Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering

Stochastic Comparison and NCD Markov

This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the rst numerical results with the type of algorithm discussed. The given two-level algorithm uses aggregation and stochastic comparison with the strong stochastic (st) order. In order to improve accurac...

Stochastic bounds for a single server queue with general retrial times

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds‎. ‎The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques‎.

Quasi{lumpability, Lower Bounding Coupling Matrices, and Nearly Completely Decomposable Markov Chains

In this paper, it is shown that nearly completely decomposable (NCD) Markov chains are quasi{lumpable. The state space partition is the natural one, and the technique may be used to compute lower and upper bounds on the stationary probability of each NCD block. In doing so, a lower bounding nonnegative coupling matrix is employed. The nature of the stationary probability bounds is closely relat...

Directed Forests with Application to Algorithms Related to Markov Chains

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem.These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Mar...

On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains