Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
KIBERNETYKA TA SYSTEMNYI ANALIZ
International Theoretical Science Journal
Volume 60 >>> № 2 MARCH — APRIL 2024
-->

DOI 10.34229/KCA2522-9664.24.2.5
UDC 519.872
I.M. Kuznetsov1, A.A. Shumska2


1 Institute of Physics and Technology of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

 sea_hawk@icloud.com

2 Institute of Physics and Technology of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

 shumska-aa@ukr.net

APPLYING FAST SIMULATION TO THE EVALUATION OF CUSTOMERS BLOCKING
PROBABILITY IN THE MULTICHANNEL QUEUING SYSTEM WITH MULTICAST ACCESS

Abstract. A model of the multichannel queuing system is considered. Each channel contains some service lines. There are several input flows. Each customer requires several lines to be serviced. If the channel does not have a sufficient number of service lines, it is possible to reorient this customer to another channel. The service time has a distribution function of a general form depending both on the flow and on the number of lines required by the customer. A fast simulation method aimed to evaluate the blocking probability of customers of a certain flow with a given number of service lines is proposed. The method is compared with the Monte Carlo method using numerical example and the gain in simulation time is illustrated in particular.

Keywords: queuing system, channel, line, blocking probability, Monte Carlo method, fast simulation, multicast access, estimate, relative error.


full text

REFERENCES

  1. Ross K.W. Multiservice Loss Models for Broadband Telecommunication Networks. London: Springer Verlag, 1995. 343 p.

  2. Nyberg E., Virtamo J., Aalto S. An exact algorithm for calculating blocking probabilities in multicast networks. Proc. NETWORKING 2000. Broadband Communications, High Performance Networking, and Performance of Communication Networks (14–19 May 2000, Paris, France). Paris, 2000. LNCS. Vol. 1815. P. 275–286. https://doi.org/10.1007/3-540-45551-5_24.

  3. Karvo J. Efficient simulation of blocking probabilities for multi-layer multicast streams. Proc. NETWORKING 2002: Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications (19-24 May 2002, Pisa, Italy). Pisa, 2002. LNCS. Vol. 2345. P. 1020–1031. https://doi.org/10.1007/ 3-540-47906-6_83.

  4. Frenkel I.B., Karagrigoriou A., Lisnianski A., Kleyner A.V. Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference. New York: Wiley, 2013. 448 p.

  5. Wong E.W.M., Chan Y.-C. A century-long challenge in teletraffic theory: blocking probability evaluation for overflow loss systems with mutual overflow. IEEE Access. 2023. Vol. 11. P. 61274–61288. https://doi.org/10.1109/ACCESS.2023.3283803.

  6. Wong E.W.M., Guo J., Moran B., Zukerman M. Information exchange surrogates for approximation of blocking probabilities in overflow loss systems. Proc. 25th International. Teletraffic Congress (ITC) (10–12 September 2013, Shanghai, China). Shanghai, 2013. P. 1–9. https://doi.org/10.1109/ITC.2013.6662932.

  7. Chan Y.-C., Wong E.W.M. Blocking probability evaluation for non-hierarchical overflow loss systems. IEEE Trans. Commun. 2018. Vol. 66, Iss. 5. P. 2022–2036. https://doi.org/10.1109/TCOMM.2017.2784450.

  8. Wu J., Wong E.W.M., Guo J., Zukerman M. Performance analysis of green cellular networks with selective base-station sleeping. Perform. Eval. 2017. Vol. 111. P. 17–36. https://doi.org/10.1016/j.peva.2017.03.002.

  9. Kuznetsov M.Y., Shumska A.A. Fast simulation of steady-state call blocking probability in a two-channel system with threshold service strategies. Cybernetics and Systems Analysis. 2023. Vol. 59, N 5. P. 794–802. https://doi.org/10.1007/s10559-023-00615-w .

  10. Sagkriotis S.G., Pantelis S.K., Moscholios I.D., Vassilakis V.G. Call blocking probabilities in a two-link multirate loss system for Poisson traffic. IET Networks. 2018. Vol. 7, Iss. 4. P. 233–241. https://doi.org/10.1049/iet-net.2017.0223.

