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Queueing system with processor sharing and limited memory under control of the AQM Mechanism

  • Stochastic Systems, Queueing Systems
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Abstract

Consideration was given to the queueing system with processor sharing and limited memory which services random-capacity customers whose lengths depend on their capacities. The system performs the algorithm of active queue management, that is, at the instant of its arrival each customer can be rejected and dropped with a probability depending on the customer capacity and the total capacity of other customers sojourning in the system even if there is a free memory space available. The stationary distribution of the number of customers and the loss probability were determined for the system under consideration.

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References

  1. Berger, A.W. and Kogan, Y., Dimensioning Bandwidth for Elastic Traffic in High-speed Data Networks, IEEE/ACM Trans. Netw., 2000, vol. 8, no. 5, pp. 643–654.

    Article  Google Scholar 

  2. Bonald, T. and Massouli, L., Impact of Fairness on Internet Performance, in Proc. SIGMETRICS’01, 2001, pp. 82–91.

    Google Scholar 

  3. Chen, N. and Jordan, S., Throughput in Processor-sharing Queues, IEEE Trans. Autom. Control, 2007, vol. 52, no. 2, pp. 299–305.

    Article  MathSciNet  Google Scholar 

  4. Coffman, J.E.G., Muntz, R.R., and Trotter, H., Waiting Time Distributions for Processor-sharing Systems, J. ACM, 1970, vol. 17, no. 1, pp. 123–130.

    Article  MATH  MathSciNet  Google Scholar 

  5. Morrison, J.A., Asymptotic Analysis of the Waiting-time Distribution for a Large Closed Processorsharing System, SIAM J. Appl. Math., 1986, vol. 46, pp. 140–170.

    Article  MATH  MathSciNet  Google Scholar 

  6. Knessl, C., On the Sojourn Time Distribution in a Finite Capacity Processor Shared Queue, J. ACM, 1993, vol. 40, no. 5, pp. 1238–1301.

    Article  MATH  MathSciNet  Google Scholar 

  7. Ott, T.J., The Sojourn-time Distribution in the M/G/1 Queue with Processor Sharing, J. Appl. Prob., 1984, vol. 21, pp. 360–378.

    Article  MATH  MathSciNet  Google Scholar 

  8. Schassberger, R., A New Approach to the M/G/1 Processor-sharing Queue, Adv. Appl. Prob., 1984, vol. 16, pp. 202–213.

    Article  MATH  MathSciNet  Google Scholar 

  9. Yashkov, S.F., A Derivation of Response Time Distribution for an M/G/1 Processor-sharing Queue, Probl. Control Inf. Theory, 1983, vol. 12, no. 2, pp. 133–148.

    MATH  MathSciNet  Google Scholar 

  10. Van den Berg, J.L. and Boxma, O., The M/G/1 Queue with Processor Sharing and its Relation to a Feedback Queue, Queuing Syst., 1991, vol. 9, pp. 365–402.

    Article  MATH  Google Scholar 

  11. Yashkov, S.F. and Yashkova, A.S., Egalitarian Processor Sharing, Inform. Prots., 2006, vol. 6, no. 4, pp. 396–444.

    Google Scholar 

  12. Floyd, S. and Jacobson, V., Random Early Detection Gateways for Congestion Avoidance, IEEE/ACM Trans. Netw., 1993, vol. 1, no. 4, pp. 397–412.

    Article  Google Scholar 

  13. Liu, S., Basar, T., and Srikant, R., Exponential RED: A Stabilizing AQM Scheme for Low- and Highspeed TCP Protocols, IEEE/ACM Trans. Netw., 2005, vol.13, no. 5, pp. 1068–1081.

    Article  Google Scholar 

  14. Zhou, K., Yeung, KL., and Li, V.O.K., Nonlinear RED: A Simple yet Efficient Active Queue Management Scheme, Comput. Netw., 2006, vol. 50, no. 18, pp. 3784–3794.

    Article  MATH  Google Scholar 

  15. 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, 2011, vol. 47, no. 6, pp. 930–943.

    MATH  MathSciNet  Google Scholar 

  16. Yashkov, S.F., Analiz ocheredei v EVM (Analysis of Computer Queues), Moscow: Radio i Svyaz’, 1989

    Google Scholar 

  17. Tikhonenko, O.M., Modeli massovogo obsluzhivaniya v sistemakh obrabotki informatsii (Queuing System Models in Information Processing Systems), Minsk: Universitetskoe, 1990

    Google Scholar 

  18. Tikhonenko, O., Metody probabilistyczne anaizy system´ow informacijnych (Probabilistic Methods of Information System Analysis) Warsaw: Akademicka Oficyna Wydawnicza EXIT, 2006 (in Polish).

    Google Scholar 

  19. Tikhonenko, O. and Kempa, W.M., The Generalization of AQM Algorithms for Queuing Systems with Bounded Capacity, Lect. Notes Comput. Sci., 2012, vol. 7204, pp. 242–251.

    Article  Google Scholar 

  20. Tikhonenko, O. and Kempa, W.M., Queue-size Distribution in M/G/1-type System with Bounded Capacity and Packet Dropping, Comm. Comp. Inf. Sci., 2013, vol. 356, pp. 177–186.

    Article  Google Scholar 

  21. Tikhonenko, O. and Kempa, W.M., On the Queue-size Distribution in the Multiserver System with Bounded Capacity and Packet Dropping, Kybernetika, 2013, vol. 49, no. 6, pp. 855–867.

    MATH  MathSciNet  Google Scholar 

  22. Tikhonenko, O.M., Queuing Systems with Processor Sharing and Limited Resources, Autom. Remote Control, 2010, vol. 71, no. 5, pp. 803–815.

    Article  MATH  MathSciNet  Google Scholar 

  23. Matveev, V.F. and Ushakov, V.G., Sistemy massovogo obsluzhivaniya (Queuing Systems), Moscow: Mosk. Gos. Univ., 1984

    Google Scholar 

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Correspondence to O. M. Tikhonenko or W. Kempa.

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Original Russian Text © O.M. Tikhonenko, W. Kempa, 2015, published in Avtomatika i Telemekhanika, 2015, No. 10, pp. 90–105.

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Tikhonenko, O.M., Kempa, W. Queueing system with processor sharing and limited memory under control of the AQM Mechanism. Autom Remote Control 76, 1784–1796 (2015). https://doi.org/10.1134/S0005117915100069

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