An open tool to compute stochastic bounds on steady-state distributions and rewards

Abstract

We present X-Bounds, a new tool to implement a methodology based on stochastic ordering, algorithmic derivation of simpler Markov chains and numerical analysis of these chains. The performance indices defined by reward functions are stochastically bounded by reward functions computed on much simpler or smaller Markov chains obtained after aggregation or simplification. This leads to an important reduction on numerical complexity. Typically, chains are ten times smaller and the accuracy may be good enough.