Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Queueing Systems: Theory and Applications
Provable bounds for the mean queue lengths in a heterogeneous priority queue
Queueing Systems: Theory and Applications
Proceedings of the 4th International Conference on Queueing Theory and Network Applications
Tail asymptotics for a Lévy-driven tandem queue with an intermediate input
Queueing Systems: Theory and Applications
Exact tail asymptotics in a priority queue--characterizations of the preemptive model
Queueing Systems: Theory and Applications
Rare event asymptotics for a random walk in the quarter plane
Queueing Systems: Theory and Applications
Networks with cascading overloads
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
Queues with boundary assistance: the effects of truncation
Queueing Systems: Theory and Applications
Revisit to the tail asymptotics of the double QBD process by the analytic function method
ACM SIGMETRICS Performance Evaluation Review
Queueing Systems: Theory and Applications
Analysis of exact tail asymptotics for singular random walks in the quarter plane
Queueing Systems: Theory and Applications
Stationary distribution of a two-dimensional SRBM: geometric views and boundary measures
Queueing Systems: Theory and Applications
Wireless three-hop networks with stealing II: exact solutions through boundary value problems
Queueing Systems: Theory and Applications
Join the shortest queue among k parallel queues: tail asymptotics of its stationary distribution
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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A double quasi-birth-and-death (QBD) process is the QBD process whose background process is a homogeneous birth-and-death process, which is a synonym of a skip-free random walk in the two-dimensional positive quadrant with homogeneous reflecting transitions at each boundary face. It is also a special case of a 0-partially homogenous chain introduced by Borovkov and Mogul'skii. Our main interest is in the tail decay behavior of the stationary distribution of the double QBD process in the coordinate directions and that of its marginal distributions. In particular, our problem is to get their rough and exact asymptotics from primitive modeling data. We first solve this problem using the matrix analytic method. We then revisit the problem for the 0-partially homogenous chain, refining existing results. We exemplify the decay rates for Jackson networks and their modifications.