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Two Types of Single-Server Queueing Systems with Threshold-Based Renovation Mechanism

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Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 13144))

Abstract

This work is devoted to the analysis of two GI/M/1 infinite capacity queuing systems with threshold control of the renovation mechanism, which is responsible for the probabilistic dropping of claims entered into the system upon service completions. In the system of the first type, the threshold value is the value of the queue length, upon passing which the renovation mechanism is activated. For a system of the second type, the threshold value not only activates the renovation, but also specifies the area in the queue where from the customers cannot be dropped. For both systems, the main stationary time-probabilistic characteristics are derived and also the results of simulation, which illustrate the performance of the queues, are presented.

This paper has been supported by the RUDN University Strategic Academic Leadership Program (Zaryadov I.S.—mathematical model development, Viana C. C. Hilquias—simulation model development). Also the publication has been funded by Russian Foundation for Basic Research (RFBR) according to the research project No. 19-07-00739 and No. 20-07-00804 (I. S. Zaryadov, T. A. Milovanova—numerical analysis based on the obtained analytical results).

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References

  1. Baker, F., Fairhurst, G.: IETF recommendations regarding active queue management. RFC 7567. Internet Engineering Task Force. https://tools.ietf.org/html/rfc7567. Accessed 27 May 2021

  2. Floyd, S., Jacobson, V.: Random early detection gateways for congestion avoidance. IEEE/ACM Trans. Netw. 4(1), 397–413 (1993). https://doi.org/10.1109/90.251892

    Article  Google Scholar 

  3. Ramakrishnan, K., Floyd, S., Black, D.: The addition of explicit congestion notification (ECN) to IP. RFC 3168. Internet Engineering Task Force. https://tools.ietf.org/html/rfc3168. Accessed 27 May 2021

  4. Floyd, S., Gummadi, R., Shenker, S.: Adaptive RED: an algorithm for increasing the robustness of RED’s active queue management (2001). http://www.icir.org/floyd/ papers/adaptiveRed.pdf

  5. Floyd, S.: RED: discussions of setting parameters (1997). http://www.aciri.org/floyd/REDparameters.txt

  6. Korolkova, A.V., Zaryadov, I.S.: The mathematical model of the traffic transfer process with a rate adjustable by RED. In: International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia, pp. 1046–1050. IEEE (2010). https://doi.org/10.1109/ICUMT.2010.5676505

  7. Jacobson, V., Nichols, K., Poduri, K.: RED in a different light. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.9406. Accessed 29 May 2021

  8. Class-based weighted fair queueing and weighted random early detection. http://www.cisco.com/c/en/us/td/docs/ios/12_0s/feature/guide/fswfq26.html. Accessed 27 May 2021

  9. Floyd, S., Gummadi, R., Shenker, S.: Adaptive RED: an algorithm for increasing the robustness of RED’s active queue management (2001). http://www.icir.org/floyd/papers/adaptiveRed.pdf. Accessed 1 Sept 2019

  10. Changwang, Z., Jianping, Y., Zhiping, C., Weifeng, C.: RRED: robust RED algorithm to counter low-rate denial-of-service attacks. IEEE Commun. Lett. 14(5), 489–491 (2010). https://doi.org/10.1109/LCOMM.2010.05.091407

    Article  Google Scholar 

  11. Ott, T.J., Lakshman, T.V., Wong, L.H.: SRED: stabilized RED. In: Proceedings IEEE INFOCOM 1999, New York, NY, USA, vol. 3, pp. 1346–1355 IEEE (1999). https://doi.org/10.1109/INFCOM.1999.752153

  12. Lin, D., Morris, R.: Dynamics of random early detection. Comput. Commun. Rev. 27(4), 127–137 (1997)

    Article  Google Scholar 

  13. Anjum, F.M., Tassiulas, L.: Balanced RED: an algorithm to achieve fairness in the Internet. Technical Research Report (1999). http://www.dtic.mil/dtic/tr/fulltext/u2/a439654.pdf

