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Computation and optimization methods for multiresource queues

  • Systems Analysis
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Cybernetics and Systems Analysis Aims and scope

Conclusion

Our survey naturally could not encompass all the results available in this promising field of the theory of multistream queueing systems. We have attempted to systematize the main computation and optimization methods for MRQ models, highlighting the topical issues of the theory and practice of MRQ. Even this partial survey of work on MRQ leads to the conclusion that the main sources stimulating the development of MRQ theory are the requirements of modern teletraffic theory, and in particular problems that arise in DIQN. Moreover, MRQ provide a generalization of classical multistream models, and their study is thus of independent interest for probability experts. These conclusions are borne out by the publications in recent years, and there is every reason to expect that the next decade will promote MRQ research into one of the central places in the theory of multistream queueing systems.

I would like to thank Academician V. S. Korolyuk for formulating a number of research topics for multiresource queues and Academician I. N. Korolenko for his support of this study.

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References

  1. K. J. Omahen, “Capacity bounds for multiresource queues,” J. ACM,24, No. 4, 646–663 (1977).

    MATH  MathSciNet  Google Scholar 

  2. L. A. Ponomarenko and A. Z. Melikov, “Finding an optimal service discipline in a multiresource system with finite switching time,” Elektron. Modelirov.,11, No. 2, 67–70 (1989).

    Google Scholar 

  3. Y. de Serre and L. G. Mason, “A multiserver queue with narrow-and wide-band customers and wide-band restricted access,” IEEE Trans. Commun.,36, No. 6, 675–684 (1988).

    Google Scholar 

  4. L. Green, “A queueing system in which customers require a random number of servers,” Oper. Res.,28, No. 9, 1335–1346 (1980).

    MATH  MathSciNet  Google Scholar 

  5. L. Green, “A queueing system with auxiliary servers,” Manag. Sci.,30, No. 10, 1207–1216 (1984).

    MATH  Google Scholar 

  6. A. Federgruen and L. Green, “AnM/G/S queue in which the number of servers required is random,” J. Appl. Prob.,21, No. 3, 583–601 (1984).

    MathSciNet  Google Scholar 

  7. A. F. Seila, “On waiting times for a queue in which customers require simultaneous service from a random number of servers,” Oper. Res.32, 1181–1184 (1984).

    MATH  Google Scholar 

  8. L. A. Gimpelson, “Analysis of mixtures of wide-and narrow-band traffic,” IEEE Trans. Commun. Technol.,13, No. 3, 258–266 (1965).

    Google Scholar 

  9. W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Techn. J.,64, No. 8, 1807–1856 (1985).

    MATH  MathSciNet  Google Scholar 

  10. F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Stat. Lab., Univ. of Cambridge (1985).

  11. B. A. Sevast'yanov, “Ergodic theorem for Markov processes and its application to telephone systems with refusals,” Teor. Veroyat. Primen.,2, No. 1, 104–113 (1957).

    MathSciNet  Google Scholar 

  12. I. N. Kovalenko, “On independence of stationary distributions of the form of the service-time distribution law,” Probl. Pered. Inform., No.11, 147–151 (1963).

    Google Scholar 

  13. F. Kamoun and L. Kleinrock, “Analysis of shared finite storage in a computer network node environment under general traffic conditions,” IEEE Trans. Commun.,28, No. 7, 992–1003 (1980).

    MathSciNet  Google Scholar 

  14. J. S. Kaufman, “Blocking in shared resource environment,” IEEE Trans. Commun.,10, No. 10, 1474–1481 (1981).

    Google Scholar 

  15. J. P. Buzen, “Computational algorithms for closed networks with exponential servers,” Comm. ACM,16, No. 9, 527–531 (1973).

    MATH  MathSciNet  Google Scholar 

  16. A. Z. Melikov, “A computational algorithm for multiresource queues,” Elektron. Modelirov.,14, No. 5, 52–56 (1992).

    Google Scholar 

  17. G. P. Basharin, P. P. Bocharov, and Ya. A. Kogan, Analysis of Queues in Computer Networks. Theory and Computational methods [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  18. G. P. Basharin, B. E. Kurenkov, and A. V. Chumaev, “Analysis of mixed traffic service in a server-switching subsystem of a digital integral-service queueing network,” 15th All-Union School-Seminar on Computer Networks, Abstracts of Papers [in Russian], Part III, Moscow (1990), pp. 9–13.

  19. Y. Conrandt and A. Bucheister, “Considerations on loss probability of multi-slot connections,” Proc. 11th Int. Teletraffic Congress, 3.4.4.B2, Kyoto (1985), pp. 1–17.

  20. F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. Appl. Prob.,18, No. 2, 473–505 (1986).

    MATH  Google Scholar 

  21. K. W. Ross and D. H. Tsang, “Algorithms for determining exact blocking probabilities in tree networks,” IEEE Trans. Commun.,38, No. 8, 1266–1271 (1990).

    Google Scholar 

  22. K. W. Ross and D. H. Tsang, “Teletraffic engineering for product-form circuit-switched networks,” Adv. Appl. Prob.,22, No. 3, 657–675 (1990).

    MathSciNet  Google Scholar 

  23. M. Pioro, J. Lubacz, and U. Korner, “Traffic enginering problems in multi-service circuit-switched networks,” Comput. Networks and ISDN Systems,20, 127–136 (1990).

    Google Scholar 

  24. W. Wang and E. Pinsky, “An asymptotic analysis of complete sharing policy,” IEEE INFOCOM '89 Conf. Comput. Commun., Proc. 8th Annual Joint Conf. IEEE Comput. and Commun. Soc. Technol., Vol. 3, Ottawa, April 23–27, (1989), pp. 1038–1046.

