### Abstract

We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon-Newell network although alternative interpretations are possible. The main tool is the detailed balance equations. The difference compared to earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known product formula.

Original language | English (US) |
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Pages (from-to) | 448-462 |

Number of pages | 15 |

Journal | Journal of Applied Probability |

Volume | 53 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2016 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

Gannon, M., Pechersky, E., Suhov, Y., & Yambartsev, A. (2016). Random walks in a queueing network environment.

*Journal of Applied Probability*,*53*(2), 448-462. https://doi.org/10.1017/jpr.2016.12