  14. Aweya, J., Ouellette, M., Montuno, D.Y.: A control theoretic approach to active queue management. Comput. Netw. 36, 203–235 (2001)

    Article  Google Scholar 

  15. Sally Floyd website. http://www.icir.org/floyd/. Accessed 29 May 2021

  16. Chrysostomoua, C., Pitsillidesa, A., Rossidesa, L., Polycarpoub, M., Sekercioglu, A.: Congestion control in differentiated services networks using fuzzy-RED. Control. Eng. Pract. 11, 1153–1170 (2003)

    Article  Google Scholar 

  17. Feng, W.-C.: Improving Internet congestion control and queue management algorithms. http://thefengs.com/wuchang/umich_diss.html. Accessed 29 May 2021

  18. Al-Raddady, F., Woodward, M.: A new adaptive congestion control mechanism for the Internet based on RED. In: 21st International Conference on Advanced Information Networking and Applications, AINAW 2007 Workshops (2007)

    Google Scholar 

  19. Feng, W., Kandlur, D.D., Saha, D., Shin, K.G.: BLUE: a new class of active queue management algorithms. UM CSE-TR-387-99 (1999). https://www.cse.umich.edu/techreports/cse/99/CSE-TR-387-99.pdf

  20. Nichols, K., Jacobson, V., McGregor, A., Iyengar, J.: Controlled delay active queue management. RFC 8289. Internet Engineering Task Force. https://tools.ietf.org/html/rfc8289. Accessed 29 Aug 2019

  21. Hoeiland-Joergensen, T., McKenney, P., Taht, D., Gettys, J., Dumazet, E.: The flow queue CoDel packet scheduler and active queue management algorithm. Internet Engineering Task Force (2018). https://tools.ietf.org/html/rfc8290

  22. IETF working group on active queue management and packet scheduling (AQM): description of the working group. http://tools.ietf.org/wg/aqm/charters. Accessed 29 Aug 2019

  23. McKenney, P. E.: Stochastic fairness queueing. In: Proceedings of IEEE International Conference on Computer Communications, San Francisco, CA, USA, vol. 2, pp. 733–740. IEEE (1990). https://doi.org/10.1109/INFCOM.1990.91316

  24. Adams, R.: Active queue management: a survey. IEEE Commun. Surv. Tut. 15(3), 1425–1476 (2013)

    Article  Google Scholar 

  25. Paul, A.K., Kawakami, H., Tachibana, A., Hasegawa, T.: An AQM based congestion control for eNB RLC in 4G/LTE network. In: 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), Vancouver, BC, Canada, pp. 1–5. IEEE (2016). https://doi.org/10.1109/CCECE.2016.7726792

  26. Irazabal, M., Lopez-Aguilera, E., Demirkol, I.: Active queue management as quality of service enabler for 5G networks. In: European Conference on Networks and Communications (EuCNC), Valencia, Spain, pp. 421–426. IEEE (2019). https://doi.org/10.1109/EuCNC.2019.8802027

  27. Beshay, J.D., Nasrabadi, A.T., Prakash, R., Francini, A.: On active queue management in cellular networks. In: 2017 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Atlanta, GA, USA, pp. 384–389. IEEE (2017). https://doi.org/10.1109/INFCOMW.2017.8116407

  28. Pesántez-Romero, I.S., Pulla-Lojano, G.E., Guerrero-Vásquez, L.F., Coronel-González, E.J., Ordoñez-Ordoñez, J.O., Martinez-Ledesma, J.E.: Performance evaluation of hybrid queuing algorithms for QoS provision based on DiffServ architecture. In: Yang, X.-S., Sherratt, S., Dey, N., Joshi, A. (eds.) Proceedings of 6th International Congress on Information and Communication Technology. LNNS, vol. 216, pp. 333–345. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-1781-2_31

