We apply regenerative theory to derive certain relations between steady state probabilities of a Markov chain. These relations are then used to develop a numerical algorithm to find these probabilities. The algorithm is a modification of the Gauss-Jordan method, in which all elements used in numerical computations are nonnegative; as a consequence, the algorithm is numerically stable.

GDM may be an important driver for the T2DM epidemic in many subpopulations. Because GDM is a readily identifiable, preventable, and treatable condition, investments in prevention, rapid diagnosis, and evidence-based treatment of GDM in at-risk populations may offer substantial benefit in lowering the T2DM burden over many generations. Model-informed data collection can aid in assessing intervention tradeoffs.

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In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

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