| Title:
|
On the queue-size distribution in the multi-server system with bounded capacity and packet dropping (English) |
| Author:
|
Tikhonenko, Oleg |
| Author:
|
Kempa, Wojciech M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
49 |
| Issue:
|
6 |
| Year:
|
2013 |
| Pages:
|
855-867 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
AQM algorithms |
| Keyword:
|
loss probability |
| Keyword:
|
multi-server queueing system |
| Keyword:
|
queue-size distribution |
| MSC:
|
60K25 |
| MSC:
|
90B22 |
| idZBL:
|
Zbl 1302.90052 |
| idMR:
|
MR3182644 |
| . |
| Date available:
|
2014-01-27T12:24:59Z |
| Last updated:
|
2015-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143575 |
| . |
| Reference:
|
[1] Athuraliya, S., Low, S. H., Li, V. H., Qinghe, Y.: REM: active queue management..IEEE Network 15 (2001), 3, 48-53. 10.1109/65.923940 |
| Reference:
|
[2] Aweya, J., Ouellette, M., Montuno, D. Y., Chapman, A.: A control theoretic approach to Active Queue Management.. |
| Reference:
|
[3] Bocharov, P. P., D'Apice, C., Pechinkin, A. V., Salerno, S.: Queueing Theory..VSP, Utrecht-Boston, 2004. Zbl 1061.60093, MR 2125874 |
| Reference:
|
[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. |
| Reference:
|
[5] Chrost, L., Brachman, A., Chydzinski, A.: On the performance of AQM algoritms with small buffers..Comput. Network CCIS 39 (2009), 168-173. 10.1007/978-3-642-02671-3_20 |
| Reference:
|
[6] Chydzinski, A.: Towards a stable AQM via dropping function shaping..In: Proc. Ninth International Conference on Networks (ICN) (2010), pp. 93-97. |
| Reference:
|
[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. Zbl 1237.60069, MR 2883897, 10.2478/v10006-011-0045-7 |
| Reference:
|
[8] Chydzinski, A.: Optimization problems in the theory of queues with dropping functions..HET-NETs (2011), 121-132. |
| Reference:
|
[9] Feller, W.: Introduction to Probability Theory and Its Applications..Wiley, 1971. Zbl 0598.60003, MR 0270403 |
| Reference:
|
[10] Floyd, S., Jacobson, V.: Random early detection gateways for congestion avoidance..IEEE ACM T. Network 1 (1993), 4, 397-412. 10.1109/90.251892 |
| Reference:
|
[11] Floyd, S.: Recommendations on using the gentle variant of RED..http://www.aciri.org/floyd/red/gentle.html, March 2000. |
| Reference:
|
[12] Floyd, S.: Adaptive RED: an algorithm for increasing the robustness of RED's Active Queue Management..http://www.aciri.org/floyd/papers/adaptiveRed.pdf |
| Reference:
|
[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. 10.1007/11534310_43 |
| Reference:
|
[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. Zbl 1241.90035, MR 2907852 |
| Reference:
|
[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. MR 3028710, 10.12785/amis/070308 |
| Reference:
|
[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. 10.1109/TNET.2005.857110 |
| Reference:
|
[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. 10.1145/505724.505728 |
| Reference:
|
[18] Sun, L., Wang, L.: A novel RED scheme with preferential dynamic threshold deployment..In: Computational Intelligence and Security Workshops 2007, pp. 854-857. |
| Reference:
|
[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. |
| Reference:
|
[20] Tikhonenko, O.: Queueing systems of a random length demands with restrictions..Automat. Remote Control 52 (1991), 10, 1431-1437. MR 1152868 |
| Reference:
|
[21] Tikhonenko, O.: Generalized Erlang problem for service systems with finite total capacity..Probl. Inform. Transmission 41 (2005), 3, 243-253. Zbl 1098.90025, MR 2163852, 10.1007/s11122-005-0029-z |
| Reference:
|
[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. 10.1007/978-3-642-31500-8_25 |
| Reference:
|
[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. |
| Reference:
|
[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. Zbl 1103.68364, 10.1016/j.comnet.2006.04.007 |
| . |
