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PERFORMANCE MEASURES FOR THE TWO-NODE QUEUE WITH FINITE BUFFERS

Published online by Cambridge University Press:  26 June 2019

Yanting Chen ,
Xinwei Bai ,
Richard J. Boucherie  and
Jasper Goseling
Yanting Chen
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P. R. China E-mail: yantingchen@hnu.edu.cn
Xinwei Bai
Affiliation:
Stochastic Operations Research, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands E-mail: xinwei.bai@ibeo-as.com; r.j.boucherie@utwente.nl; j.goseling@utwente.nl
Richard J. Boucherie
Affiliation:
Stochastic Operations Research, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands E-mail: xinwei.bai@ibeo-as.com; r.j.boucherie@utwente.nl; j.goseling@utwente.nl
Jasper Goseling
Affiliation:
Stochastic Operations Research, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands E-mail: xinwei.bai@ibeo-as.com; r.j.boucherie@utwente.nl; j.goseling@utwente.nl
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Abstract

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks. The approximation scheme is developed in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. The modified approximation scheme and the corresponding applications for a two-node queueing system in which only one of the buffers has finite capacity have also been discussed.

Keywords

error boundsfinite state spaceperformance measureproduct-formrandom walktwo-node queue

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 4 , October 2020 , pp. 522 - 549
Copyright
Copyright © Cambridge University Press 2019

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Footnotes

*

Current address: Ibeo Automotive Eindhoven, High Tech Campus 69, 5656 AE Eindhoven, The Netherlands

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