### 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.

Original language | English |
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Number of pages | 28 |

Journal | Probability in the engineering and informational sciences |

DOIs | |

Publication status | E-pub ahead of print/First online - 26 Jun 2019 |

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### Keywords

- error bounds
- finite state space
- performance measure
- product-form
- random walk
- two-node queue

### Cite this

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**Performance measures for the two-node queue with finite buffers.** / Chen, Yanting; Bai, Xinwei; Boucherie, Richard J.; Goseling, Jasper.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Performance measures for the two-node queue with finite buffers

AU - Chen, Yanting

AU - Bai, Xinwei

AU - Boucherie, Richard J.

AU - Goseling, Jasper

PY - 2019/6/26

Y1 - 2019/6/26

N2 - 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.

AB - 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.

KW - error bounds

KW - finite state space

KW - performance measure

KW - product-form

KW - random walk

KW - two-node queue

UR - http://www.scopus.com/inward/record.url?scp=85068180565&partnerID=8YFLogxK

U2 - 10.1017/S0269964819000238

DO - 10.1017/S0269964819000238

M3 - Article

AN - SCOPUS:85068180565

JO - Probability in the engineering and informational sciences

JF - Probability in the engineering and informational sciences

SN - 0269-9648

ER -