### Abstract

We consider M/G/ 1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/ 1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain’s G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/l preemptive priority queue, yielding significant reductions in computation time.

Original language | English (US) |
---|---|

Pages (from-to) | 487-517 |

Number of pages | 31 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 25 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2011 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering

### Cite this

}

*Probability in the Engineering and Informational Sciences*, vol. 25, no. 4, pp. 487-517. https://doi.org/10.1017/S0269964811000155

**The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals.** / Perez, Juan F.; Houdt, Benny Van.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The M/G/1-type markov chain with restricted transitions and its application to queues with batch arrivals

AU - Perez, Juan F.

AU - Houdt, Benny Van

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We consider M/G/ 1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/ 1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain’s G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/l preemptive priority queue, yielding significant reductions in computation time.

AB - We consider M/G/ 1-type Markov chains where a transition that decreases the value of the level triggers the phase to a small subset of the phase space. We show how this structure—referred to as restricted downward transitions—can be exploited to speed up the computation of the stationary probability vector of the chain. To this end we define a new M/G/ 1-type Markov chain with a smaller block size, the G matrix of which is used to find the original chain’s G matrix. This approach is then used to analyze the BMAP/PH/1 queue and the BMAP[2]/PH[2]/l preemptive priority queue, yielding significant reductions in computation time.

UR - http://www.scopus.com/inward/record.url?scp=84870669375&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870669375&partnerID=8YFLogxK

U2 - 10.1017/S0269964811000155

DO - 10.1017/S0269964811000155

M3 - Article

AN - SCOPUS:84870669375

VL - 25

SP - 487

EP - 517

JO - Probability in the Engineering and Informational Sciences

JF - Probability in the Engineering and Informational Sciences

SN - 0269-9648

IS - 4

ER -