Near complete decomposability: Bounding the error by a stochastic comparison method

An aggregation technique of ‘near complete decomposable’ Markovian systems has been proposed by Courtois. It is an approximate method in many cases, except for some queuing networks, so the error between the exact and the approximate solution is an important problem. We know that the error is O(ϵ), where ϵ is defined as the maximum coupling between aggregates. Some authors developed techniques to obtain a O(ϵ^k) error with k > 1 error with k > 1, while others developed a technique called ‘bounded aggregation’. All these techniques use linear algebra tools and do not utilize the fact that the steady-state probability vector represents the distribution of a random variable. In this work we propose a stochastic approach and we give a method to obtain stochastic bounds on all possible Markovian approximations of the two main dynamics: short-term and long-term dynamics.