Exponential convergence rates for stochastically ordered Markov processes under perturbation

Julia Gaudio*, Saurabh Amin, Patrick Jaillet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Article number104515
JournalSystems and Control Letters
Volume133
DOIs
StatePublished - Nov 2019

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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