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

Robert C. Hampshire; Mor Harchol-Balter; William A. Massey

doi:10.1007/s11134-006-7584-x

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

Robert C. Hampshire, Mor Harchol-Balter, William A. Massey

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

21 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	19-30
Number of pages	12
Journal	Queueing Systems
Volume	53
Issue number	1-2
DOIs	https://doi.org/10.1007/s11134-006-7584-x
State	Published - Jun 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

Keywords

Diffusion limits
Fluid limits
Processor sharing
Sojourn times
Time-varying queues
Transient behavior
Uniform acceleration
Virtual customers

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10.1007/s11134-006-7584-x

Cite this

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AU - Harchol-Balter, Mor

AU - Massey, William A.

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AB - 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/Mt/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.

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KW - Fluid limits

KW - Processor sharing

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KW - Time-varying queues

KW - Transient behavior

KW - Uniform acceleration

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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