The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.

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The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems

Cited by 2 publications

References 65 publications

Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue

Analysis of A Two-queue Discrete-time Model with Random Alternating Service Under High Occupancy in One Queue

Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

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