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2016 | 26 | 4 | 841-854
Tytuł artykułu

Performance evaluation of an M/G/n -type queue with bounded capacity and packet dropping

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.
Rocznik
Tom
26
Numer
4
Strony
841-854
Opis fizyczny
Daty
wydano
2016
otrzymano
2015-12-10
poprawiono
2016-04-19
zaakceptowano
2016-06-06
Twórcy
  • Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw, Wóycickiego 1/3, 01-938 Warsaw, Poland
  • Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
  • Adan, I. and Resing, J. (2002). Queueing Theory, Eindhoven University of Technology, Eindheren.
  • Athuraliya, S., Low, S.H., Li, V.H. and Qinghe, Y. (2001). REM: Active queue management, IEEE Networks 15(3): 48-53.
  • Bocharov, P.P., D'Apice, C., Pechinkin, A.V. and Salerno, S. (2004). Queueing Theory, VSP, Utrecht/Boston, MA.
  • Bonald, T., May, M. and Bolot, J.C. (2000). Analytic evaluation of RED performance, Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies 3 (IEEE Infocom 2000), Tel Aviv, Israel, pp. 1415-1424.
  • Chydziński, A. (2010). Towards a stable AQM via dropping function shaping, Proceedings of the 9th International Conference on Networks (ICN), Menuires, France, pp. 93-97.
  • Chydziński, A. and Chróst, L. (2011). Analysis of AQM queues with queue size based packet dropping, International Journal of Applied Mathematics and Computer Science 21(3): 567-577, DOI: 10.2478/v10006-011-0045-7.
  • Domańska, J., Domański, A., Augustyn, D.R. and Klamka, J. (2014). A RED modified weighted moving average for soft real-time application, International Journal of Applied Mathematics and Computer Science 24(3): 697-707, DOI: 10.2478/amcs-2014-0051.
  • Floyd, S. (2000). Recommendations on using the gentle variant of RED, http://www.aciri.org/floyd/red/gentle.html.
  • Floyd, S. (2001). Adaptive RED: An algorithm for increasing the robustness of RED's active queue management, http://www.aciri.org/floyd/papers/adaptivered.pdf.
  • Floyd, S. and Jacobson, V. (1993). Random early detection gateways for congestion avoidance, IEEE ACM Telecommunication Network 1(4): 397-412.
  • Hao, W. and Wei, Y. (2005). An extended GIX/M/1/N queueing model for evaluating the performance of AQM algorithms with aggregate traffic, in X. Lu and W. Zhao (Eds.), Networking and Mobile Computing, Lecture Notes in Computer Science, Vol. 3619, Springer-Verlag, Berlin/Heidelberg, pp. 395-404.
  • Kempa, W.M. (2011). On main characteristics of the M/M/1/N queue with single and batch arrivals and the queue size controlled by AQM algorithms, Kybernetika 47(6): 930-943.
  • Kempa, W.M. (2013a). A direct approach to transient queue-size distribution in a finite-buffer queue with AQM, Applications of Mathematics & Information Sciences 7(1): 909-915.
  • Kempa, W.M. (2013b). On non-stationary queue-size distribution in a finite-buffer queue controlled by a dropping function, Proceedings of the 12th International Conference on Informatics, Informatics'13, Spišská Nová Ves, Slovakia, pp. 67-72.
  • Kempa, W.M. (2013c). Time-dependent queue-size distribution in the finite GI/M/1 model with AQM-type dropping, Acta Electrotechnica et Informatica 13(4): 85-90.
  • Klemm, A., Lindemann, C. and Lohmann, M. (2003). Modeling IP traffic using the batch Markovian arrival process, Performance Evaluation 54(2): 149-173.
  • Liu, S., Basar, T. and Srikant, R. (2005). Exponential RED: A stabilizing AQM scheme for low- and ligh-speed TCP protocols, IEEE/ACM Transactions on Networking 13(5): 1068-1081.
  • Rosolen, V., Bonaventure, O. and Leduc, G. (1999). A RED discard strategy for ATM networks and its performance evaluation with TCP/IP traffic, Computer Communication Review 29(3): 23-43.
  • Rusek, K., Janowski, L. and Papir, Z. (2014). Transient and stationary characteristics of a packet buffer modelled as an M AP/SM/1/b system, International Journal of Applied Mathematics and Computer Science 24(2): 429-442, DOI: 10.2478/amcs-2014-0033.
  • Sun, L. and Wang, L. (2007). A novel RED scheme with preferential dynamic threshold deployment, Proceedings of the Computational Intelligence and Security Workshops, Harbin, Heilongjiang, China, pp. 854-857.
  • Suresh, S. and Gol, O. (2005). Congestion management of self similar IP traffic-application of the RED scheme, Proceedings of the Second IFIP International Conference Wireless and Optical Communications Networks, Dubai, United Arab Emirates, pp. 372-376.
  • Tikhonenko, O. (1991). Queueing systems of a random length demands with restrictions, Automation and Remote Control 52(10): 1431-1437.
  • Tikhonenko, O. (2005). Generalized Erlang problem for service systems with finite total capacity, Problems of Information Transmission 41(3): 243-253.
  • Tikhonenko, O. (2006). Probability Analysis of Information Systems, EXIT, Warsaw.
  • Tikhonenko, O. and Kempa, W.M. (2012). The generalization of AQM algorithms for queueing systems with bounded capacity, in R. Wyrzykowski et al. (Eds.), Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science, Vol. 7204, pp. 242-251.
  • Tikhonenko, O. and Kempa, W.M. (2013). On the queue-size distribution in the multi-server system with bounded capacity and packet dropping, Kybernetika 49(6): 855-867.
  • Tikhonenko, O. and Kempa, W.M. (2015). Queueing system with processor sharing and limited memory under control of the AQM mechanism, Automation and Remote Control 76(10): 1784-1796.
  • Woźniak, M., Kempa, W.M., Gabryel, M. and Nowicki, R.K. (2014). A finite-buffer queue with a single vacation policy: An analytical study with evolutionary positioning, International Journal of Applied Mathematics and Computer Science 24(4): 887-900, DOI: 10.2478/amcs-2014-0065.
  • Xiong, N., Yang, Y., Defago, X. and He, Y. (2005). LRC-RED: A self-tuning robust and adaptive AQM scheme, Proceedings of the 6th International Conference on Parallel and Distributed Computing Applications and Technologies, Dalian, China, pp. 655-659.
  • Zhou, K., Yeung, K.L. and Li, V.O.K. (2006). Nonlinear RED: A simple yet efficient active queue management scheme, Computer Networks 50(18): 3784-3794.
Typ dokumentu
Bibliografia
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