Ciucu, Florin, Poloczek, Felix and Rizk, Amr (2019) Queue and loss distributions in finite-buffer queues. In: ACM Sigmetrics / IFIP Networking 2019, Phoenix, Arizona, USA , 24-28 Jun 2019. Published in: Proceedings of the ACM on Measurement and Analysis of Computing Systems (POMACS), 3 (2). doi:10.1145/3341617.3326146 ISSN 2476-1249.

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Abstract

We derive simple bounds on the queue distribution in finite-buffer queues with Markovian arrivals. Our technique relies on a subtle equivalence between tail events and stopping times orderings. The bounds capture a truncated exponential behavior, involving joint horizontal and vertical shifts of an exponential function; this is fundamentally different than existing results capturing horizontal shifts only. Using the same technique, we obtain similar bounds on the loss distribution, which is a key metric to understand the impact of finite-buffer queues on real-time applications. Simulations show that the bounds are accurate in heavy-traffic regimes, and improve existing ones by orders of magnitude. In the limiting regime with utilization ρ = 1 and iid arrivals, the bounds on the queue size distribution are insensitive to the arrivals distribution.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Queuing theory , Queuing networks (Data transmission)
Journal or Publication Title:	Proceedings of the ACM on Measurement and Analysis of Computing Systems (POMACS)
Publisher:	ACM
ISSN:	2476-1249
Official Date:	16 April 2019
Dates:	Date Event 16 April 2019 Accepted
Volume:	3
Number:	2
Article Number:	31
DOI:	10.1145/3341617.3326146
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in POMACS, https://doi.org/10.1145/3341617.3326146
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	2 May 2019
Date of first compliant Open Access:	22 May 2019
Conference Paper Type:	Paper
Title of Event:	ACM Sigmetrics / IFIP Networking 2019
Type of Event:	Conference
Location of Event:	Phoenix, Arizona, USA
Date(s) of Event:	24-28 Jun 2019
Related URLs:	Organisation Publisher

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