Equivalence criterion for the global and detailed balance equations of Markov chains (Q1287297)

The central problem in the study of mathematical models based on the Markov processes is the solution of the Kolmogorov equations for the stationary states of these models. For Markov chains these linear algebraic equations are called the global balance equations. The dimension of this system is equal to the number of states and hence it can be quite large and difficult to solve. The authors give conditions for the transition probabilities of a Markov chain so that the equations of global and detailed balance are equivalent. A mathematical model for an adaptive terminal measurement system is formulated as a queueing system satisfying these conditions.