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## International Journal of Applied Mathematics and Computer Science

2014 | 24 | 3 | 519-534
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Rocznik
Tom
Numer
Strony
519-534
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-08-19
poprawiono
2014-02-26
Twórcy
autor
• Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow 117198, Russia
autor
• Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow 119333, Russia
autor
• Institute of Problems of Informatics, Russian Academy of Sciences, Vavilova str., 44-2, Moscow 119333, Russia
• Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow 117198, Russia
autor
• Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow 117198, Russia
autor
• Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str., 6, Moscow 117198, Russia
Bibliografia
• Abaev, P., Gaidamaka, Y. and Samouylov, K. (2011). Signaling load hysteretic control in the SIP-servers network, Bulletin of Peoples' Friendship University of Russia: Mathematics, Informatics, Physics 1(4): 54-71.
• Abaev, P., Gaidamaka, Y. and Samouylov, K. (2012a). Queuing model for loss-based overload control in a SIP server using a hysteretic technique, in S. Andreev, S. Balandin and Y. Koucheryavy (Eds.), Internet of Things, Smart Spaces, and Next Generation Networking, Springer-Verlag, Berlin, pp. 371-378.
• Abaev, P.O., Gaidamaka, Y.V., Pechinkin, A.V., Razumchik, R.V. and Shorgin, S.Y. (2012b). Simulation of overload control in SIP server networks, Proceedings of the 26th European Conference on Modelling and Simulation, ECMS 2012, Koblenz, Germany, pp. 533-539.
• Abaev, P., Gaidamaka, Y., Samouylov, K., Pechinkin, A., Razumchik, R. and Shorgin, S. (2014). Hysteretic control technique for overload problem solution in network of SIP servers, Computing and Informatics 33(1): 1-18.
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• Bocharov, P.P., D'Apice, C., Pechinkin, A.V. and Salerno, S. (2004). Queueing Theory, VSP, Utrecht/Boston, MA.
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• Olwal, T.O., Djouani, K., Kogeda, O.P. and van Wyk, B.J. (2012). Joint queue-perturbed and weakly coupled power control for wireless backbone networks, International Journal of Applied Mathematics and Computational Science 22(3): 749-764, DOI: 10.2478/v10006-012-0056-z.
• Pechinkin, A.V., Razumchik, R.V. (2013a). Approach for analysis of M₂|M₂|1|R with hysteric policy for SIP server hop-by-hop load control, Proceedings of the 27th European Conference on Modelling and Simulation, ECMS 2013, Alesund, Norway, pp. 573-579.
• Pechinkin, A.V., Razumchik, R.V. (2013b). Stationary distribution of M₂|G|1|r queue with bi-level hysteric policy, Journal of Communications Technology and Electronics 58(12): 1220-1229.
• Roughan, M. and Pearce, C. (2000). A martingale analysis of hysteretic overload control, Advances in Performance Analysis: A Journal of Teletraffic Theory and Performance Analysis of Communication Systems and Networks 3(1): 1-30.
• Russell, T. (2006). Signaling System #7, 5th Edition, McGraw-Hill, New York, NY.
• Sindal, R. and Tokekar, S. (2008). Modeling and analysis of voice/data call admission control scheme in CDMA cellular network for variation in soft handoff threshold parameters, Proceedings of the 16th IEEE International Conference on Networks, ICON 2008, New Delhi, India, pp. 1-6.
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Bibliografia
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