An algorithmic approach for a special class of Markov chains (Q797477)

The paper gives an algorithm for solving special systems of linear equations occurring e.g. when calculating the steady state probabilities for queuing models. The linear system has to be of the form \(xR=d\) where x and d are m-vectors, \(d=(0,0,...,0,1)\), \(R=L+U\) is an \(m\times m\)- matrix, L is lower triangular with nonzero diagonal elements and U is upper triangular with only \(\ell(<m)\) nonzero columns. So, essentially only a linear system of the size \(\ell \times \ell\) has to be solved.