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

Tikhonenko, Oleg; Kempa, Wojciech M.

doi:10.1515/amcs-2016-0060

Abstract

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.

References

Adan, I. and Resing, J. (2002). Queueing Theory, Eindhoven University of Technology, Eindheren.
Search in Google Scholar Back to article
Athuraliya, S., Low, S.H., Li, V.H. and Qinghe, Y. (2001). REM: Active queue management, IEEE Networks 15(3): 48-53.10.1109/65.923940
Search in Google Scholar Back to article
Bocharov, P.P., D’Apice, C., Pechinkin, A.V. and Salerno, S. (2004). Queueing Theory, VSP, Utrecht/Boston, MA.10.1515/9783110936025
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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/v10006-011-0045-7.10.2478/v10006-011-0045-7
Search in Google Scholar Back to article
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-2014-0051.10.2478/amcs-2014-0051
Search in Google Scholar Back to article
Floyd, S. (2000). Recommendations on using the gentle variant of RED, http://www.aciri.org/floyd/red/gentle.html.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Floyd, S. and Jacobson, V. (1993). Random early detection gateways for congestion avoidance, IEEE ACM Telecommunication Network 1(4): 397-412.10.1109/90.251892
Search in Google Scholar Back to article
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. 395-404.10.1007/11534310_43
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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): 909-915.10.12785/amis/070308
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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): 85-90.10.15546/aeei-2013-0054
Search in Google Scholar Back to article
Klemm, A., Lindemann, C. and Lohmann, M. (2003). Modeling IP traffic using the batch Markovian arrival process, Performance Evaluation 54(2): 149-173.10.1016/S0166-5316(03)00067-1
Search in Google Scholar Back to article
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): 1068-1081.10.1109/TNET.2005.857110
Search in Google Scholar Back to article
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): 23-43.10.1145/505724.505728
Search in Google Scholar Back to article
Rusek, K., Janowski, L. and Papir, Z. (2014). Transient and stationary characteristics of a packet buffer modelled as an MAP/SM/1/b system, International Journal of Applied Mathematics and Computer Science 24(2): 429-442, DOI: 10.2478/amcs-2014-0033.10.2478/amcs-2014-0033
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
Tikhonenko, O. (1991). Queueing systems of a random length demands with restrictions, Automation and Remote Control 52(10): 1431-1437.
Search in Google Scholar Back to article
Tikhonenko, O. (2005). Generalized Erlang problem for service systems with finite total capacity, Problems of Information Transmission 41(3): 243-253.10.1007/s11122-005-0029-z
Search in Google Scholar Back to article
Tikhonenko, O. (2006). Probability Analysis of Information Systems, EXIT,Warsaw.
Search in Google Scholar Back to article
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. 242-251.10.1007/978-3-642-31500-8_25
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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-2014-0065.10.2478/amcs-2014-0065
Search in Google Scholar Back to article
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.
Search in Google Scholar Back to article
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. 10.1016/j.comnet.2006.04.007
Search in Google Scholar Back to article

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

Abstract

Paradigm

My account