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Tandem Queues with Dependent Service Times in Light Traffic

Author

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  • Ronald W. Wolff

    (University of California, Berkeley, California)

Abstract

Light traffic results about delay in queue are obtained for r single-channel queues in tandem with Poisson arrivals where the r service times of the same customer at different stations have an arbitrary joint distribution. By light traffic, we mean asymptotic behavior as server utilization approaches zero. A detailed analysis of delay at the second station is presented for r = 2. An expression for expected delay is obtained for r = 3. Methods developed for these purposes may be used for arbitrary r > 3. For arbitrary r , an expression for expected delay is obtained in the special case where the r service times of the same customer are equal. For exponential service, a simple closed form expression is obtained. For r = 2, it is shown that when service times are positively quadrant dependent , expected delay is greater than when service times are independent. In some cases, the ratio between expected delays in the dependent and independent cases is very large, particularly when r is large. This agrees with and generalizes published results in several papers and conflicts with results in one paper. An explanation for this conflict is given.

Suggested Citation

  • Ronald W. Wolff, 1982. "Tandem Queues with Dependent Service Times in Light Traffic," Operations Research, INFORMS, vol. 30(4), pages 619-635, August.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:4:p:619-635
    DOI: 10.1287/opre.30.4.619
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    Cited by:

    1. Wu, Kan & Zhao, Ning, 2015. "Dependence among single stations in series and its applications in productivity improvement," European Journal of Operational Research, Elsevier, vol. 247(1), pages 245-258.

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