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Authors: Evgueni Gordienko and Juan Ruiz de Chávez

Affiliation: Autonomous Metropolitan University - Iztapalapa, Mexico

Keyword(s): Queueing, Inventory and Water Release Models, Markov Control Process, Stability Index, Prokhorov Metric.

Related Ontology Subjects/Areas/Topics: Decision Support Systems ; Informatics in Control, Automation and Robotics ; Intelligent Control Systems and Optimization

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 $m^{\frac{-1}{3}}$. (More)

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Paper citation in several formats:
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; ISSN 2184-2809, SciTePress, pages 309-312. DOI: 10.5220/0004012603090312

@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},
issn={2184-2809},
}

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
IS - 2184-2809
AU - Gordienko, E.
AU - Ruiz de Chávez, J.
PY - 2012
SP - 309
EP - 312
DO - 10.5220/0004012603090312
PB - SciTePress

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