7 research outputs found
Two approaches to the construction of perturbation bounds for continuous-time Markov chains
The paper is largely of a review nature. It considers two main methods used
to study stability and obtain appropriate quantitative estimates of
perturbations of (inhomogeneous) Markov chains with continuous time and a
finite or countable state space. An approach is described to the construction
of perturbation estimates for the main five classes of such chains associated
with queuing models. Several specific models are considered for which the limit
characteristics and perturbation bounds for admissible "perturbed" processes
are calculated
On the Three Methods for Bounding the Rate of Convergence for some Continuous-time Markov Chains
Consideration is given to the three different analytical methods for the
computation of upper bounds for the rate of convergence to the limiting regime
of one specific class of (in)homogeneous continuous-time Markov chains. This
class is particularly suited to describe evolutions of the total number of
customers in (in)homogeneous queueing systems with possibly
state-dependent arrival and service intensities, batch arrivals and services.
One of the methods is based on the logarithmic norm of a linear operator
function; the other two rely on Lyapunov functions and differential
inequalities, respectively. Less restrictive conditions (compared to those
known from the literature) under which the methods are applicable, are being
formulated. Two numerical examples are given. It is also shown that for
homogeneous birth-death Markov processes defined on a finite state space with
all transition rates being positive, all methods yield the same sharp upper
bound
On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models
Finite inhomogeneous continuous-time Markov chains are studied. For a wide class of such processes an approach is proposed for obtaining sharp bounds on the rate of convergence to the limiting characteristics. Queueing examples are considered. © 2018, Springer International Publishing AG
On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models
Finite inhomogeneous continuous-time Markov chains are studied. For a wide class of such processes an approach is proposed for obtaining sharp bounds on the rate of convergence to the limiting characteristics. Queueing examples are considered. © 2018, Springer International Publishing AG