### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 20 |

Volume | 2008-50 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2008-50 |

### Fingerprint

### Keywords

- Markov chain
- Interval uncertainty
- Ellipsoidal uncertainty
- Linear Programming
- Second Order Cone Optimization

### Cite this

*On Markov Chains with Uncertain Data*. (CentER Discussion Paper; Vol. 2008-50). Tilburg: Operations research.

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**On Markov Chains with Uncertain Data.** / Blanc, J.P.C.; den Hertog, D.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - On Markov Chains with Uncertain Data

AU - Blanc, J.P.C.

AU - den Hertog, D.

N1 - Pagination: 20

PY - 2008

Y1 - 2008

N2 - In this paper, a general method is described to determine uncertainty intervals for performance measures of Markov chains given an uncertainty region for the parameters of the Markov chains. We investigate the effects of uncertainties in the transition probabilities on the limiting distributions, on the state probabilities after n steps, on mean sojourn times in transient states, and on absorption probabilities for absorbing states. We show that the uncertainty effects can be calculated by solving linear programming problems in the case of interval uncertainty for the transition probabilities, and by second order cone optimization in the case of ellipsoidal uncertainty. Many examples are given, especially Markovian queueing examples, to illustrate the theory.

AB - In this paper, a general method is described to determine uncertainty intervals for performance measures of Markov chains given an uncertainty region for the parameters of the Markov chains. We investigate the effects of uncertainties in the transition probabilities on the limiting distributions, on the state probabilities after n steps, on mean sojourn times in transient states, and on absorption probabilities for absorbing states. We show that the uncertainty effects can be calculated by solving linear programming problems in the case of interval uncertainty for the transition probabilities, and by second order cone optimization in the case of ellipsoidal uncertainty. Many examples are given, especially Markovian queueing examples, to illustrate the theory.

KW - Markov chain

KW - Interval uncertainty

KW - Ellipsoidal uncertainty

KW - Linear Programming

KW - Second Order Cone Optimization

M3 - Discussion paper

VL - 2008-50

T3 - CentER Discussion Paper

BT - On Markov Chains with Uncertain Data

PB - Operations research

CY - Tilburg

ER -