Optimal design of measurements on queueing systems
Optimal design of measurements on queueing systems
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 are 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.
design of experiments, maximum likelihood estimation, M/M/1 queue, active measurements
365-390
Parker, Ben
26c5a5ab-17b3-4d6c-ae11-abf3a2554529
Gilmour, Steven
984dbefa-893b-444d-9aa2-5953cd1c8b03
Schormans, John
17a57e50-4342-4278-8b7a-27bfecd6837b
Maruri-Aguilar, Hugo
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April 2015
Parker, Ben
26c5a5ab-17b3-4d6c-ae11-abf3a2554529
Gilmour, Steven
984dbefa-893b-444d-9aa2-5953cd1c8b03
Schormans, John
17a57e50-4342-4278-8b7a-27bfecd6837b
Maruri-Aguilar, Hugo
c90e1deb-f0f3-43f0-9344-13e898c12642
Parker, Ben, Gilmour, Steven and Schormans, John et al.
(2015)
Optimal design of measurements on queueing systems.
Queueing Systems, 79 (3), .
(doi:10.1007/s11134-014-9421-y).
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 are 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.
Text
MM1QueueDesignv20.pdf
- Accepted Manuscript
More information
e-pub ahead of print date: 5 October 2014
Published date: April 2015
Keywords:
design of experiments, maximum likelihood estimation, M/M/1 queue, active measurements
Organisations:
Statistical Sciences Research Institute
Identifiers
Local EPrints ID: 383915
URI: http://eprints.soton.ac.uk/id/eprint/383915
ISSN: 0257-0130
PURE UUID: d7440a12-9419-4c45-9b9e-e96419fdafe8
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Date deposited: 18 Nov 2015 13:54
Last modified: 14 Mar 2024 21:49
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Contributors
Author:
Ben Parker
Author:
Steven Gilmour
Author:
John Schormans
Author:
Hugo Maruri-Aguilar
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