NDLI: Transient analysis of tree-Like processes and its application to random access systems

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Transient analysis of tree-Like processes and its application to random access systems

Content Provider	ACM Digital Library
Author	Van Velthoven, J. Blondia, C. Van Houdt, B.
Abstract	A new methodology to assess transient performance measures of tree-like processes is proposed by introducing the concept of tree-like processes with marked time epochs. As opposed to the standard tree-like process, such a process marks part of the time epochs by following a set of Markovian rules. Our interest lies in obtaining the system state at the n-th marked time epoch as well as the mean time at which this n-th marking occurs. The methodology transforms the transient problem into a stationary one by applying a discrete Erlangization and constructing a reset Markov chain. A fast algorithm, with limited memory usage, that exploits the block structure of the reset Markov chain is developed and is based, among others, on Sylvester matrix equations and fast Fourier transforms. The theory of tree-like processes generalizes the well-known paradigm of Quasi-Birth-Death Markov chains and has various applications. We demonstrate our approach on the celebrated Capetanakis-Tsybakov-Mikhailov (CTM) random access protocol yielding new insights on its initial behavior both in normal and overload conditions.
Starting Page	181
Ending Page	190
Page Count	10
File Format	PDF
ISBN	1595933190
DOI	10.1145/1140277.1140299
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-06-26
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Matrix analytic methods Random access algorithms Contention resolution Tree-like processes Transient analysis
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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