### Abstract

We consider the $M/M/N/N+R$ service system, characterized by $N$ servers, $R$ waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of $R$, $N$ and the arrival rate $\lambda$, allowing $\lambda$ to be a function of $N.$

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 18 |

Publication status | Published - Jul 2010 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Department of Applied Mathematics |

No. | 1923 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- EWI-18166
- MSC-90B22
- METIS-270921
- MSC-60K25
- IR-72428

## Cite this

van Doorn, E. A. (2010).

*Rate of convergence to stationarity of the system $M/M/N/N+R$*. (Memorandum / Department of Applied Mathematics; No. 1923). Enschede: University of Twente, Department of Applied Mathematics.