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Cybernetics And Systems Analysis
International Theoretical Science Journal
Volume 56 >>> № 1 JANUARY — FEBRUARY 2020
UDC 519.872
A.Z. Melikov1, L.A. Ponomarenko2, E.V. Mekhbaliyeva3


1 Institute of Control Systems, National Academy of Sciences
of Azerbaijan, Baku, Azerbaijan

 agassi.melikov@rambler.ru

2 International Scientific and Training Center of Information Technologies and Systems, National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kyiv, Ukraine

 laponomarenko@ukr.net

3 Sumqayit State University, Sumqayit, Azerbaijan

ANALYZING THE MODELS OF SYSTEMS WITH HETEROGENEOUS SERVERS

Abstract. The mathematical model of a queueing system with heterogeneous servers, without queues and two types of calls is investigated. High priority calls are processed in fast servers while low priority calls are processed in slow servers. If all servers in some group are busy then reassigning of calls to another group is allowed. Reassigning is based on random schemes and reassignment probability depends on the number of busy servers in appropriate group. Exact and approximate methods are developed for the analysis of characteristics of the system. Explicit approximate formulas to calculate the approximate values of characteristics are proposed.

Keywords: queuing-inventory system, heterogeneous servers, priority, customers of different types, optimization.



FULL TEXT

REFERENCES

  1. Gumbel H. Waiting lines with heterogeneous servers. Operations Research. 1960. Vol. 8, Iss. 4. P. 504–511.

  2. Singh V.S. Two-server Markovian queues with balking: Heterogeneous vs homogeneous servers. Operations Research. 1970. Vol. 18, Iss 1. P. 145–159.

  3. Singh V.S. Markovian queues with three servers. IIE Transactions. 1971. Vol. 3, Iss. 1. P. 45–48.

  4. Fakinos D. The blocking system with heterogeneous servers. Journal of Operations Research Society. 1980. Vol. 31, Iss. 10. P. 919–927.

  5. Fakinos D. The generalized blocking system with heterogeneous servers. Journal of Operations Research Society. 1982. Vol. 33, Iss. 9. P. 801–809.

  6. Nath G., Enns E. Optimal service rates in the multi-server loss system with heterogeneous servers. Journal of Applied Probability. 1981. Vol. 18, Iss. 3. P. 776–781.

  7. Alpaslan F., Shahbazov A. An analysis and optimization of stochastic service with heterogeneous channels and Poisson arrivals. Pure and Apllied Mathematika Science. 1996. Vol. 43. P. 15–20.

  8. Lin B.W., Elsayed E.A. A general solution for multichannel queueing systems with ordered entry. Computers & Operations Research. 1978. Vol. 5, Iss. 4. P. 219–225.

  9. Elsayed E.A. Multichannel queueing systems with ordered entry and finite source. Computers & Operations Research. 1983. Vol. 10, Iss. 3. P. 213–222.

  10. Yao D.D. The arrangement of servers in an ordered-entry system. Operations Research. 1987. Vol. 35, Iss. 5. P. 759–763.

  11. Pourbabai B., Sonderman D. Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers. Journal of Applied Probability. 1986. Vol. 23, Iss. 1. P. 236–242.

  12. Pourbabai B. Markovian queueing systems with retrials and heterogeneous servers. Computers & Mathematics with Applications. 1987. Vol. 13, Iss. 12. P. 917–923.

  13. Nawijn W.M. On a two-server finite queuing system with ordered entry and deterministic arrivals. European Journal of Operations Research. 1984. Vol. 18, Iss. 3. P. 388–395.

  14. Nawijn W.M. A Note on many-server queueing systems with ordered entry with an application to conveyor theory. Journal of Applied Probability. 1983. Vol. 20. P. 144–152.

  15. Yao D.D. Convexity properties of the overflow in an ordered-entry system with heterogeneous servers. Operations Research Letters. 1986. Vol. 5, Iss. 3. P. 145–147.

  16. Isguder H.O., Kocer U.U. Analysis of queueing system with ordered entry and no waiting line. Applied Mathematical Modelling. 2014. Vol. 38, Iss. 3. P. 1024–1032.

  17. Larsen R.L., Agrawala A.K. Control of heterogeneous two-server exponential queueing system. IEEE Transactions on Software Engineering. 1983. Vol. SE-9, Iss. 4. P. 522–526.

  18. Koole G. A simple proof of the optimality of a threshold policy in a two-server queueing system. Systems & Control Letter. 1995. Vol. 26, Iss. 5. P. 301–303.

  19. Lin W., Kumar P.R. Optimal control of queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control. 1984. Vol. 29, Iss. 8. P. 696–703.

  20. Luh H.P., Viniotis I. Threshold control policies for heterogeneous servers systems. Mathematical Methods in Operational Research. 2002. Vol. 55, Iss. 1. P. 121–142.

  21. Weber R. On a conjecture about assigning jobs to processors of different speeds. IEEE Transactions on Automatic Control. 1993. Vol. 38, Iss. 1. P. 166–170.

  22. Efrosinin D. Sztrik J. Optimal control of a two-server heterogeneous queueing system with breakdowns and constant retrials. In: Information Technologies and Mathematical Modelling — Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science. Dudin A., Gortsev A., Nazarov A., Yakupov R. (Eds.). 2016. Vol. 638. P. 57–72.

  23. Efrosinin D. Sztrik J., Farkhadov M., Stepanova N. Reliability analysis of two-server heterogeneous queueing system with threshold control policy. In: Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2017. Communications in Computer and Information Science. Dudin A., Nazarov A., Kirpichnikov A. (Eds.). 2017. Vol. 800. P. 13–27.

  24. Viniotis I., Ephremides A. Extension of the optimality of a threshold policy in heterogeneous multi-server queueing systems. IEEE Transactions on Automatic Control. 1988. Vol. 33, Iss. 1. P. 104–109.

  25. Rosberg Z., Makowski A.M. Optimal routing to parallel heterogeneous servers — Small arrival rates. IEEE Transactions on Automatic Control. 1990. Vol. 35, Iss. 7. P. 789–796.

  26. Rykov V.V. Monotone control of queueing systems with heterogeneous servers. Queueing Systems. 2001. Vol. 37. P. 391–403.

  27. Rykov V.V., Efrosinin D. On the slow server problem. Automation and Remote Control. 2009. Vol. 70, Iss. 12. P. 2013–2023.

  28. Neuts M.F. Matrix-geometric solutions in stochastic models: An algorithmic approach. Baltimore: John Hopkins University Press, 1981. 332 р.

  29. Mitrani I., Chakka R. Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method. Performance Evaluation. 1995. Vol. 23, Iss. 3. P. 241–260.

  30. Chakka R. Spectral expansion solution for some finite capacity queues. Annals of Operations Research. 1998. Vol. 79. P. 27–44.

  31. Мelikov A.Z., Ponomarenko L.A., Rustamov A.M. Hierarchical space merging algorithm to analysis of open tandem queueing networks. Cybernetics and Systems Analysis. 2016. Vol. 52, N 6. P. 867–877.

  32. Melikov A.Z., Ponomarenko L.A., Kim C.S. Performance analysis and optimization of multi-traffic on communication networks. Berlin: Springer, 2010. 208 p.
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