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The serial correlation coefficients for waiting times in the stationary GI/M/m queue

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Abstract

Serial correlation coefficients are useful measures of the interdependence of successive waiting times. Potential applications include the development of linear predictors and determining simulation run lengths. This paper presents the algorithm for calculating such correlations in the multiserver exponential service queue, and relates it to known results for single server queues.

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References

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    A.G. Pakes, The serial correlation coefficients of waiting times in the stationary GI/M/1 queue, Ann. Math. Statistics, 42 (1971) 1727–1734.

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    D. Gross and C.M. Harris,Fundamentals of Queueing Theory (Wiley, New York, 1974).

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    D.A. Stanford, B. Pagurek and C.M. Woodside, Optimal prediction of times and queue lengths in the GI/M/1 queue, Opns. Res. 31 (1983) 322–337.

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Stanford, D.A., Pagurek, B. & Woodside, C.M. The serial correlation coefficients for waiting times in the stationary GI/M/m queue. Queueing Syst 2, 373–380 (1987). https://doi.org/10.1007/BF01150048

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Keywords

  • Correlation
  • estimation
  • waiting times
  • GI/M/m queue