<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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<sup>[X]</sup>|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 </p></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

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

Department of Applied Probability and Informatics Peoples’ Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow 117198, Russia

Institute of Problems of Informatics Russian Academy of Sciences, Vavilova str., 44-2, Moscow 119333, Russia

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

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...

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

Published Online: Sep 25, 2014

Page range: 519 - 534

Received: Aug 19, 2013

DOI: https://doi.org/10.2478/amcs-2014-0038

Keywords
queueing system, batch arrival, general service time, overload, hysteretic load control

© by Yuliya Gaidamaka

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 25, 2014

Page range: 519 - 534

Received: Aug 19, 2013

DOI: https://doi.org/10.2478/amcs-2014-0038

Keywordsqueueing system, batch arrival, general service time, overload, hysteretic load control

© by Yuliya Gaidamaka

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
queueing system, batch arrival, general service time, overload, hysteretic load control