On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process

Dmitry Efrosinin; Natalia Stepanova

doi:10.1007/978-3-030-36614-8_14

On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process

Dmitry Efrosinin
, Natalia Stepanova

Institut für Stochastik

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

Abstract

In this paper we consider an optimal control problem for the MAP(t)/M/2 queueing system with heterogeneous servers is introduced. The Markov arrival process (MAP) has time-dependent and periodic rates for phase transitions. We built a continuous time finite-horizon Markov decision process (MDP) with the aim to minimize a cost function. We solve a Bellman equation as a system of ordinary differential equations with time-dependent coefficients. We show that the optimal policy is of threshold type with threshold levels depending on the phases of arrival process. Moreover, the periodic variation of arrival attributes makes a threshold control policy piecewise constant time-dependent and periodic. We study numerically the speed of convergence of the policy to a periodic pattern. For the fixed control policy we calculate a transient solution. and provide a sensitivity analysis to determine how sensitive the performance measures are to changes in parameter values and in inter-arrival time correlation.

Originalsprache	Englisch
Titel	Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers
Herausgeber*innen	Vladimir M. Vishnevskiy, Dmitry V. Kozyrev, Konstantin E. Samouylov, Dmitry V. Kozyrev
Verlag	Springer
Seiten	179-194
Seitenumfang	16
Band	11965
ISBN (Print)	978-3-030-36613-1
DOIs	https://doi.org/10.1007/978-3-030-36614-8_14
Publikationsstatus	Veröffentlicht - 2019

Publikationsreihe

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

Wissenschaftszweige

101 Mathematik
101014 Numerische Mathematik
101018 Statistik
101019 Stochastik
101024 Wahrscheinlichkeitstheorie

JKU-Schwerpunkte

Digital Transformation

Zugriff auf Dokument

10.1007/978-3-030-36614-8_14

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Verknüpfung zur Publikation in Scopus

Dieses zitieren

Efrosinin, D., & Stepanova, N. (2019). On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process. in V. M. Vishnevskiy, D. V. Kozyrev, K. E. Samouylov, & D. V. Kozyrev (Hrsg.), Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers (Band 11965, S. 179-194). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 11965 LNCS). Springer. https://doi.org/10.1007/978-3-030-36614-8_14

Efrosinin, Dmitry ; Stepanova, Natalia. / On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process. Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Hrsg. / Vladimir M. Vishnevskiy ; Dmitry V. Kozyrev ; Konstantin E. Samouylov ; Dmitry V. Kozyrev. Band 11965 Springer, 2019. S. 179-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process",

abstract = "In this paper we consider an optimal control problem for the MAP(t)/M/2 queueing system with heterogeneous servers is introduced. The Markov arrival process (MAP) has time-dependent and periodic rates for phase transitions. We built a continuous time finite-horizon Markov decision process (MDP) with the aim to minimize a cost function. We solve a Bellman equation as a system of ordinary differential equations with time-dependent coefficients. We show that the optimal policy is of threshold type with threshold levels depending on the phases of arrival process. Moreover, the periodic variation of arrival attributes makes a threshold control policy piecewise constant time-dependent and periodic. We study numerically the speed of convergence of the policy to a periodic pattern. For the fixed control policy we calculate a transient solution. and provide a sensitivity analysis to determine how sensitive the performance measures are to changes in parameter values and in inter-arrival time correlation.",

author = "Dmitry Efrosinin and Natalia Stepanova",

year = "2019",

doi = "10.1007/978-3-030-36614-8\_14",

language = "English",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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pages = "179--194",

editor = "Vishnevskiy, \{Vladimir M.\} and Kozyrev, \{Dmitry V.\} and Samouylov, \{Konstantin E.\} and Kozyrev, \{Dmitry V.\}",

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Efrosinin, D & Stepanova, N 2019, On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process. in VM Vishnevskiy, DV Kozyrev, KE Samouylov & DV Kozyrev (Hrsg.), Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Bd. 11965, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Bd. 11965 LNCS, Springer, S. 179-194. https://doi.org/10.1007/978-3-030-36614-8_14

On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process. / Efrosinin, Dmitry; Stepanova, Natalia.
Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Hrsg. / Vladimir M. Vishnevskiy; Dmitry V. Kozyrev; Konstantin E. Samouylov; Dmitry V. Kozyrev. Band 11965 Springer, 2019. S. 179-194 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Band 11965 LNCS).

Publikation: Beitrag in Buch/Bericht/Konferenzband › Konferenzbeitrag › Begutachtung

TY - GEN

T1 - On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process

AU - Efrosinin, Dmitry

AU - Stepanova, Natalia

PY - 2019

Y1 - 2019

N2 - In this paper we consider an optimal control problem for the MAP(t)/M/2 queueing system with heterogeneous servers is introduced. The Markov arrival process (MAP) has time-dependent and periodic rates for phase transitions. We built a continuous time finite-horizon Markov decision process (MDP) with the aim to minimize a cost function. We solve a Bellman equation as a system of ordinary differential equations with time-dependent coefficients. We show that the optimal policy is of threshold type with threshold levels depending on the phases of arrival process. Moreover, the periodic variation of arrival attributes makes a threshold control policy piecewise constant time-dependent and periodic. We study numerically the speed of convergence of the policy to a periodic pattern. For the fixed control policy we calculate a transient solution. and provide a sensitivity analysis to determine how sensitive the performance measures are to changes in parameter values and in inter-arrival time correlation.

AB - In this paper we consider an optimal control problem for the MAP(t)/M/2 queueing system with heterogeneous servers is introduced. The Markov arrival process (MAP) has time-dependent and periodic rates for phase transitions. We built a continuous time finite-horizon Markov decision process (MDP) with the aim to minimize a cost function. We solve a Bellman equation as a system of ordinary differential equations with time-dependent coefficients. We show that the optimal policy is of threshold type with threshold levels depending on the phases of arrival process. Moreover, the periodic variation of arrival attributes makes a threshold control policy piecewise constant time-dependent and periodic. We study numerically the speed of convergence of the policy to a periodic pattern. For the fixed control policy we calculate a transient solution. and provide a sensitivity analysis to determine how sensitive the performance measures are to changes in parameter values and in inter-arrival time correlation.

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

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

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A2 - Kozyrev, Dmitry V.

A2 - Samouylov, Konstantin E.

A2 - Kozyrev, Dmitry V.

PB - Springer

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Efrosinin D, Stepanova N. On Optimal control policy of MAP(t)/M/2 queueing system with heterogeneous servers and periodic arrival process. in Vishnevskiy VM, Kozyrev DV, Samouylov KE, Kozyrev DV, Hrsg., Distributed Computer and Communication Networks - 22nd International Conference, DCCN 2019, Revised Selected Papers. Band 11965. Springer. 2019. S. 179-194. (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_14