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A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals

Author

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  • Linda V. Green

    (Columbia Business School, Columbia University, New York, New York 10027-6902)

  • Peter J. Kolesar

    (Columbia Business School, Columbia University, New York, New York 10027-6902)

Abstract

We study the M t /G/\infty queue where customers arrive according to a sinusoidal function \lambda t = \lambda + A sin(2\pi t/T) and the service rate is \mu . We show that the expected number of customers in the system during peak congestion can be closely approximated by (\lambda + A)/\mu for service distributions with coefficient of variation between 0 and 1. Motivated by a result derived by Eick, Massey, and Whitt that the time lag of the peak congestion from the peak of the customer arrivals is 1/2\mu for models with deterministic service times, we show that the time lag for exponential service times is closely approximated by 1/\mu . Based on a cycle length of 24 hours and regardless of the values of other system parameters, these approximations are of the order of 1% accuracy for \mu = 1, and the accuracy increases rapidly with increasing \mu .

Suggested Citation

  • Linda V. Green & Peter J. Kolesar, 1998. "A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals," Management Science, INFORMS, vol. 44(11-Part-2), pages 137-144, November.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:11-part-2:p:s137-s144
    DOI: 10.1287/mnsc.44.11.S137
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    References listed on IDEAS

    as
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