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

Linda V. Green and Peter J. Kolesar
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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

Management Science, 1998, vol. 44, issue 11-Part-2, S137-S144

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 .

Keywords: Queues; Nonstationarity; Approximations (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (5)

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