On a single server queue fed by scheduled traffic with Pareto perturbations

Victor F. Araman (), Hong Chen (), Peter W. Glynn () and Li Xia ()
Additional contact information
Victor F. Araman: American University of Beirut
Hong Chen: Shanghai Jiaotong University
Peter W. Glynn: Stanford University
Li Xia: Sun Yat-Sen University

Queueing Systems: Theory and Applications, 2022, vol. 100, issue 1, No 5, 91 pages

Abstract: Abstract A“scheduled” arrival process is one in which the nth arrival is scheduled for time n, but instead occurs at $$n+\xi _n$$ n + ξ n , where the $$\xi _j$$ ξ j ’s are i.i.d. We describe here the behavior of a single server queue fed by such traffic in which the processing times are deterministic. A particular focus is on perturbations with Pareto-like tails but with finite mean. We obtain tail approximations for the steady-state workload in both cases where the queue is critically loaded and under a heavy-traffic regime. A key to our approach is our analysis of the tail behavior of a sum of independent Bernoulli random variables with parameters of the form $$p_n\sim c \,n^{-\alpha }$$ p n ∼ c n - α as $$n\rightarrow \infty $$ n → ∞ , for $$c>0$$ c > 0 and $$\alpha >1$$ α > 1 .

Keywords: Scheduled traffic; Heavy-tailed distribution; Limit theorems; Bernoulli sums; Heavy traffic; Tail asymptotics; Primary 60F05; 60F10; 60K25; Secondary 60G07 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11134-021-09732-9 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:100:y:2022:i:1:d:10.1007_s11134-021-09732-9

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

DOI: 10.1007/s11134-021-09732-9

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 ().