  11. Glynn P.W. Likelihood ratio gradient estimation for stochastic systems. Communications of the ACM. 1990. Vol. 33, Iss. 10. P. 75–84. https://doi.org/10.1145/84537.84552.

  12. Heidelberger P. Fast simulation of rare events in queueing and reliability models. ACM Transactions on Modeling and Computer Simulation. 1995. Vol. 5, Iss. 1. P. 43–85. https://doi.org/10.1145/203091.203094.

  13. Falkner M., Devetsikiotis M., Lambadaris I. Fast simulation of networks of queues with effective and decoupling bandwidths. ACM Transactions on Modeling and Computer Simulation. 1999. Vol. 9, Iss. 1. P. 45–58. https://doi.org/10.1145/301677.301684.

  14. Li J., Mosleh A., Kang R. Likelihood ratio gradient estimation for dynamic reliability applications. Reliab. Engin. and System Safety. 2011. Vol. 96, Iss. 12. P. 1667–1679. https://doi.org/10.1016/j.ress.2011.08.001.

  15. Kovalenko I.N., Kuznetsov N.Yu. Methods for calculating highly reliable systems [in Russian]. Moscow: Radio i svyaz', 1988. 176 p.

  16. Kovalenko I.N., Kuznetsov N.Yu., Pegg Ph.A. Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications. Chichester: Wiley, 1997. 303 p. https://doi.org/10.34229/1028-0979-2023-3-5.

  17. Shumskaya A.A. Fast simulation of unavailability of a repairable system with a bounded relative error of estimate. Cybernetics and Systems Analysis. 2003. Vol. 39, N 3. P. 357–366. https://doi.org/10.1023/A:1025753309479.

  18. Kuznetsov N.Yu. Fast simulation technique in reliability evaluation of Markovian and non-Markovian systems. In: Simulation and Optimization Methods in Risk and Reliability Theory. New York: Nova Science Publishers, 2009. P. 69–112.

  19. Kuznetsov N.Yu., Shumskaya A.A. Assessment of the risk of failure of a redundant system using accelerated modeling. Problemy upravleniya i informatiki. 2013. N 3. P. 50–62. https://doi.org/10.1615/JAutomatInfScien.v45.i5.40.

  20. Glasserman P., Heіdelberger Ph., Shahabuddіn P., Zajіc T. Multilevel splitting for estimating rare event probabilities. Oper. Research. 1999. Vol. 47, N 4. P. 585–600.

  21. Glasserman P. Monte Carlo Methods in Financial Engineering. New York: Springer, 2004. 575 p. https://doi.org/10.1007/978-0-387-21617-1.

  22. Lagnoux A. Rare event simulation. Probab. Eng. and Inf. Sci. 2006. Vol. 20, Iss. 1. P. 45–66. https://doi.org/10.1017/S0269964806060025.

  23. Gertsbakh I.B., Shpungin Y. Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo. Boca Raton: CRC Press, 2012. 217 p. https://doi.org/10.1201/b12536.

  24. Blanchet J., Lam H. Rare event simulation techniques. Proc. 2011 Winter Simulation Conference. (11–14 December 2011, Phoenix, USA). Phoenix, 2011. P. 146–160.

  25. Kuznetsov N.Y., Kuznetsov I.N. Fast simulation of the customer blocking probability in queueing networks with multicast access. Cybernetics and Systems Analysis. 2021. Vol. 57, N 4. P. 530–541. https://doi.org/10.1007/s10559-021-00378-2.

  26. Kuznetsov M.Yu., Kuznetsov I.M., Shumska A.A. Accelerated simulation of the probability of blocking demands in a service network with multiple access and periodic intensities of incoming flows. Problemy keruvannya ta informatyky. 2023. Vol. 68, N 3. P. 32–46. https://doi.org/10.34229/1028-0979-2023-3-5.




Editorial Board Announcements Abstracts Authors Archive
about scope office editorial board instructions for authors subscriptions contacts
© 2024 Kibernetika.org. All rights reserved.