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A sample path analysis of M/GI/1 queues with workload restrictions

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Abstract

A simple random time change is used to analyze M/GI/1 queues with workload restrictions. The types of restrictions considered include workload bounds and rejection of jobs whose waiting times exceed a (possibly random) threshold. Load dependent service rates and vacations are also allowed and in each case the steady state distribution of the workload process for the system with workload restrictions is obtained in terms of that of the corresponding M/ GI/1 queue without restrictions. The novel sample path arguments used simplify and generalize previous results.

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References

  1. S. Asmussen,Applied Probability and Queues (Wiley, 1987).

  2. D.V. Barrer, Queueing with impatient customers and indifferent clerks, Oper. Res. 5 (1957) 650–656.

    Google Scholar 

  3. P. Brémaud,Point Processes and Queues (Springer-Verlag, 1981).

  4. C.G. Cassandras and S.G. Strickland, On-line sensitivity analysis of Markov chains, IEEE Trans. Autom. Control. 34 (1989) 76–86.

    Google Scholar 

  5. J.W. Cohen, Single server queue with uniformly bounded virtual waiting time, J. Appl. Prob. 5 (1968) 93–122.

    Google Scholar 

  6. P. Franken, D. Köning, U. Arndt and V. Schmidt,Queues and Point Processes (Wiley, New York, 1982).

    Google Scholar 

  7. J. Gani and N.U. Prabhu, Continuous time treatment of a storage problem, Nature 182 (1958) 39–0.

    Google Scholar 

  8. A. Ghosal, Queues with finite waiting time, Oper. Res. 11 (1963) 919–921.

    Google Scholar 

  9. P. Glasserman and W.B. Gong, Time-changing and truncating K-capacity queues from oneK to another, J. Appl. Prob. 28 (1991) 647–655.

    Google Scholar 

  10. B.V. Gnedenko and I.N. Kovalenko,Introduction to Queueing Theory, 2nd ed. (Birkhauser, Boston, 1989).

    Google Scholar 

  11. Y.C. Ho and S. Li, Extensions of infinitesimal perturbation analysis, IEEE Trans. Autom. Control AC-33 (1988) 427–438.

    Google Scholar 

  12. H.P. McKean Jr.,Stochastic Integrals (Academic Press, 1969).

  13. M. Miyazawa, The intensity conservation law for queues with randomly changed service rate, J. Appl. Prob. 22 (1985) 408 18.

    Google Scholar 

  14. L. Takács, The distribution of the content of finite dams, J. Appl. Prob. 4 (1967) 151–161.

    Google Scholar 

  15. L. Takács, A single server queue with limited virtual waiting time, J. Appl. Prob. 11 (1974) 612–617.

    Google Scholar 

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Hu, JQ., Zazanis, M.A. A sample path analysis of M/GI/1 queues with workload restrictions. Queueing Syst 14, 203–213 (1993). https://doi.org/10.1007/BF01153534

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  • DOI: https://doi.org/10.1007/BF01153534

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