    Google Scholar 

  25. H. Saito, “Analysis of measured loss probability and grade-of-service in ISDNs,” Computer Networks and ISDN Systems,15, No. 5, 359–367 (1988).

    Google Scholar 

  26. K. Miyake, “Traffic study of primary rate ISDN user-network interface,” Computer Networks and ISDN Systems,15, No. 5, 359–367 (1988).

    MATH  Google Scholar 

  27. M. D. Nico, “Blocking of finite source inputs which require simultaneous servers with general think and holding times,” Oper. Res. Lett.,8, No. 1, 45–52 (1989).

    MathSciNet  Google Scholar 

  28. H. Brill and L. Green, “Queues in which customers receive simultaneous service from a random number of servers: a system point approach,” Manag. Sci.,30, No. 1, 51–68 (1984).

    MathSciNet  Google Scholar 

  29. A. R. Unwin, “Results for dual resource queues,” Lect. Notes Contr. Inform. Sci.,60, 351–370 (1984).

    MATH  MathSciNet  Google Scholar 

  30. G. Y. Fletcher, H. G. Perros, and W. Stewart, “A queueing system where customers require a random number of servers simultaneously,” Eur. J. Oper. Res.,23, No. 3, 331–342 (1986).

    MathSciNet  Google Scholar 

  31. G. Y. Fletcher, H. G. Perros, and W. Stewart, “A queueing network model of a circuit-switching access scheme in an integrated services environment,” IEEE Trans. Commun.,34, No. 1, 25–30 (1986).

    Google Scholar 

  32. K. W. Ross and D. H. Tsang, “Optimal circuit access policies in an ISDN environment: A Markov decision approach,” IEEE Trans. Commun.,37, No. 9, 934–939 (1989).

    MathSciNet  Google Scholar 

  33. S. P. Evans, “Optimal bandwidth management and capacity provision in a broadband network using virtual paths,” Perform. Eval.,13, 27–43 (1991).

    Article  MATH  Google Scholar 

  34. C. A. Courcoubetis and M. I. Reiman, “Optimal control of queueing system with simultaneous service requirements,” IEEE Trans. Autom. Contr.,AC-32, No. 8, 717–727 (1987).

    MathSciNet  Google Scholar 

  35. C. A. Courcoubetis and M. I. Reiman, “The optimal control ofN servers and customers with simultaneous service requirements,” Proc. 24th IEEE Conf. Decision and Control, Vol. 3, Fort Lauderdale, Florida, Dec. 11–13, (1985), pp. 2036–2040.

    Google Scholar 

  36. A. Z. Melikov, “Approximate optimization of multiresource queueing systems,” Kibernetika, No. 6, 120–122 (1990).

    MathSciNet  Google Scholar 

  37. A. Z. Melikov, “Methods of analysis and optimization of multistream queueing systems,” Avtomat. Vychisl. Tekhn., No. 3, 13–21 (1992).

    Google Scholar 

  38. A. Z. Melikov, “On multiresource queueing systems,” Elektron. Modelirov.,12, No. 5, 21–24 (1990).

    Google Scholar 

  39. A. Z. Melikov, “Approximate optimization of multiresource queueing systems,” Elektron. Modelirov.,13, 92–98 (1991).

    Google Scholar 

  40. A. Z. Melikov, A. A. Molchanov, and L. A. Ponomarenko, “Multiresource queueing systems with partially switchable servers,” Elektron. Modelirov.,14, No. 2, 87–91 (1992).

    Google Scholar 

  41. A. Z. Melikov and L. A. Ponomarenko, “Optimal access strategies in digital integral-service queueing networks,” Avtomat. Vychisl. Tekhn. No. 2, 28–36 (1992).

    Google Scholar 

  42. A. Z. Melikov and L. A. Ponomarenko, “Optimization of digital integral-service queueing network with finitely many users and blocking,” Avtomat. Telemekh., No. 6, 86–92 (1992).

    MathSciNet  Google Scholar 

  43. L. A. Ponomarenko and A. Z. Melikov, “Customer scheduling in multiresource systems with pure losses,” Kibernetika, No. 1, 109–112 (1989).

    Google Scholar 

  44. L. A. Ponomarenko and A. Z. Melikov, “Closed multiresource queueing systems with controlled priorities,” Kibernetika, No. 5, 90–93 (1989).

    MathSciNet  Google Scholar 

  45. L. A. Ponomarenko and A. Z. Melikov, “Control of a queueing system with a paired server,” in: Theoretical and Applied Topics of Algorithm and Software Design for MIS [in Russian], Inst. Kibern. AN Ukr., Kiev (1988), pp. 73–78.

    Google Scholar 

  46. A. Z. Melikov, A. A. Molchanov, and L. A. Ponomarenko, “Finding optimal strategy of access in multiresource queue,” Proc. Int. Conf. on System Sci., XI, Wroclaw, Poland (1992), p. 96.

  47. V. V. Mova, L. A. Ponomarenko, and N. A. Ryumshin Priority Service Organization in MIS [in Russian], Tekhnika, Kiev (1977).

    Google Scholar 

  48. A. Z. Melikov, L. A. Ponomarenko, and N. A. Ryumshin, Mathematical Models of Multistream Queueing Systems [in Russian], Tekhnika, Kiev (1991).

    Google Scholar 

  49. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  50. A. Hahnewald-Busch, “Verfahren zur aggregation in zustandstraum bei markovschen Entscheidungsproblemen,” Wiss. Ber. Techn. Hochsch. Leipzig, No. 7, 10–12 (1986).

    Google Scholar 

Download references

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 92–112, November–December, 1996.

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Melikov, A.Z. Computation and optimization methods for multiresource queues. Cybern Syst Anal 32, 821–836 (1996). https://doi.org/10.1007/BF02366862

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