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ON STATE-INDEPENDENT IMPORTANCE SAMPLING FOR THE GI|GI|1 TANDEM QUEUE1

Published online by Cambridge University Press:  05 November 2018

Anne Buijsrogge,
Pieter-Tjerk de Boer and
Werner R.W. Scheinhardt
Anne Buijsrogge
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands E-mail: a.buijsrogge@utwente.nl; p.t.deboer@utwente.nl; w.r.w.scheinhardt@utwente.nl
Pieter-Tjerk de Boer
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands E-mail: a.buijsrogge@utwente.nl; p.t.deboer@utwente.nl; w.r.w.scheinhardt@utwente.nl
Werner R.W. Scheinhardt
Affiliation:
Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands E-mail: a.buijsrogge@utwente.nl; p.t.deboer@utwente.nl; w.r.w.scheinhardt@utwente.nl
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Abstract

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In this paper, we consider a d-node GI|GI|1 tandem queue with i.i.d. inter-arrival process and service processes that are independent of each other. Our main interest is to estimate the probability to reach a high level N in a busy cycle of the system using simulation. As crude simulation does not give a sufficient precision in reasonable time, we use importance sampling. We introduce a method to find a state-independent change of measure and we show that this is equivalent to a change of measure that was earlier, but implicitly, described by Parekh and Walrand [8]. We also show that this change of measure is the only exponential state-independent change of measure that may result in an asymptotically efficient estimator. Lastly, we provide necessary conditions for this state-independent change of measure to give an asymptotically efficient estimator.

Keywords

GI|GI|1 queuetandem queuerare event simulationimportance sampling

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020, pp. 131 - 156
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2018

References

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