Quantitative Estimates of Stability in Controlled GI | D | 1 | #INF# Queueing Systems and in Control of Water Release in a Simple Dam Model

Evgueni Gordienko, Juan Ruiz de Chávez

2012

Abstract

We consider two applied discrete-time Markov control models: waiting times process in $\mbox{GI}\mid \mbox{D}\mid 1 \mid\infty$ queues with a controlled service rate and water release control in a simple dam model with independent water inflows. The stochastic dynamics of both models is determinated by a sequence of independent and identically distributed random variables with a distribution function $F$. In the situation when an available approximation $\tilde{F}$ is used in place of the unknown ${F}$, we estimate the deterioration of performance of control policies optimal with respect to the total discounted cost and the average cost per unit of time. For this purpose we introduce a stability index and find uppers bounds for this index expressed in terms of the Prokhorov distance between the distributions functions $F$ and $\tilde{F}$. When $\tilde{F} \equiv \tilde{F_{m}}$ is the empirical distribution function obtained from a sample of size m in average the stability index is less than a constant times $m^{\frac{-1}{3}}$.

Paper Citation

in Harvard Style

Gordienko E. and Ruiz de Chávez J. (2012). Quantitative Estimates of Stability in Controlled GI | D | 1 | #INF# Queueing Systems and in Control of Water Release in a Simple Dam Model . In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-21-1, pages 309-312. DOI: 10.5220/0004012603090312

in Bibtex Style

@conference{icinco12,
author={Evgueni Gordienko and Juan Ruiz de Chávez},
title={Quantitative Estimates of Stability in Controlled GI | D | 1 | #INF# Queueing Systems and in Control of Water Release in a Simple Dam Model},
booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2012},
pages={309-312},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004012603090312},
isbn={978-989-8565-21-1},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Quantitative Estimates of Stability in Controlled GI | D | 1 | #INF# Queueing Systems and in Control of Water Release in a Simple Dam Model
SN - 978-989-8565-21-1
AU - Gordienko E.
AU - Ruiz de Chávez J.
PY - 2012
SP - 309
EP - 312
DO - 10.5220/0004012603090312