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2014 | 24 | 3 | 519-534
Tytuł artykułu

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

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.
Rocznik
Tom
24
Numer
3
Strony
519-534
Opis fizyczny
Daty
wydano
2014
otrzymano
2013-08-19
poprawiono
2014-02-26
Twórcy
  • 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
  • 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
  • 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.
  • Bekker, R. (2009). Queues with levy input and hysteretic control, Queueing Systems 63(1): 281-299.
  • Benaboud, H. and Mikou, N. (2002). Analysis by queuing model of multi-threshold mechanism in ATM switches, Proceedings of the 5th IEEE International Conference on High Speed Networks and Multimedia Communications, HSNMC 2002, Jeju Island, Korea, pp. 147-151.
  • Bocharov, P.P., D'Apice, C., Pechinkin, A.V. and Salerno, S. (2004). Queueing Theory, VSP, Utrecht/Boston, MA.
  • Brown, P., Chemouil, P. and Delosme, B. (1984). A congestion control policy for signalling networks, Proceedings of the 7th International Conference on Computer Communications, ICCC 1984, Sydney, Australia, pp. 717-724.
  • Dshalalow, J.H. (1997). Queueing systems with state dependent parameters, in J. Dshalalow (Ed.), Frontiers in Queueing: Models and Applications in Science and Engineering, CRC Press, Boca Raton, FL, pp. 61-116.
  • Gebhart, R.F. (1967). A queuing process with bilevel hysteretic service-rate control, Naval Research Logistics Quarterly 14(1): 55-68.
  • Golubchik, L. and Lui, J.C.S. (1997). Bounding of performance measures for a threshold-based queueing system with hysteresis, Proceedings of the ACM SIGMETRICS Conference, ACC 2001, Seattle, WA, USA, pp. 147-157.
  • Hilt, V., Noel, E., Shen, C. and Abdelal, A. (2011). Design considerations for session initiation protocol (SIP) overload control, Technical Report RFC-6357, Internet Engineering Task Force.
  • Kaczorek, T. (2013). Minimum energy control of positive continuous-time linear systems with bounded inputs, International Journal of Applied Mathematics and Computational Science 23(4): 725-730, DOI: 10.2478/amcs-2013-0054.
  • Krasnoselskii, M.A. and Pokrovskii, A.V. (1989). Systems with Hysteresis, Springer-Verlag, Berlin/Heidelberg.
  • Moltchanov, D., Koucheryavy, Y. and Harju, J. (2006). Loss performance model for wireless channels with autocorrelated arrivals and losses, Computer Communications 29(13-14): 2646-2660.
  • 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.
  • Takagi, H. (1985). Analysis of a finite-capacity M/G/1 queue with a resume level, Performance Evaluation 5(3): 197-203.
  • Takshing, P. Y. and Yen, H.-M. (1983). Design algorithm for a hysteresis buffer congestion control strategy, Proceedings of the IEEE International Conference on Communications, Boston, MA, USA, pp. 499-503.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv24i3p519bwm
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