Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
Strong approximations for time-dependent queues
Mathematics of Operations Research
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Analysis of SRPT scheduling: investigating unfairness
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Fluid approximations for a processor-sharing queue
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory
Queueing Systems: Theory and Applications
Size-based scheduling to improve web performance
ACM Transactions on Computer Systems (TOCS)
Modeling integration of streaming and data traffic
Performance Evaluation
On performance bounds for the integration of elastic and adaptive streaming flows
Proceedings of the joint international conference on Measurement and modeling of computer systems
Sojourn time distribution in a MAP/M/1 processor-sharing queue
Operations Research Letters
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Mean characteristics of Markov queueing systems
Automation and Remote Control
A note on the event horizon for a processor sharing queue
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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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 Mt/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.