On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

Markov chain convergence: From finite to infinite

Rosenthal, Jeffrey S.

Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by ...

A functional limit theorem for continuous Markov processes

Ankirchner, Stefan
Kruse, Thomas
Urusov, Mikhail

August 2018

We present an algorithm for approximating one-dimensional regular continuous strong Markov processes...

Diffusion limits for networks of Markov-modulated infinite-server queues

Jansen, H. M.
Mandjes, M.
De Turck, K.
Wittevrongel, S.

November 2019

This paper studies the diffusion limit for a network of infinite-server queues operating under Marko...

On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

Zeifman A.
Sipin A.
Korolev V.
Shilova G.
Kiseleva K.
Korotysheva A.
Satin Y.

Finite inhomogeneous continuous-time Markov chains are studied. For a wide class of such processes a...

Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Zeifman A.
Razumchik R.
Satin Y.
Kiseleva K.
Korotysheva A.
Korolev V.

In this paper we present a method for the computation of convergence bounds for four classes of mult...

Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space

Zeifman A.I.
Korolev V.Y.
Satin Y.A.
Kiseleva K.M.

March 2020

An approach is proposed to the construction of general lower bounds for the rate of convergence of p...

On three methods for bounding the rate of convergence for some continuous–time Markov chains

Zeifman Alexander
Satin Yacov
Kryukova Anastasia
Razumchik Rostislav
Kiseleva Ksenia
Shilova Galina

June 2020

Consideration is given to three different analytical methods for the computation of upper bounds for...

Bounding the Rate of Convergence for One Class of Finite Capacity Time Varying Markov Queues

Zeifman A.
Satin Y.
Razumchik R.
Kryukova A.
Shilova G.

Consideration is given to the two finite capacity time varying Markov queues: the analogue of the we...

Bounds on the Rate of Convergence for <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">t</mi><mi mathvariant="bold-italic">X</mi></msubsup></mrow></semantics></math></inline-formula>/<inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">t</mi><mi mathvariant="bold-italic">X</mi></msubsup></mrow></semantics></math></inline-formula>/1 Queueing Models

Alexander Zeifman
Yacov Satin
Alexander Sipin

July 2021

We apply the method of differential inequalities for the computation of upper bounds for the rate of...

Quantitative bounds on convergence of time-inhomogeneous Markov Chains

R. Douc
E. Moulines
Jeffrey S. Rosenthal

January 2002

Convergence rates of Markov chains have been widely studied in recent years. In particu-lar, quantit...

On the class of Markov chains with finite convergence time

Subelman, Eduardo J.

August 1976

AbstractWe study the necessary and sufficient conditions for a finite ergodic Markov chain to conver...

An adiabatic approach to analysis of time inhomogeneous Markov chains : a queueing policy application

September 2011

Graduation date: 2012In this thesis, convergence of time inhomogeneous Markov chains is studied usin...

Markov chain convergence: From finite to infinite, Stochastic processes and their Applications 62

Jeffrey S. Rosenthal

January 1996

Summary. Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated la...

Bounds for markovian queues with possible catastrophes

Zeifman A.
Korotysheva A.
Satin Y.
Kiseleva K.
Korolev V.
Shorgin S.

We consider a general Markovian queueing model with possible catastrophes and obtain new and sharp b...

Bounds and approximations for continuous-time Markovian transition probabilities and large systems

Mercier, Sophie

January 2008

International audienceWe propose new bounds and approximations for the transition probabilities of a...

Markov chain convergence: From finite to infinite

Rosenthal, Jeffrey S.

Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by ...

A functional limit theorem for continuous Markov processes

Ankirchner, Stefan
Kruse, Thomas
Urusov, Mikhail

August 2018

We present an algorithm for approximating one-dimensional regular continuous strong Markov processes...

Diffusion limits for networks of Markov-modulated infinite-server queues

Jansen, H. M.
Mandjes, M.
De Turck, K.
Wittevrongel, S.

November 2019

This paper studies the diffusion limit for a network of infinite-server queues operating under Marko...

On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

Zeifman A.
Sipin A.
Korolev V.
Shilova G.
Kiseleva K.
Korotysheva A.
Satin Y.

Finite inhomogeneous continuous-time Markov chains are studied. For a wide class of such processes a...

Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Zeifman A.
Razumchik R.
Satin Y.
Kiseleva K.
Korotysheva A.
Korolev V.

In this paper we present a method for the computation of convergence bounds for four classes of mult...

Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space

Zeifman A.I.
Korolev V.Y.
Satin Y.A.
Kiseleva K.M.

March 2020

An approach is proposed to the construction of general lower bounds for the rate of convergence of p...

On three methods for bounding the rate of convergence for some continuous–time Markov chains

Zeifman Alexander
Satin Yacov
Kryukova Anastasia
Razumchik Rostislav
Kiseleva Ksenia
Shilova Galina

June 2020

Consideration is given to three different analytical methods for the computation of upper bounds for...

Bounding the Rate of Convergence for One Class of Finite Capacity Time Varying Markov Queues

Zeifman A.
Satin Y.
Razumchik R.
Kryukova A.
Shilova G.

Consideration is given to the two finite capacity time varying Markov queues: the analogue of the we...

Bounds on the Rate of Convergence for <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">t</mi><mi mathvariant="bold-italic">X</mi></msubsup></mrow></semantics></math></inline-formula>/<inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">t</mi><mi mathvariant="bold-italic">X</mi></msubsup></mrow></semantics></math></inline-formula>/1 Queueing Models

Alexander Zeifman
Yacov Satin
Alexander Sipin

July 2021

We apply the method of differential inequalities for the computation of upper bounds for the rate of...

Quantitative bounds on convergence of time-inhomogeneous Markov Chains

R. Douc
E. Moulines
Jeffrey S. Rosenthal

January 2002

Convergence rates of Markov chains have been widely studied in recent years. In particu-lar, quantit...

On the class of Markov chains with finite convergence time

Subelman, Eduardo J.

August 1976

AbstractWe study the necessary and sufficient conditions for a finite ergodic Markov chain to conver...

An adiabatic approach to analysis of time inhomogeneous Markov chains : a queueing policy application

September 2011

Graduation date: 2012In this thesis, convergence of time inhomogeneous Markov chains is studied usin...

Markov chain convergence: From finite to infinite, Stochastic processes and their Applications 62

Jeffrey S. Rosenthal

January 1996

Summary. Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated la...

Bounds for markovian queues with possible catastrophes

Zeifman A.
Korotysheva A.
Satin Y.
Kiseleva K.
Korolev V.
Shorgin S.

We consider a general Markovian queueing model with possible catastrophes and obtain new and sharp b...

Bounds and approximations for continuous-time Markovian transition probabilities and large systems

Mercier, Sophie

January 2008

International audienceWe propose new bounds and approximations for the transition probabilities of a...

Markov chain convergence: From finite to infinite

Rosenthal, Jeffrey S.

Bounds on convergence rates for Markov chains are a very widely-studied topic, motivated largely by ...

A functional limit theorem for continuous Markov processes

Ankirchner, Stefan
Kruse, Thomas
Urusov, Mikhail

August 2018

We present an algorithm for approximating one-dimensional regular continuous strong Markov processes...

Diffusion limits for networks of Markov-modulated infinite-server queues

Jansen, H. M.
Mandjes, M.
De Turck, K.
Wittevrongel, S.

November 2019

This paper studies the diffusion limit for a network of infinite-server queues operating under Marko...

On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

Abstract

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On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

Abstract

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