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- Title
The kernel method tail asymptotics analytic approach for stationary probabilities of two-dimensional queueing systems.
- Authors
Zhao, Yiqiang Q.
- 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.
- Subjects
RANDOM walks; PROBABILITY theory; COMBINATORICS; TWO-dimensional models; GENERATING functions; MARKOV processes
- Publication
Queueing Systems, 2022, Vol 100, Issue 1/2, p95
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-021-09727-6