Exponential convergence rates for stochastically ordered Markov processes under perturbation

Julia Gaudio; Saurabh Amin; Patrick Jaillet

doi:10.1016/j.sysconle.2019.104515

Exponential convergence rates for stochastically ordered Markov processes under perturbation

Julia Gaudio^*, Saurabh Amin, Patrick Jaillet

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this technical note we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge.

Original language	English (US)
Article number	104515
Journal	Systems and Control Letters
Volume	133
DOIs	https://doi.org/10.1016/j.sysconle.2019.104515
State	Published - Nov 2019

Funding

We thank the anonymous reviewers for their comments. This work was partially supported by the National Research Foundation Singapore through the Singapore-MIT Alliance for Research and Technology (SMART) Centre for Future Urban Mobility (FM). Julia Gaudio is supported by a Microsoft Research PhD Fellowship. We thank the anonymous reviewers for their comments. This work was partially supported by the National Research Foundation Singapore through the Singapore-MIT Alliance for Research and Technology (SMART) Centre for Future Urban Mobility (FM). Julia Gaudio is supported by a Microsoft Research PhD Fellowship.

Keywords

Markov processes
Queueing

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

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title = "Exponential convergence rates for stochastically ordered Markov processes under perturbation",

abstract = "In this technical note we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge.",

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T1 - Exponential convergence rates for stochastically ordered Markov processes under perturbation

AU - Gaudio, Julia

AU - Amin, Saurabh

AU - Jaillet, Patrick

PY - 2019/11

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N2 - In this technical note we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge.

AB - In this technical note we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge.

KW - Markov processes

KW - Queueing

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JO - Systems and Control Letters

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ER -

Exponential convergence rates for stochastically ordered Markov processes under perturbation

Abstract

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Keywords

ASJC Scopus subject areas

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