    Chapter  Google Scholar 

  29. George, J., Santhosh, R.: Congestion control mechanism for unresponsive flows in internet through active queue management system (AQM). In: Shakya, S., Bestak, R., Palanisamy, R., Kamel, K.A. (eds.) Mobile Computing and Sustainable Informatics. LNDECT, vol. 68, pp. 765–777. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-1866-6_58

    Chapter  Google Scholar 

  30. Singha, S., Jana, B., Jana, S., Mandal, N.K.: A novel congestion control algorithm using buffer occupancy RED. In: Das, A.K., Nayak, J., Naik, B., Dutta, S., Pelusi, D. (eds.) Computational Intelligence in Pattern Recognition. AISC, vol. 1349, pp. 519–528. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-2543-5_44

    Chapter  Google Scholar 

  31. Korolkova, A.V., Kulyabov, D.S., Chernoivanov, A.I.: On the classification of RED algorithms. Bull. Peoples’ Friendship Univ. Russ. Ser. Math. Inf. Sci. Phys. 3, 34–46 (2009)

    Google Scholar 

  32. Korolkova, A.V., Velieva, T.R., Abaev, P.O., Sevastianov, L.A., Kulyabov, D.S.: Hybrid simulation of active traffic management. In: Proceedings of 30th European Conference on Modelling and Simulation (ECMS), Regensburg, Germany, pp. 692–697. ECMS (2016). https://doi.org/10.7148/2016-0685

  33. Bonald, T., May, M., Bolot, J.: Analytic evaluation of RED performance. In: Proceedings IEEE INFOCOM 2000 Conference on Computer Communications, Tel Aviv, Israel, vol. 3, pp. 1415–1424. IEEE (2000). https://doi.org/10.1109/INFCOM.2000.832539

  34. Chydzinski, A., Chrost, L.: Analysis of AQM queues with queue size based packet dropping. Int. J. Appl. Math. Comput. Sci. 21(3), 567–577 (2011). https://doi.org/10.2478/v10006-011-0045-7

    Article  MathSciNet  MATH  Google Scholar 

  35. Chydzinski, A.: Improving quality of multimedia transmissions via dropping functions. In: Proceedings 2018 3rd International Conference on Smart and Sustainable Technologies (SpliTech), pp. 1–6 (2018)

    Google Scholar 

  36. Chydzinski, A.: On the transient queue with the dropping function. Entropy 22, 825 (2020). https://doi.org/10.3390/e22080825

    Article  MathSciNet  Google Scholar 

  37. Barczyk, M., Chydzinski, A.: Experimental testing of the performance of packet dropping schemes. In: 2020 IEEE Symposium on Computers and Communications (ISCC), pp. 1–7, (2020). https://doi.org/10.1109/ISCC50000.2020.9219624

  38. Konovalov, M.G., Razumchik, R.: Numerical analysis of improved access restriction algorithms in a \(GI|G|1|N\) system. J. Commun. Technol. Electron. 63(6), 616–625 (2018). https://doi.org/10.1134/S1064226918060141

    Article  Google Scholar 

  39. Kreinin, A.: Queueing systems with renovation. J. Appl. Math. Stochast. Anal. 10(4), 431–443 (1997). https://doi.org/10.1155/S1048953397000464

    Article  MathSciNet  MATH  Google Scholar 

  40. Gelenbe, E.: Product-form queueing networks with negative and positive customers. J. Appl. Probab. 28(3), 656–663 (1991). https://doi.org/10.2307/3214499

    Article  MathSciNet  MATH  Google Scholar 

  41. Pechinkin, A.V., Razumchik, R.V.: The stationary distribution of the waiting time in a queueing system with negative customers and a bunker for superseded customers in the case of the LAST-LIFO-LIFO discipline. J. Commun. Technol. Electron. 57(12), 1331–1339 (2012). https://doi.org/10.1134/S1064226912120054

