Stein’s method for diffusive limits of queueing processes

Eustache Besançon (), Laurent Decreusefond () and Pascal Moyal ()
Additional contact information
Eustache Besançon: Institut polytechnique de Paris
Laurent Decreusefond: Institut polytechnique de Paris
Pascal Moyal: Université de Lorraine

Queueing Systems: Theory and Applications, 2020, vol. 95, issue 3, No 1, 173-201

Abstract: 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.

Keywords: Diffusion approximation; Queueing systems; Stein’s method; 60F17; 60H07 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11134-020-09658-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:queues:v:95:y:2020:i:3:d:10.1007_s11134-020-09658-8

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/11134/

DOI: 10.1007/s11134-020-09658-8

Access Statistics for this article

Queueing Systems: Theory and Applications is currently edited by Sergey Foss

More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().