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A semi-Markovian population model can be used to describe patient movements in a health-care delivery system. The recovery progress of a patient at any time is defined by one of a finite number of "states." The movement of a patient among the states is governed by a discrete-time semi-Markov process which is called a " path." The inputs to the system are various patient "groups." Each group is characterized by a distinct input distribution with known mean and variance. Assuming that the input distributions are relatively stable in the long run, estimates of the means and variances of steady-state census mix are derived. On a short-term basis, the model will accommodate daily fluctuations in input distributions and use an information vector, which summarizes the state of the system at the time of prediction, to improve the estimation. An illustrative example using field data is presented.