    Article  Google Scholar 

  42. Razumchik, R.V.: Analysis of finite capacity queue with negative customers and bunker for ousted customers using Chebyshev and Gegenbauer polynomials. Asia Pac. J. Oper. Res. 31(04), 1450029 (2014). https://doi.org/10.1142/S0217595914500298

    Article  MathSciNet  MATH  Google Scholar 

  43. Semenova, O.V.: Multithreshold control of the \(BMAP/G/1\) queuing system with MAP flow of Markovian disasters. Autom. Remote. Control. 68(1), 95–108 (2007). https://doi.org/10.1134/S0005117907010092

    Article  MathSciNet  MATH  Google Scholar 

  44. Kim, C., Klimenok, V.I., Dudin, A.N.: Analysis of unreliable \(BMAP|PH|N\) type queue with Markovian flow of breakdowns. Appl. Math. Comput. 314, 154–172 (2017). https://doi.org/10.1016/j.amc.2017.06.035

    Article  MathSciNet  MATH  Google Scholar 

  45. Gudkova, I., et al.: Modeling and analyzing licensed shared access operation for 5G network as an inhomogeneous queue with catastrophes. In: International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, Lisbon, Portugal, pp. 282–287. IEEE (2016). https://doi.org/10.1109/ICUMT.2016.7765372

  46. Dudin, A.N., Klimenok, V.I., Vishnevsky, V.M.: Mathematical methods to study classical queuing systems. In: The Theory of Queuing Systems with Correlated Flows, pp. 1–61. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-32072-0_1

  47. Krishnamoorthy, A., Pramod, P.K., Chakravarthy, S.R.: Queues with interruptions: a survey. TOP 22(1), 290–320 (2014). https://doi.org/10.1007/s11750-012-0256-6

    Article  MathSciNet  MATH  Google Scholar 

  48. Vishnevsky, V.M., Kozyrev, D.V., Semenova, O.V.: Redundant queuing system with unreliable servers. In: International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, St. Petersburg, Russia, pp. 283–286. IEEE (2014). https://doi.org/10.1109/ICUMT.2014.7002116

  49. Jain, M., Kaur, S., Singh, P.: Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI). Oper. Res. Int. J. (2019). https://doi.org/10.1007/s12351-019-00519-8

  50. Rykov, V.V., Kozyrev, D.V.: Analysis of renewable reliability systems by Markovization method. In: Rykov, V.V., Singpurwalla, N.D., Zubkov, A.M. (eds.) ACMPT 2017. LNCS, vol. 10684, pp. 210–220. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71504-9_19

    Chapter  Google Scholar 

  51. Rykov, V., Kozyrev, D.: On the reliability function of a double redundant system with general repair time distribution. Appl. Stoch. Models Bus. Ind. 35, 191–197 (2019). https://doi.org/10.1002/ASMB.2368

    Article  MathSciNet  MATH  Google Scholar 

  52. Nguyen, D.P., Kozyrev, D.: Reliability analysis of a multirotor flight module of a high-altitude telecommunications platform operating in a random environment. In: 2020 International Conference Engineering and Telecommunication (En&T), pp. 1–5 (2020). https://doi.org/10.1109/EnT50437.2020.9431312

  53. Bocharov, P.P., Zaryadov, I.S.: Probability distribution in queueing systems with renovation. Bull. Peoples’ Friendship Univ. Russ. Ser. Math. Inf. Sci. Phys. 1–2, 15–25 (2007). (in Russian)

    Google Scholar 

  54. Zaryadov, I.S., Pechinkin, A.V.: Stationary time characteristics of the \(GI/M/n/\infty \) system with some variants of the generalized renovation discipline. Autom. Remote. Control. 70(12), 2085–2097 (2009). https://doi.org/10.1134/S0005117909120157

    Article  MathSciNet  MATH  Google Scholar 

  55. Zaryadov, I., Razumchik, R., Milovanova, T.: Stationary waiting time distribution in G\(|\)M\(|\)n\(|\)r with random renovation policy. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2016. CCIS, vol. 678, pp. 349–360. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-51917-3_31

