Queueing Systems

, Volume 53, Issue 1–2, pp 19–30 | Cite as

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


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.


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


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Robert C. Hampshire
    • 1
  • Mor Harchol-Balter
    • 2
  • William A. Massey
    • 1
  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrinceton
  2. 2.School of Computer ScienceCarnegie Mellon UniversityUSA

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