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On bounds of response time performance achievable by multiclass single-server queues

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Abstract

MulticlassM/G/1 systems in steady-state with work-conserving scheduling strategies are studied. Restricting a system's scheduling strategy to making no direct use of the required service times, every time the server becomes idle its memory is cleared, and service may only be interrupted by newly arriving customers, a conservation law is developed by means of inequalities. The conservation law states that if a response time vector composed of the expected response times of the different classes of a system in steady-state is achievable, then it must belong to a well-defined convex polytope (a set bounded by hyperplanes). Furthermore, on each hyperplane bounding the relevant polytope there lies at least one vertex of the convex set of achievable response time vectors. Therefore, this polytope is the least one including the set of all achievable response time vectors.

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References

  1. Coffman, E.G., Jr., Mitrani, I.: A characterisation of waiting time performance realisable by single-server queues. Oper. Res.28 (2), 810–821 (1980)

    Google Scholar 

  2. Fayolle, G., Mitrani, I., Iasnogorodski, R.: Sharing a processor among many job classes. J. ACM27 (3), 519–532 (1980)

    Google Scholar 

  3. Federgruen, G., Groenevelt, H.:M/G/c queueing systems with multiple customer classes: characterization and control of achievable performance under nonpreemptive priority rules. Manag. Sci.34 (9), 1121–1138 (1988)

    Google Scholar 

  4. Federgruen, G., Groenevelt, H.: Characterization and optimization of achievable performance in general queueing systems. Oper. Res.36 (5), 733–741 (1988)

    Google Scholar 

  5. Gelenbe, E., Mitrani, I.: Analysis and synthesis of computer systems. New York: Academic Press 1980

    Google Scholar 

  6. Kleinrock, L.: A conservation law for a wide class of queueing disciplines. Nav. Res. Log. Qu.12 (2), 181–192 (1965)

    Google Scholar 

  7. Kleinrock, L.: Queueing systems, vol. 2. New York: John Wiley & Son 1976

    Google Scholar 

  8. Mitrani, I.: Modelling of computer and communication systems. Cambridge: Cambridge University Press 1987

    Google Scholar 

  9. Mitrani, I., Hine, J.H.: Complete parameterized families of job scheduling strategies. Acta Inf.8, 61–73 (1977)

    Google Scholar 

  10. Schrage, L.: An alternative proof of a conservation law for the queueG/G/1. Oper. Res.18, 185–187 (1970)

    Google Scholar 

  11. Shanthikumar, J.G., Yao, D.D.: Multiclass queueing systems: polymatroidal structure and optimal scheduling control. Oper. Res.40 (Suppl. 2), S293-S299 (1992)

    Google Scholar 

  12. Wolff, R.W.: Work-conserving priorities. J. Appl. Probab.7, 327–337 (1970)

    Google Scholar 

  13. Wolff, R.W.: Stochastic modelling and the theory of queues. Englewood Cliffs, NJ: Prentice-Hall 1989

    Google Scholar 

Download references

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  1. Lehrstuhl Informatik IV, Universität Dortmund, D-44221, Dortmund, Germany

    Astrid R. Rühl

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  1. Astrid R. Rühl
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Rühl, A.R. On bounds of response time performance achievable by multiclass single-server queues. Acta Informatica 31, 629–650 (1994). https://doi.org/10.1007/BF01177549

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  • DOI: https://doi.org/10.1007/BF01177549

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