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.
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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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Parker, B.M., Gilmour, S., Schormans, J. et al. Optimal design of measurements on queueing systems. Queueing Syst 79, 365–390 (2015). https://doi.org/10.1007/s11134-014-9421-y
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DOI: https://doi.org/10.1007/s11134-014-9421-y