Error Bounds for Arbitrary Approximations of "Nearly Reversible" Markov Chains and an Aloha-Applications
Nico M. Van DIJK, P.J. Veltkamp · RePEc: Research Papers in Economics · 1991
A condition is provided to conclude error bounds for an arbitrary steady state approximation of a "nearly reversible" Markov chain.The error bound is of the form A.R, where (i)A can be computed merely by the approximation in order, (ii) R is to be obtained by bounding so-called bias terms for the system of interest.This can be established analytically.The results will be illustrated for ALOHA-type systems with different source characteristics.An approximation is suggested based on truncating the corresponding Mobiüs-function.The R-value is computed by an inductive Markov reward prooftechnique.Numerical illustration indicates that the analytic error bound can be reasonable for practical purposes.Keyvords Markov chain * Approximation * Error bound * Nearly reversible * Bias terms * ALOHA-systems.