Skip to Main content Skip to Navigation
Journal articles

Stein's method for diffusive limit of queueing processes

Abstract : Donsker 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [20 references]  Display  Hide  Download
Contributor : Laurent Decreusefond Connect in order to contact the contributor
Submitted on : Saturday, May 2, 2020 - 4:37:02 PM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM


Files produced by the author(s)



Eustache Besançon, Laurent Decreusefond, Pascal Moyal. Stein's method for diffusive limit of queueing processes. Queueing Systems, Springer Verlag, 2020, 95, pp.173--201. ⟨10.1007/s11134-020-09658-8⟩. ⟨hal-01784139v3⟩



Record views


Files downloads