A Toolbox for Component-Wise Bounds for Steady-State Distribution of a DTMC

We present new algorithms we have recently introduced and which provide iterative component-wise bounds of the steady-state distribution of Markov chains. At each iteration we improve the quality of the bounds and these bounds are tight as the limit is the exact solution. As the algorithms are based on the product matrix-vector and properties of (max, +) sequences, they can easily be included into numerical packages. We present some examples and how we have implemented these algorithms in the Xborne tool.