    Chapter  Google Scholar 

  56. Konovalov, M., Razumchik, R.: Queueing systems with renovation vs. queues with RED. Supplementary material (2017). https://arxiv.org/abs/1709.01477

  57. Konovalov, M., Razumchik, R.: Comparison of two active queue management schemes through the M/D/1/N queue. Informatika i ee Primeneniya (Inf. Appl.) 12(4), 9–15 (2018). https://doi.org/10.14357/19922264180402

  58. Bogdanova, E.V., Zaryadov, I.S., Milovanova, T.A., Korolkova, A.V., Kulyabov, D.S.: Characteristics of lost and served packets for retrial queueing system with general renovation and recurrent input flow. In: Vishnevskiy, V.M., Kozyrev, D.V. (eds.) DCCN 2018. CCIS, vol. 919, pp. 327–340. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99447-5_28

    Chapter  Google Scholar 

  59. Zaryadov, I., Bogdanova, E., Milovanova, T., Matushenko, S., Pyatkina, D.: Stationary characteristics of the \(GI|M|1\) queue with general renovation and feedback. In: 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia. IEEE (2019). Article no. 8631244. https://doi.org/10.1109/ICUMT.2018.8631244

  60. Hilquias, V.C.C., et al.: The general renovation as the active queue management mechanism. some aspects and results. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2019. CCIS, vol. 1141, pp. 488–502. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36625-4_39

    Chapter  Google Scholar 

  61. Meykhanadzhyan, L.A., Zaryadov, I.S., Milovanova, T.A.: Stationary characteristics of the two-node Markovian tandem queueing system with general renovation. Sistemy i Sredstva Informatiki [Syst. Means Inform.] 30(3), 14–31 (2020)

    Google Scholar 

  62. Gorbunova, A.V., Lebedev, A.V.: Queueing system with two input flows, preemptive priority, and stochastic dropping. Autom. Remote. Control. 81(12), 2230–2243 (2020). https://doi.org/10.1134/S0005117920120073

    Article  MathSciNet  MATH  Google Scholar 

  63. Hilquias, C.C.V., Zaryadov, I.S.: Comparation of two single-server queueing systems with exponential service times and threshold-based renovation. In: CEUR Workshop Proceedings, vol. 2946, pp. 54–63 (2021)

    Google Scholar 

  64. Pechinkin, A.V., Razumchik, R.R., Zaryadov, I.S.: First passage times in \(M_2^{[X]} | G | 1 | R\) queue with hysteretic overload control policy. In: AIP Conference Proceedings, Rhodes, vol. 1738. American Institute of Physics Inc. (2016). Article no. 220007. https://doi.org/10.1063/1.4952006

  65. Razumchik, R.: Analysis of finite \(MAP|PH|1\) queue with hysteretic control of arrivals. In: International Congress on Ultra Modern Telecommunications and Control Systems and Workshops, Lisbon. Portugal, pp. 288–293. IEEE (2016). Article no. 7765373. https://doi.org/10.1109/ICUMT.2016.7765373

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Authors and Affiliations

  1. Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya Street 6, Moscow, 117198, Russia

    Viana C. C. Hilquias, I. S. Zaryadov & T. A. Milovanova

  2. Institute of Informatics Problems, FRC CSC RAS, IPI FRC CSC RAS, 44-2 Vavilova Street, Moscow, 119333, Russia

    I. S. Zaryadov

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  1. Viana C. C. Hilquias
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  2. I. S. Zaryadov
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  3. T. A. Milovanova
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Correspondence to I. S. Zaryadov .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. Applied Probability and Informatics Department, RUDN University, Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Hilquias, V.C.C., Zaryadov, I.S., Milovanova, T.A. (2021). Two Types of Single-Server Queueing Systems with Threshold-Based Renovation Mechanism. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_17

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