Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates

Ruslana Nekrasova; Evsey Morozov; Dmitry Efrosinin

Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates

Ruslana Nekrasova
, Evsey Morozov
, Dmitry Efrosinin

Institute of Stochastics

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

Abstract

A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the ‘end’ of a virtual ith class orbit, and the ‘oldest’ customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ‘top’ of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a cμ-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.

Original language	English
Title of host publication	Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science
Editors	Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V.
Publisher	Springer
Pages	297-308
Number of pages	12
Volume	13766
ISBN (Print)	978-3-031-23206-0
Publication status	Published - 2023

Publication series

Name	Lecture Notes in Computer Science (LNCS)

Fields of science

101 Mathematics
101014 Numerical mathematics
101018 Statistics
101019 Stochastics
101024 Probability theory

JKU Focus areas

Digital Transformation

Cite this

Nekrasova, R., Morozov, E., & Efrosinin, D. (2023). Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. In Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (Ed.), Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science (Vol. 13766, pp. 297-308). (Lecture Notes in Computer Science (LNCS)). Springer.

Nekrasova, Ruslana ; Morozov, Evsey ; Efrosinin, Dmitry. / Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science. editor / Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. Vol. 13766 Springer, 2023. pp. 297-308 (Lecture Notes in Computer Science (LNCS)).

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title = "Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates",

abstract = "A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the {\textquoteleft}end{\textquoteright} of a virtual ith class orbit, and the {\textquoteleft}oldest{\textquoteright} customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the {\textquoteleft}top{\textquoteright} of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a cμ-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.",

author = "Ruslana Nekrasova and Evsey Morozov and Dmitry Efrosinin",

year = "2023",

language = "English",

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series = "Lecture Notes in Computer Science (LNCS)",

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booktitle = "Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science",

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Nekrasova, R, Morozov, E & Efrosinin, D 2023, Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. in Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (ed.), Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science. vol. 13766, Lecture Notes in Computer Science (LNCS), Springer, pp. 297-308.

Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. / Nekrasova, Ruslana; Morozov, Evsey; Efrosinin, Dmitry.
Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science. ed. / Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. Vol. 13766 Springer, 2023. p. 297-308 (Lecture Notes in Computer Science (LNCS)).

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

TY - CHAP

T1 - Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates

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N2 - A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the ‘end’ of a virtual ith class orbit, and the ‘oldest’ customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ‘top’ of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a cμ-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.

AB - A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new ith class customer joins the ‘end’ of a virtual ith class orbit, and the ‘oldest’ customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ‘top’ of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a cμ-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.

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BT - Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science

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Nekrasova R, Morozov E, Efrosinin D. Verification of Stability Condition in Unreliable Two-Class Retrial System with Constant Retrial Rates. In Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V., editor, Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science. Vol. 13766. Springer. 2023. p. 297-308. (Lecture Notes in Computer Science (LNCS)).