Discrete time Reward Models for homogeneous semi-Markov Systems

Previously,continuous time Markov and semi Markow models have been developed for a multi-grade system with a number of transient states and a single absorbing state.Such systems have been studied with Poisson arrivals with known growth.Such models have been applied to manpower planning and the movement of patients through a hospital system.In this paper,we develop a reward model for a discrete time homogeneous semi Markov system with Poisson arrivals and the same model where the system has growth with known size at each time point.Discrete time is employed here to accommodate a discrete reward structure.Results are obtained for the distribution,and mean of daily rewards of such system at any time,and in steady state;the expected reward in a period of time is also determined.These results are illustrated using data on employees moving through a company hierarchy and data for hospital patients. Key Words: Homogeneity; Poisson recruitment; Semi-Markov process; Stochastic population model; Rewards.