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.
References
J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms, Advan. Appl. Probab. 20 (1988) 145–178.
S. Csörgő and J.L. Teugels, Empirical Laplace transform and approximation of compound distributions, J. Appl. Probab. 27 (1990), to appear.
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.
M.R. Middleton, Transient effects in M/G/1 queues, Ph.D. Dissertation, Stanford University (1979).
M.F. Neuts and J.L. Teugels, Exponential ergodicity of the M/G/1 queue, SIAM J. Appl. Math. 17 (1969) 921–929.
A.R. Odini and A. Roth, An empirical investigation of the transient behavior of stationary queueing systems, Oper. Res. 31 (1983) 432–455.
L. Takács,Introduction to the Theory of Queues (Oxford Univ. Press, New York, 1962).
J.L. Teugels, Exponential decay in Markov renewal processes, J. Appl. Probab. 5 (1968) 387–400.
J.L. Teugels, Estimation of ruin probabilities, Insurance: Math. Econom. 1 (1982) 163–175.
D. Widder,The Laplace Transform (Princeton Univ. Press, Princeton, NJ, 1941).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02411481