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AQM algorithms; loss probability; multi-server queueing system; queue-size distribution
A multi-server $M/M/n$-type queueing system with a bounded total volume and finite queue size is considered. An AQM algorithm with the “accepting” function is being used to control the arrival process of incoming packets. The stationary queue-size distribution and the loss probability are derived. Numerical examples illustrating theoretical results are attached as well.
[1] Athuraliya, S., Low, S. H., Li, V. H., Qinghe, Y.: REM: active queue management. IEEE Network 15 (2001), 3, 48-53. DOI 10.1109/65.923940
[2] Aweya, J., Ouellette, M., Montuno, D. Y., Chapman, A.: A control theoretic approach to Active Queue Management.
[3] Bocharov, P. P., D'Apice, C., Pechinkin, A. V., Salerno, S.: Queueing Theory. VSP, Utrecht-Boston, 2004. MR 2125874 | Zbl 1061.60093
[4] Bonald, T., May, M., Bolot, J. Ch.: Analytic evaluation of RED performance. In: Proc. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies 3 (2000), pp. 1415-1424.
[5] Chrost, L., Brachman, A., Chydzinski, A.: On the performance of AQM algoritms with small buffers. Comput. Network CCIS 39 (2009), 168-173. DOI 10.1007/978-3-642-02671-3_20
[6] Chydzinski, A.: Towards a stable AQM via dropping function shaping. In: Proc. Ninth International Conference on Networks (ICN) (2010), pp. 93-97.
[7] Chydzinski, A., Chrost, L.: Analysis of AQM queues with queue size based packet dropping. Int. J. Appl. Math. Comput. Sci. 21 (2011), 3, 567-577. DOI 10.2478/v10006-011-0045-7 | MR 2883897 | Zbl 1237.60069
[8] Chydzinski, A.: Optimization problems in the theory of queues with dropping functions. HET-NETs (2011), 121-132.
[9] Feller, W.: Introduction to Probability Theory and Its Applications. Wiley, 1971. MR 0270403 | Zbl 0598.60003
[10] Floyd, S., Jacobson, V.: Random early detection gateways for congestion avoidance. IEEE ACM T. Network 1 (1993), 4, 397-412. DOI 10.1109/90.251892
[11] Floyd, S.: Recommendations on using the gentle variant of RED., March 2000.
[12] Floyd, S.: Adaptive RED: an algorithm for increasing the robustness of RED's Active Queue Management.
[13] Hao, W., Wei, Y.: An extended $GI^{X}/M/1/N$ queueing model for evaluating the performance of AQM algorithms with aggregate traffic. Lect. Notes Comput. Sci. 3619 (2005), 395-404. DOI 10.1007/11534310_43
[14] Kempa, W. M.: 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 (2011), 6, 930-943. MR 2907852 | Zbl 1241.90035
[15] Kempa, W. M.: A direct approach to transient queue-size distribution in a finite-buffer queue with AQM. Appl. Math. Inform. Sci. 7 (2013), 3, 909-915. DOI 10.12785/amis/070308 | MR 3028710
[16] Liu, S., Basar, T., Srikant, R.: Exponential RED: A stabilizing AQM scheme for low- and high-speed TCP protocols. IEEE/ACM Trans. Newtorking 13 (2005), 5, 1068-1081. DOI 10.1109/TNET.2005.857110
[17] Rosolen, V., Bonaventure, O., Leduc, G.: A RED discard strategy for ATM networks and its performance evaluation with TCP/IP traffic. Comput. Commun. Rew. 29 (1999), 3, 23-43. DOI 10.1145/505724.505728
[18] Sun, L., Wang, L.: A novel RED scheme with preferential dynamic threshold deployment. In: Computational Intelligence and Security Workshops 2007, pp. 854-857.
[19] Suresh, S., Gol, O.: Congestion management of self similar IP traffic - application of the RED scheme. In: Wireless and Optical Communications Networks, Second IFIP International Conference 2005, pp. 372-376.
[20] Tikhonenko, O.: Queueing systems of a random length demands with restrictions. Automat. Remote Control 52 (1991), 10, 1431-1437. MR 1152868
[21] Tikhonenko, O.: Generalized Erlang problem for service systems with finite total capacity. Probl. Inform. Transmission 41 (2005), 3, 243-253. DOI 10.1007/s11122-005-0029-z | MR 2163852 | Zbl 1098.90025
[22] Tikhonenko, O., Kempa, W. M.: The generalization of AQM algorithms for queueing systems with bounded capacity. Lect. Notes Comput. Sci. 7204 (2012), 242-251. DOI 10.1007/978-3-642-31500-8_25
[23] Xiong, N., Yang, Y., Defago, X., He, Y.: LRC-RED: A self-tuning robust and adaptive AQM scheme. In: Sixth International Conference on Parallel and Distributed Computing Applications and Technologies 2005, pp. 655-659.
[24] Zhou, K., Yeung, K. L., Li, V. O. K.: Nonlinear RED: A simple yet efficient active queue management scheme. Comput. Networks 50 (2006), 18, 3784-3794. DOI 10.1016/j.comnet.2006.04.007 | Zbl 1103.68364
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