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M/M/1 queues with interdependent arrival and service processes

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  • C. R. Mitchell
  • A. S. Paulson

Abstract

We study via simulation an M/M/1 queueing system with the assumption that a customer's service time and the interarrival interval separating his arrival from that of his predecessor are correlated random variables having a bivariate exponential distribution. We show that positive correlation reduces the mean and variance of the total waiting time and that negative correlation has the opposite effect. By using spectral analysis and a nonparametric test applied to the sample power spectra associated with certain simulated waiting times we show the effect to be statistically significant.

Suggested Citation

  • C. R. Mitchell & A. S. Paulson, 1979. "M/M/1 queues with interdependent arrival and service processes," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(1), pages 47-56, March.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:1:p:47-56
    DOI: 10.1002/nav.3800260106
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    Cited by:

    1. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

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