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The average virtual waiting time as a measure of performance

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Abstract

Under weak conditions the average virtual waiting time converges exponentially fast to its limit. For this reason this quantity has been suggested as a measure of performance for queueing systems.

We consider theM/G/1 queue and provide estimation and limiting behaviour of the index of exponential decay.

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References

  1. J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Advan. Appl. Probab. 20 (1988) 145–178.

    Article  Google Scholar 

  2. S. Csörgő and J.L. Teugels, Empirical Laplace transform and approximation of compound distributions, J. Appl. Probab. 27 (1990), to appear.

  3. D.P. Gaver and P.A. Jacobs, On inference concerning time-dependent queue performance: the M/G/1 example, Queueing Systems 6 (1990) 261–276.

    Google Scholar 

  4. M.R. Middleton, Transient effects in M/G/1 queues, Ph.D. Dissertation, Stanford University (1979).

  5. M.F. Neuts and J.L. Teugels, Exponential ergodicity of the M/G/1 queue, SIAM J. Appl. Math. 17 (1969) 921–929.

    Article  Google Scholar 

  6. A.R. Odini and A. Roth, An empirical investigation of the transient behavior of stationary queueing systems, Oper. Res. 31 (1983) 432–455.

    Article  Google Scholar 

  7. L. Takács,Introduction to the Theory of Queues (Oxford Univ. Press, New York, 1962).

    Google Scholar 

  8. J.L. Teugels, Exponential decay in Markov renewal processes, J. Appl. Probab. 5 (1968) 387–400.

    Article  Google Scholar 

  9. J.L. Teugels, Estimation of ruin probabilities, Insurance: Math. Econom. 1 (1982) 163–175.

    Article  Google Scholar 

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

    Google Scholar 

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Teugels, J.L. The average virtual waiting time as a measure of performance. Queueing Syst 6, 327–333 (1990). https://doi.org/10.1007/BF02411481

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  • DOI: https://doi.org/10.1007/BF02411481

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