Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment

Udo R. Krieger; Natalia Markovich

doi:10.1007/978-3-030-36614-8_23

Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment

Udo R. Krieger
, Natalia Markovich

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

2 Scopus citations

Abstract

We consider the multipath communication between a client and a server that is established at the transport and session layers of an SDN/NFV protocol stack in a fog computing scenario. We analyze the reliability function of an associated redundant transport system comprising two logical channels that are susceptible to failures. The failure processes of both channels are described by Markov-modulated failure times that are driven by the transitions of a common Markovian environment. We model the error-prone system with repair and independent phase-type distributed repair times by a continuous-time Markov chain. We identify its generator matrix in terms of Kronecker products of the underlying parameter matrices that are determined by the interarrival times driven by Markov-modulated failure processes and the independent phase-type distributed repair times. We show that the steady-state distribution of the restoration model can be effectively calculated by an iterative aggregation-disaggregation method for block matrices and compute the associated reliability function of the transport system by a uniformization method.

Original language	English
Title of host publication	Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers
Editors	Vladimir M. Vishnevskiy, Dmitry V. Kozyrev, Konstantin E. Samouylov, Dmitry V. Kozyrev
Publisher	Springer
Pages	302-314
Number of pages	13
ISBN (Print)	9783030366131
DOIs	https://doi.org/10.1007/978-3-030-36614-8_23
State	Published - 1 Jan 2019
Externally published	Yes
Event	22nd International Conference on Distributed and Computer and Communication Networks, DCCN 2019 - Moscow, Russian Federation Duration: 23 Sep 2019 → 27 Sep 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11965 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	22nd International Conference on Distributed and Computer and Communication Networks, DCCN 2019
Country/Territory	Russian Federation
City	Moscow
Period	23/09/19 → 27/09/19

Keywords

Kronecker matrices
Markov-modulated process
Phase-type distributed repair times
Reliability function
Reliability modeling
SDN/NFV

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-36614-8_23

Cite this

Krieger, U. R., & Markovich, N. (2019). Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment. In V. M. Vishnevskiy, D. V. Kozyrev, K. E. Samouylov, & D. V. Kozyrev (Eds.), Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers (pp. 302-314). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11965 LNCS). Springer. https://doi.org/10.1007/978-3-030-36614-8_23

Krieger, Udo R. ; Markovich, Natalia. / Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment. Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. editor / Vladimir M. Vishnevskiy ; Dmitry V. Kozyrev ; Konstantin E. Samouylov ; Dmitry V. Kozyrev. Springer, 2019. pp. 302-314 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment",

abstract = "We consider the multipath communication between a client and a server that is established at the transport and session layers of an SDN/NFV protocol stack in a fog computing scenario. We analyze the reliability function of an associated redundant transport system comprising two logical channels that are susceptible to failures. The failure processes of both channels are described by Markov-modulated failure times that are driven by the transitions of a common Markovian environment. We model the error-prone system with repair and independent phase-type distributed repair times by a continuous-time Markov chain. We identify its generator matrix in terms of Kronecker products of the underlying parameter matrices that are determined by the interarrival times driven by Markov-modulated failure processes and the independent phase-type distributed repair times. We show that the steady-state distribution of the restoration model can be effectively calculated by an iterative aggregation-disaggregation method for block matrices and compute the associated reliability function of the transport system by a uniformization method.",

keywords = "Kronecker matrices, Markov-modulated process, Phase-type distributed repair times, Reliability function, Reliability modeling, SDN/NFV",

author = "Krieger, \{Udo R.\} and Natalia Markovich",

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Krieger, UR & Markovich, N 2019, Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment. in VM Vishnevskiy, DV Kozyrev, KE Samouylov & DV Kozyrev (eds), Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11965 LNCS, Springer, pp. 302-314, 22nd International Conference on Distributed and Computer and Communication Networks, DCCN 2019, Moscow, Russian Federation, 23/09/19. https://doi.org/10.1007/978-3-030-36614-8_23

Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment. / Krieger, Udo R.; Markovich, Natalia.
Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. ed. / Vladimir M. Vishnevskiy; Dmitry V. Kozyrev; Konstantin E. Samouylov; Dmitry V. Kozyrev. Springer, 2019. p. 302-314 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11965 LNCS).

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

TY - GEN

T1 - Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment

AU - Krieger, Udo R.

AU - Markovich, Natalia

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider the multipath communication between a client and a server that is established at the transport and session layers of an SDN/NFV protocol stack in a fog computing scenario. We analyze the reliability function of an associated redundant transport system comprising two logical channels that are susceptible to failures. The failure processes of both channels are described by Markov-modulated failure times that are driven by the transitions of a common Markovian environment. We model the error-prone system with repair and independent phase-type distributed repair times by a continuous-time Markov chain. We identify its generator matrix in terms of Kronecker products of the underlying parameter matrices that are determined by the interarrival times driven by Markov-modulated failure processes and the independent phase-type distributed repair times. We show that the steady-state distribution of the restoration model can be effectively calculated by an iterative aggregation-disaggregation method for block matrices and compute the associated reliability function of the transport system by a uniformization method.

AB - We consider the multipath communication between a client and a server that is established at the transport and session layers of an SDN/NFV protocol stack in a fog computing scenario. We analyze the reliability function of an associated redundant transport system comprising two logical channels that are susceptible to failures. The failure processes of both channels are described by Markov-modulated failure times that are driven by the transitions of a common Markovian environment. We model the error-prone system with repair and independent phase-type distributed repair times by a continuous-time Markov chain. We identify its generator matrix in terms of Kronecker products of the underlying parameter matrices that are determined by the interarrival times driven by Markov-modulated failure processes and the independent phase-type distributed repair times. We show that the steady-state distribution of the restoration model can be effectively calculated by an iterative aggregation-disaggregation method for block matrices and compute the associated reliability function of the transport system by a uniformization method.

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KW - Markov-modulated process

KW - Phase-type distributed repair times

KW - Reliability function

KW - Reliability modeling

KW - SDN/NFV

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M3 - Conference contribution

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SN - 9783030366131

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 302

EP - 314

BT - Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers

A2 - Vishnevskiy, Vladimir M.

A2 - Kozyrev, Dmitry V.

A2 - Samouylov, Konstantin E.

A2 - Kozyrev, Dmitry V.

PB - Springer

T2 - 22nd International Conference on Distributed and Computer and Communication Networks, DCCN 2019

Y2 - 23 September 2019 through 27 September 2019

ER -

Krieger UR, Markovich N. Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment. In Vishnevskiy VM, Kozyrev DV, Samouylov KE, Kozyrev DV, editors, Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Springer. 2019. p. 302-314. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-36614-8_23

Modeling and Reliability Analysis of a Redundant Transport System in a Markovian Environment

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Keywords

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