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

Yiqiang Q. Zhao ()
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Yiqiang Q. Zhao: Carleton University

Queueing Systems: Theory and Applications, 2022, vol. 100, issue 1, No 7, 95-131

Abstract: Abstract Many queueing systems can be modelled as two-dimensional random walks with reflective boundaries, discrete, continuous or mixed. Stationary probabilities are one of the most sought after statistical quantities in queueing analysis. However, explicit expressions are only available for a very limited number of models. Therefore, tail asymptotic properties become more important, since they provide insightful information on the structure of the tail probabilities, and often lead to approximations, performance bounds, algorithms, among possible other applications. In this survey, we provide key ideas of a kernel method, developed from the classical kernel method in analytic combinatorics, for studying so-called exact tail asymptotic properties in stationary probabilities for this type of random walk.

Keywords: Kernel method; Generating functions; Laplace-transform; Fundamental form; Two-dimensional Markov chains; Random walks in the quarter plane; Stationary probabilities; Analytic continuation; Asymptotic analysis; Dominant singularity; Exact tail asymptotics; 60K25; 60J10; 30E15; 05A15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-021-09727-6

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