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- Title
Stein's method for diffusive limits of queueing processes.
- Authors
Besançon, Eustache; Decreusefond, Laurent; Moyal, Pascal
- Abstract
Donsker's theorem is perhaps the most famous invariance principle result for Markov processes. It states that, when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general Markov processes whose driving parameters are taken to a limit, which can lead to insightful results in contexts like large distributed systems or queueing networks. The purpose of this paper is to assess the rate of convergence in these so-called diffusion approximations, in a queueing context. To this end, we extend the functional Stein method, introduced for the Brownian approximation of Poisson processes, to two simple examples: the single-server queue and the infinite-server queue. By doing so, we complete the recent applications of Stein's method to queueing systems, with results concerning the whole trajectory of the considered process, rather than its stationary distribution.
- Subjects
POISSON processes; MARKOV processes; RANDOM walks; QUEUEING networks; BROWNIAN motion; WIENER processes
- Publication
Queueing Systems, 2020, Vol 95, Issue 3/4, p173
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-020-09658-8