## 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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Pages (from-to) | 522-549 |

Number of pages | 28 |

Journal | Probability in the engineering and informational sciences |

Volume | 34 |

Issue number | 4 |

Early online date | 26 Jun 2019 |

DOIs | |

Publication status | Published - 1 Oct 2020 |

## Keywords

- Error bounds
- Finite state space
- Performance measure
- Product-form
- Random walk
- Two-node queue