1. Exponential convergence rates for stochastically ordered Markov processes under perturbation.
- Author
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Gaudio, Julia, Amin, Saurabh, and Jaillet, Patrick
- Subjects
- *
MARKOV processes , *ORDER picking systems , *TECHNOLOGY convergence , *RATES - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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