### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2000 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1554 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-60J80
- IR-65741
- EWI-3374

### Cite this

*On the convergence to stationarity of birth-death processes*. (Memorandum / Department of Applied Mathematics; No. 1554). Enschede: University of Twente, Department of Applied Mathematics.

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*On the convergence to stationarity of birth-death processes*. Memorandum / Department of Applied Mathematics, no. 1554, University of Twente, Department of Applied Mathematics, Enschede.

**On the convergence to stationarity of birth-death processes.** / Coolen-Schrijner, P.; van Doorn, Erik A.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - On the convergence to stationarity of birth-death processes

AU - Coolen-Schrijner, P.

AU - van Doorn, Erik A.

N1 - Imported from MEMORANDA

PY - 2000

Y1 - 2000

N2 - Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

AB - Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

KW - MSC-60J80

KW - IR-65741

KW - EWI-3374

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - On the convergence to stationarity of birth-death processes

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -