Decomposable stochastic networks: Some observations

Abstract

Global balance equations of the type pQ=O, where Q is the transition intensity matrix of an irreducible ergodic Markov chain and p is the corresponding invariant probability vector, sometimes exhibit a property of so-called partial balance. In all such examples known to the author, such partial balance means that Q can be written in a nontrivial way as Q=ΣQ_i, where the Q_i are themselves transition intensity matrices and satisfy pQ_i=O for the mentioned p. The paper elaborates on this phenomenon.