On the transient behavior of the processor sharing queue

Large deviations for sojourn times in processor sharing queues. Mandjes, M.R.H.; Zwart, B.Published in: Queueing Systems DOI:10.1007/s11134-006-5567-6Link to publication Citation for published version (APA):Mandjes, M. R. H., & Zwart, B. (2006). Large deviations for sojourn times in processor sharing queues. Queueing Systems, 52(4), 237-250. DOI: 10.1007/s11134-006-5567-6 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Abstract This paper presents a large deviation analysis of the steady-state sojourn time distribution in the GI/G/1 PS queue. Logarithmic estimates are obtained under the assumption of the service time distribution having a light tail, thus supplementing recent results for the heavy-tailed setting. Our proof gives insight in the way a large sojourn time occurs, enabling the construction of an (asymptotically efficient) importance sampling algorithm. Finally our results for PS are compared to a number of other service disciplines, such as FCFS, LCFS, and SRPT.

Section: Discussionmentioning

confidence: 99%

Section: Theorem 31 If Assumptions 31 and 32 Are Valid Thenmentioning

confidence: 99%

Large deviations of sojourn times in processor sharing queues

Mandjes

Zwart

2006

“…Similar work on the M/G/l/PS transient queue was done later by Kitaev [9]. This was followed by a key paper in the area of transient analysis of the M/G/1/PS queue by Jean-Marie and Robert [8] who provide a fluid approximation for the case of fixed load ρ > 1. For this overloaded regime, they derive the asymptotic growth rate for the number of customers after t time units of overload (for large t), where this rate is the solution to a simple integral equation.…”

Section: Introductionmentioning

confidence: 82%

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

Hampshire

Massey

2006

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M t /M t /1 processor-sharing queue. Our analysis is enabled by the introduction of a "virtual customer" which differs from the notion of a "tagged customer" in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.

“…[1]). An example of performance measures that depend on the whole distribution of service times but is insensitive to correlations is the growth rate of the number of customers or of the sojourn time in a (discriminatory) processor sharing queue in overload [2], [3]. Other insensitivity results on bandwidth sharing in a network can be found in [4], [5].…”

mentioning

confidence: 99%

Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times

Groenevelt

Altman

2005

Abstract-This paper analyzes a single server queueing system in which service is alternated between two queues and the server requires a (finite) switchover time to switch from one queue to the other. The distinction from classical results is that the sequence of switchover times from each of the queues need not be i.i.d. nor independent from each other; each sequence is merely required to form a stationary ergodic sequence. With the help of stochastic recursive equations explicit expressions are derived for a number of performance measures, most notably for the average delay of a customer and the average queue lengths under different service disciplines. With these expressions a comparison is made between the service disciplines and the influence of correlation is studied. Finally, through a number of examples it is shown that the correlation can significantly increase the mean delay and the average queue lengths indicating that the correlation between switchover times should not be ignored. This has important implications for communication systems in which a common communication channel is shared amongst various users and where the time between consecutive data transfers is correlated (for example in ad-hoc networks).