Series expansions of generalized matrix products

Haralambie Leahu; Bernd Heidergott

doi:10.1109/CDC.2005.1583421

Series expansions of generalized matrix products

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We consider generalized products of random matrices. They arise in discrete event systems (DES), such as queueing networks or stochastic Petri nets, where they are used to express the state transition dynamic. Instances of such DES are those whose state dynamic can be modelled through a matrix-vector multiplication in conventional, max-plus and min-plus algebra. We will present a Taylor series approach to numerical evaluation of finite horizon performance characteristics of systems modelled by generalized matrix products. The cornerstone of our analysis is the introduction of a differential calculus, based on the concept of weak derivative of a random matrix. We illustrate our results with a couple of numerical computations performed on a classical DES example.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	7793-7798
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1583421
Publication status	Published - 1 Dec 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

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10.1109/CDC.2005.1583421

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Leahu, H., & Heidergott, B. (2005). Series expansions of generalized matrix products. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 7793-7798). Article 1583421 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583421

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abstract = "We consider generalized products of random matrices. They arise in discrete event systems (DES), such as queueing networks or stochastic Petri nets, where they are used to express the state transition dynamic. Instances of such DES are those whose state dynamic can be modelled through a matrix-vector multiplication in conventional, max-plus and min-plus algebra. We will present a Taylor series approach to numerical evaluation of finite horizon performance characteristics of systems modelled by generalized matrix products. The cornerstone of our analysis is the introduction of a differential calculus, based on the concept of weak derivative of a random matrix. We illustrate our results with a couple of numerical computations performed on a classical DES example.",

author = "Haralambie Leahu and Bernd Heidergott",

year = "2005",

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doi = "10.1109/CDC.2005.1583421",

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booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

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Leahu, H & Heidergott, B 2005, Series expansions of generalized matrix products. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583421, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 7793-7798, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583421

Series expansions of generalized matrix products. / Leahu, Haralambie; Heidergott, Bernd.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 7793-7798 1583421 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Series expansions of generalized matrix products

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