Performance analysis and optimal control for queueing system with a reserve unreliable server pool

Dmitry Efrosinin; Irina Gudkova; Natalia Stepanova

doi:10.1007/978-3-030-33388-1_10

Performance analysis and optimal control for queueing system with a reserve unreliable server pool

Institute of Stochastics

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

Abstract

In this paper a Markovian queueing system supplied with main and reserve unreliable service facility which we refer to as pools is introduced. Usage of the reserve pool is controlled by a hysteretic policy that depends on upper and lower threshold levels of queue length to increase and decrease the total service rate. The system is analysed as a process of type quasi-birth-and-death (QBD), and expressions for the stationary state probabilities are derived. For the cost structure we evaluate the long-run average cost per unit of time and determine the optimal hysteretic policy by implementing genetic algorithm. The sensitivity analysis to study the effect of system parameters and threshold levels on the average cost is provided by a number of numerical examples.

Original language	English
Title of host publication	Information Technologies and Mathematical Modelling. Queueing Theory and Applications
Editors	Communications in Computer and Information Science
Publisher	Springer
Pages	109-120
Number of pages	12
Volume	1109
DOIs	https://doi.org/10.1007/978-3-030-33388-1_10
Publication status	Published - 2019

Fields of science

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

JKU Focus areas

Digital Transformation

Access to Document

10.1007/978-3-030-33388-1_10

Cite this

Efrosinin, D., Gudkova, I., & Stepanova, N. (2019). Performance analysis and optimal control for queueing system with a reserve unreliable server pool. In Communications in Computer and Information Science (Ed.), Information Technologies and Mathematical Modelling. Queueing Theory and Applications (Vol. 1109, pp. 109-120). Springer. https://doi.org/10.1007/978-3-030-33388-1_10

@inproceedings{62d453476b6b41f4b7ff54de5ebf0510,

title = "Performance analysis and optimal control for queueing system with a reserve unreliable server pool",

abstract = "In this paper a Markovian queueing system supplied with main and reserve unreliable service facility which we refer to as pools is introduced. Usage of the reserve pool is controlled by a hysteretic policy that depends on upper and lower threshold levels of queue length to increase and decrease the total service rate. The system is analysed as a process of type quasi-birth-and-death (QBD), and expressions for the stationary state probabilities are derived. For the cost structure we evaluate the long-run average cost per unit of time and determine the optimal hysteretic policy by implementing genetic algorithm. The sensitivity analysis to study the effect of system parameters and threshold levels on the average cost is provided by a number of numerical examples.",

author = "Dmitry Efrosinin and Irina Gudkova and Natalia Stepanova",

year = "2019",

doi = "10.1007/978-3-030-33388-1\_10",

language = "English",

volume = "1109",

pages = "109--120",

editor = "\{Communications in Computer and Information Science\}",

booktitle = "Information Technologies and Mathematical Modelling. Queueing Theory and Applications",

publisher = "Springer",

}

Efrosinin, D, Gudkova, I & Stepanova, N 2019, Performance analysis and optimal control for queueing system with a reserve unreliable server pool. in Communications in Computer and Information Science (ed.), Information Technologies and Mathematical Modelling. Queueing Theory and Applications. vol. 1109, Springer, pp. 109-120. https://doi.org/10.1007/978-3-030-33388-1_10

Performance analysis and optimal control for queueing system with a reserve unreliable server pool. / Efrosinin, Dmitry; Gudkova, Irina; Stepanova, Natalia.
Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ed. / Communications in Computer and Information Science. Vol. 1109 Springer, 2019. p. 109-120.

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

TY - GEN

T1 - Performance analysis and optimal control for queueing system with a reserve unreliable server pool

AU - Efrosinin, Dmitry

AU - Gudkova, Irina

AU - Stepanova, Natalia

PY - 2019

Y1 - 2019

N2 - In this paper a Markovian queueing system supplied with main and reserve unreliable service facility which we refer to as pools is introduced. Usage of the reserve pool is controlled by a hysteretic policy that depends on upper and lower threshold levels of queue length to increase and decrease the total service rate. The system is analysed as a process of type quasi-birth-and-death (QBD), and expressions for the stationary state probabilities are derived. For the cost structure we evaluate the long-run average cost per unit of time and determine the optimal hysteretic policy by implementing genetic algorithm. The sensitivity analysis to study the effect of system parameters and threshold levels on the average cost is provided by a number of numerical examples.

AB - In this paper a Markovian queueing system supplied with main and reserve unreliable service facility which we refer to as pools is introduced. Usage of the reserve pool is controlled by a hysteretic policy that depends on upper and lower threshold levels of queue length to increase and decrease the total service rate. The system is analysed as a process of type quasi-birth-and-death (QBD), and expressions for the stationary state probabilities are derived. For the cost structure we evaluate the long-run average cost per unit of time and determine the optimal hysteretic policy by implementing genetic algorithm. The sensitivity analysis to study the effect of system parameters and threshold levels on the average cost is provided by a number of numerical examples.

UR - https://www.scopus.com/pages/publications/85076118576

U2 - 10.1007/978-3-030-33388-1_10

DO - 10.1007/978-3-030-33388-1_10

M3 - Conference proceedings

VL - 1109

SP - 109

EP - 120

BT - Information Technologies and Mathematical Modelling. Queueing Theory and Applications

A2 - Communications in Computer and Information Science, null

PB - Springer

ER -

Performance analysis and optimal control for queueing system with a reserve unreliable server pool

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this