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The M/G/c queue in light traffic

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Abstract

Under light traffic, we investigate the quality of a well‐known approximation for first‐moment performance measures for an M/G/c queue, and, in particular, conditions under which the approximation is either an upper or a lower bound. The approach is to combine known relationships between quantities such as average delay and time‐average work in system with direct sample‐path comparisons of system operation under two modes of operation: conventional FIFO and a version of preemptive LIFO. We then use light traffic limit theorems to show an inequality between time‐average work of the M/G/c queue and that of the approximation. In the process, we obtain new and improved approximations.

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References

  1. O.J. Boxma, J.W. Cohen and N. Huffels, Approximations of the mean waiting time in an M/G/s queueing system, Oper. Res. 27 (1979) 1115-1127.

    Google Scholar 

  2. F.S. Hillier and F.D. Lo, Tables for multi-server queueing systems involving Erlang distribution, Technical Report 31, Department of Operations Research, Stanford University (1971).

  3. P. Hokstad, Relations for the workload of the GI/G/s queue, Adv. in Appl. Probab. 17 (1985) 887-904.

    Article  Google Scholar 

  4. F.P. Kelley, Reversibility and Stochastic Networks (Wiley, New York, 1979).

    Google Scholar 

  5. T. Kimura, Diffusion approximation for an M/G/m queue, Oper. Res. 31 (1983) 304-321.

    Google Scholar 

  6. M.I. Reiman and B. Simon, Open queueing systems in light traffic, Math. Oper. Res. 14 (1989) 26-59.

    Google Scholar 

  7. M.I. Reiman and A. Weiss, Light traffic derivatives via likelihood ratios, IEEE Trans. Inform. Theory 35 (1989) 648-654.

    Article  Google Scholar 

  8. M.I. Reiman and A. Weiss, Sensitivity analysis for simulation via likelihood ratios, Oper. Res. 37 (1989) 830-843.

    Google Scholar 

  9. D. Siegmund, Sequential Analysis (Springer, New York, 1985).

    Google Scholar 

  10. H.C. Tijms, M.H. Van Hoorn and A. Federgruen, Approximations for the steady-state probability in the M/G/c queue, Adv. in Appl. Probab. 13 (1981) 186-206.

    Article  Google Scholar 

  11. C.-L. Wang, Light traffic approximations for regenerative queueing processes, Adv. in Appl. Probab. 29 (1997) 1060-1080.

    Article  Google Scholar 

  12. D.V. Widder, The Laplace Transform (Princeton Univ. Press, Princeton, NJ, 1941).

    Google Scholar 

  13. R.W. Wolff, Tandem queues with dependent service times in light traffic, Oper. Res. 30 (1982) 619-635.

    Article  Google Scholar 

  14. R.W. Wolff, Stochastic Modeling and the Theory of Queues (Prentice-Hall, Englewood Cliffs, NJ, 1989).

    Google Scholar 

  15. D.D. Yao, Refining the diffusion approximation for the M/G/m queue, Oper. Res. 33 (1985) 1266-1277.

    Google Scholar 

  16. M.A. Zazanis, Analyticity of Poisson-driven stochastic systems, Adv. in Appl. Probab. 24 (1992) 532-541.

    Article  Google Scholar 

Download references

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Wang, C., Wolff, R.W. The M/G/c queue in light traffic. Queueing Systems 29, 17–34 (1998). https://doi.org/10.1023/A:1019171711535

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  • DOI: https://doi.org/10.1023/A:1019171711535

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