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Queueing Systems

, Volume 79, Issue 3–4, pp 365–390 | Cite as

Optimal design of measurements on queueing systems

  • Ben M. ParkerEmail author
  • Steven Gilmour
  • John Schormans
  • Hugo Maruri-Aguilar
Article

Abstract

We examine the optimal design of measurements on queues with particular reference to the M/M/1 queue. Using the statistical theory of design of experiments, we calculate numerically the Fisher information matrix for an estimator of the arrival rate and the service rate to find optimal times to measure the queue when the number of measurements is limited for both interfering and non-interfering measurements. We prove that in the non-interfering case, the optimal design is equally spaced. For the interfering case, optimal designs are not necessarily equally spaced. We compute optimal designs for a variety of queuing situations and give results obtained under the \(D\)- and \(D_s\)-optimality criteria.

Keywords

Design of experiments Maximum likelihood estimation  M/M/1 queue Active measurements 

Mathematics Subject Classification

62K05 60K99 68M20 

Notes

Acknowledgments

The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Ben M. Parker
    • 1
    Email author
  • Steven Gilmour
    • 1
  • John Schormans
    • 2
  • Hugo Maruri-Aguilar
    • 3
  1. 1.Southampton Statistical Sciences Research InstituteUniversity of SouthamptonSouthamptonUK
  2. 2.School of Electronic Engineering and Computer ScienceQueen Mary University of LondonLondonUK
  3. 3.School of Mathematical SciencesQueen Mary University of LondonLondonUK

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