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arXiv · 1807.09614

On the analysis of partially homogeneous nearest-neighbour random walks in the quarter plane

Ioannis Dimitriou
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Abstract

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities are functions of the state-space. We show that its stationary behavior is investigated by solving a finite system of linear equations, and a functional equation with the aid of the theory of Riemann(-Hilbert) boundary value problems. This work is strongly motivated by emerging applications in multiple access systems as well as in the study of a general class of queueing systems with state dependent parameters. A simple numerical illustration providing useful information about a queue-aware multiple access system is also presented.

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Ioannis Dimitriou. 2018-07-24. On the analysis of partially homogeneous nearest-neighbour random walks in the quarter plane. https://arxiv.org/abs/1807.09614

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