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On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency

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  • Ioannis Dimitriou

    (University of Patras)

Abstract

This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such random walks are characterized by the fact that the one-step transition probabilities are functions of the state-space. We show that stationary behaviour is investigated by solving a finite system of linear equations, two matrix functional 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 flow level performance of wireless networks that give rise in queueing models with scalable service capacity, as well as in queue-based random access protocols, where the network’s parameters are functions of the queue lengths. A simple numerical illustration, along with some details on the numerical implementation are also presented.

Suggested Citation

  • Ioannis Dimitriou, 2021. "On partially homogeneous nearest-neighbour random walks in the quarter plane and their application in the analysis of two-dimensional queues with limited state-dependency," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 95-143, June.
    • Handle: RePEc:spr:queues:v:98:y:2021:i:1:d:10.1007_s11134-021-09705-y
    DOI: 10.1007/s11134-021-09705-y
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    References listed on IDEAS

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