Revisiting the Tail Asymptotics of the Double QBD Process: Refinement and Complete Solutions for the Coordinate and Diagonal Directions

DOI10.1007/978-1-4614-4909-6_8zbMath1280.60044arXiv1201.3167OpenAlexW1517350773MaRDI QIDQ2841726

Masakiyo Miyazawa, Masahiro Kobayashi

Publication date: 29 July 2013

Published in: Matrix-Analytic Methods in Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3167

zbMATH Keywords

quasi-birth-and-death processanalytic function methodtail asymptotics of stationary distributiontwo-dimensional discrete time random walk

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (11)

The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems ⋮ Semi-infinite quasi-Toeplitz matrices with applications to QBD stochastic processes ⋮ Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms ⋮ Approximation of excessive backlog probabilities of two tandem queues ⋮ Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox ⋮ Solving Quadratic Matrix Equations Arising in Random Walks in the Quarter Plane ⋮ Excessive backlog probabilities of two parallel queues ⋮ Product-form characterization for a two-dimensional reflecting random walk ⋮ Tail Asymptotics of the Stationary Distribution of a Two-Dimensional Reflecting Random Walk with Unbounded Upward Jumps ⋮ Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process ⋮ Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process

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