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Estimation for queues from queue length data

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Abstract

We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure makes use of an Ornstein-Uhlenbeck diffusion approximation to the Markov process description of the queue. We demonstrate the approach through simulation studies and discuss situations in which the approximation works best.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    J. V. Ross

  2. Department of Mathematics, University of Queensland, Queensland, QLD 4072, Australia

    T. Taimre & P. K. Pollett

Authors
  1. J. V. Ross
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  2. T. Taimre
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  3. P. K. Pollett
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Correspondence to J. V. Ross.

Additional information

AMS Subject Classifications 60J20, 60J60, 60K25, 62M05, 62F10

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Ross, J.V., Taimre, T. & Pollett, P.K. Estimation for queues from queue length data. Queueing Syst 55, 131–138 (2007). https://doi.org/10.1007/s11134-006-9009-2

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  • DOI: https://doi.org/10.1007/s11134-006-9009-2

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