# 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

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topYuliya 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 -

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