A finite compensation procedure for a class of two-dimensional random walks

Ivo J.B.F. Adan; Ioannis Dimitriou

doi:10.1016/j.indag.2023.05.007

A finite compensation procedure for a class of two-dimensional random walks

Ivo J.B.F. Adan
, Ioannis Dimitriou (Corresponding author)

Research output: Contribution to journal › Article › Academic › peer-review

5 Citations (Scopus)

98 Downloads (Pure)

Abstract

Motivated by queueing applications, we consider a class of two-dimensional random walks, the invariant measure of which can be written as a linear combination of a finite number of product-form terms. In this work, we investigate under which conditions such an elegant solution can be derived by applying a finite compensation procedure. The conditions are formulated in terms of relations among the transition probabilities in the inner area, the boundaries as well as the origin. A discussion on the importance of these conditions is also given.

Original language	English
Pages (from-to)	891-935
Number of pages	45
Journal	Indagationes Mathematicae
Volume	34
Issue number	5
DOIs	https://doi.org/10.1016/j.indag.2023.05.007
Publication status	Published - Sept 2023

Bibliographical note

Special Issue dedicated to the memory of J.W. Cohen

Keywords

Finite compensation procedure
Two-dimensional random walks
Invariant measure

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10.1016/j.indag.2023.05.007

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PY - 2023/9

Y1 - 2023/9

N2 - Motivated by queueing applications, we consider a class of two-dimensional random walks, the invariant measure of which can be written as a linear combination of a finite number of product-form terms. In this work, we investigate under which conditions such an elegant solution can be derived by applying a finite compensation procedure. The conditions are formulated in terms of relations among the transition probabilities in the inner area, the boundaries as well as the origin. A discussion on the importance of these conditions is also given.

AB - Motivated by queueing applications, we consider a class of two-dimensional random walks, the invariant measure of which can be written as a linear combination of a finite number of product-form terms. In this work, we investigate under which conditions such an elegant solution can be derived by applying a finite compensation procedure. The conditions are formulated in terms of relations among the transition probabilities in the inner area, the boundaries as well as the origin. A discussion on the importance of these conditions is also given.

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KW - Two-dimensional random walks

KW - Invariant measure

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DO - 10.1016/j.indag.2023.05.007

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ER -

A finite compensation procedure for a class of two-dimensional random walks

Abstract

Bibliographical note

Keywords

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