Augmented infinitesimal perturbation analysis: An alternate explanation

Alexei A. Gaivoronski; Leyuan Y. Shi; Ramavarapu S. Sreenivas

doi:10.1007/BF01797724

Augmented infinitesimal perturbation analysis: An alternate explanation

Alexei A. Gaivoronski, Leyuan Y. Shi, Ramavarapu S. Sreenivas

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

Abstract

Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented by generalized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.

Original language	English (US)
Pages (from-to)	121-138
Number of pages	18
Journal	Discrete Event Dynamic Systems
Volume	2
Issue number	2
DOIs	https://doi.org/10.1007/BF01797724
State	Published - Nov 1992
Externally published	Yes

Keywords

DEDS
IPA
performance analysis

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Electrical and Electronic Engineering

Online availability

10.1007/BF01797724

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T2 - An alternate explanation

AU - Gaivoronski, Alexei A.

AU - Shi, Leyuan Y.

AU - Sreenivas, Ramavarapu S.

PY - 1992/11

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N2 - Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented by generalized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.

AB - Augmented infinitesimal perturbation analysis (APA) was introduced by Gaivoronski [1991] to increase the purview of the theory of Infinitesimal Perturbation Analysis (IPA). In reference [Gaivoronski 1991] it is shown that an unbiased estimate for the gradient of a class of performance measures of DEDS represented by generalized semi-Markov processes (GSMPs) (cf. [Glynn 1989] can be expressed as a sum of an IPA-estimate and a term that takes into account the event order changes. In this paper we present an alternate approach to establishing the result of Gaivoronski, and from this we derive a necessary and sufficient condition for the validity of the IPA algorithm for this class of performance measures. Finally we validate our results by simulation examples.

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Augmented infinitesimal perturbation analysis: An alternate explanation

Abstract

Keywords

ASJC Scopus subject areas

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