Large deviations of sojourn times in processor sharing queues

M.R.H. Mandjes; A.P. Zwart

doi:10.1007/s11134-006-5567-6

Large deviations of sojourn times in processor sharing queues

M.R.H. Mandjes, A.P. Zwart

Stochastic Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

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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 into 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.

Original language	English
Pages (from-to)	237-250
Journal	Queueing Systems
Volume	52
Issue number	4
DOIs	https://doi.org/10.1007/s11134-006-5567-6
Publication status	Published - 2006

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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 into 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.",

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AU - Zwart, A.P.

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AB - 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 into 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.

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DO - 10.1007/s11134-006-5567-6

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JO - Queueing Systems

JF - Queueing Systems

IS - 4

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Large deviations of sojourn times in processor sharing queues

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