Almond model for manpower systems with given size. The construction is based on the associated Markov-renewal replacement process and exploits the properties of the embedded replacement chain. The joint cumulant generating function of the grade sizes is derived and an asymptotic analysis provides conditions for these to converge in distribution to a multinominal random vector exponentially fast independently of the initial distribution, both for aperiodic and periodic embedded replacement chains. A regenerative approach to the wastage process is outlined and two numerical examples from the literature on manpower planning illustrate the theory. |
