On Main characteristics of the \(M/M/1/N\) queue with single and batch arrivals and the queue size controlled by AQM algorithms. (English) Zbl 1241.90035

Summary: Finite-buffer queueing systems of the M/M/1/N type with queue size controlled by AQM algorithms are considered, separately for single and batch arrivals. In the latter case two different acceptance strategies: WBAS (Whole Batch Acceptance Strategy) and PBAS (Partial Batch Acceptance Strategy) are distinguished. Three essential characteristics of the system are investigated: the stationary queue-size distribution, the number of consecutively dropped packets (batches of packets) and the time between two successive accepted packets (batches of packets). For these characteristics the formulae which can be easily numerically treated are derived. Numerical results obtained for three sample dropping functions are attached as well.


90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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[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] Bonald, T., May, M., Bolot, J. Ch.: Analytic evaluation of RED performance. Proc. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies 3 (2000), pp. 1415-1424.
[3] 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
[4] 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
[5] Floyd, S.: Recommendations on using the gentle variant of RED. , March 2000.
[6] Frey, A., Takahashi, Y.: An \(M^{X}/GI/1/N\) queue with close-down and vacation times. J. Appl. Math. Stoch. Anal. 12 (1999), 1, 63-83. · Zbl 0962.60088 · doi:10.1155/S1048953399000064
[7] 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
[8] Rosolen, V., Bonaventure, O., Leduc, G.: A RED discard strategy for ATM networks and its performance evaluation with TCP/IP traffic. Comput. Comm. R. 29 (1999), 3, 23-43. · doi:10.1145/505724.505728
[9] Sun, L., Wang, L.: A novel RED scheme with preferential dynamic threshold deployment. Computational Intelligence and Security Workshops 2007, pp. 854-857.
[10] Suresh, S., Gol, O.: Congestion management of self similar IP traffic - application of the RED scheme. Wireless and Optical Communications Networks, Second IFIP International Conference 2005, pp. 372-376.
[11] Takagi, H.: Queueing analysis, Volume 1: Vacation and priority systems, Part 1. North-Holland, Amsterdam - London - New York - Tokyo 1983.
[12] Xiong, N., Yang, Y., Defago, X., He, Y.: LRC-RED: A self-tuning robust and adaptive AQM scheme. Sixth International Conference on Parallel and Distributed Computing Applications and Technologies 2005, pp. 655-659.
[13] Zhou, K., Yeung, K. L., Li, V. O. K.: Nonlinear RED: A simple yet efficient active queue management scheme. Comput. Network 50 (2006), 18, 3784-3794. · Zbl 1103.68364 · doi:10.1016/j.comnet.2006.04.007
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