Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Yuliya Gaidamaka; Alexander Pechinkin; Rostislav Razumchik; Konstantin Samouylov; Eduard Sopin

International Journal of Applied Mathematics and Computer Science (2014)

  • Volume: 24, Issue: 3, page 519-534
  • ISSN: 1641-876X

Abstract

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Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M [ X ] | G | 1 ⟨ L , H ⟩ | ⟨ H , R ⟩ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.

How to cite

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Yuliya Gaidamaka, et al. "Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies." International Journal of Applied Mathematics and Computer Science 24.3 (2014): 519-534. <http://eudml.org/doc/271861>.

@article{YuliyaGaidamaka2014,
abstract = {Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system $M^\{[X]\}|G|1⟨L,H⟩|⟨H,R⟩$ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.},
author = {Yuliya Gaidamaka, Alexander Pechinkin, Rostislav Razumchik, Konstantin Samouylov, Eduard Sopin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {queueing system; batch arrival; general service time; overload; hysteretic load control},
language = {eng},
number = {3},
pages = {519-534},
title = {Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies},
url = {http://eudml.org/doc/271861},
volume = {24},
year = {2014},
}

TY - JOUR
AU - Yuliya Gaidamaka
AU - Alexander Pechinkin
AU - Rostislav Razumchik
AU - Konstantin Samouylov
AU - Eduard Sopin
TI - Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 3
SP - 519
EP - 534
AB - Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system $M^{[X]}|G|1⟨L,H⟩|⟨H,R⟩$ with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number of customers in the system. Two control policies defined by instants when it is decided to change the system’s mode are considered. The expression for an important performance characteristic of each policy (the mean time between changes in the system mode) is presented. Numerical examples that allow comparison of the efficiency of both policies are given.
LA - eng
KW - queueing system; batch arrival; general service time; overload; hysteretic load control
UR - http://eudml.org/doc/271861
ER -

References

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