Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
The M/G/1 queue with processor sharing and its relation to a feedback queue
Queueing Systems: Theory and Applications
Self-similarity in World Wide Web traffic: evidence and possible causes
Proceedings of the 1996 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
SIGMETRICS '97 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Analysis and modeling of World Wide Web traffic for capacity dimensioning of Internet access lines
Performance Evaluation - Special issue on performance and control of network systems
Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Sharing a Processor Among Many Job Classes
Journal of the ACM (JACM)
Impact of fairness on Internet performance
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Tail Asymptotics for the Busy Period in the GI/G/1 Queue
Mathematics of Operations Research
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Insensitivity in processor-sharing networks
Performance Evaluation
Insensitive Bandwidth Sharing in Data Networks
Queueing Systems: Theory and Applications
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
Mathematics of Operations Research
Reduced Load Equivalence under Subexponentiality
Queueing Systems: Theory and Applications
On Stochastic Bounds for Monotonic Processor Sharing Networks
Queueing Systems: Theory and Applications
Performance of TCP-friendly streaming sessions in the presence of heavy-tailed elastic flows
Performance Evaluation - Long range dependence and heavy tail distributions
Tail asymptotics for discriminatory processor-sharing queues with heavy-tailed service requirements
Performance Evaluation - Long range dependence and heavy tail distributions
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
The equivalence between processor sharing and service in random order
Operations Research Letters
Tail equivalence for some time-shared systems
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Tail behavior of conditional sojourn times in Processor-Sharing queues
Queueing Systems: Theory and Applications
ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review
Adaptive and scalable comparison scheduling
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Sojourn time asymptotics in Processor Sharing queues with varying service rate
Queueing Systems: Theory and Applications
The Foreground-Background queue: A survey
Performance Evaluation
Is fair resource sharing responsible for spreading long delays?
ACM SIGMETRICS Performance Evaluation Review
Optimal File Splitting for Wireless Networks with Concurrent Access
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
Effective load for flow-level performance modelling of file transfers in wireless LANs
Computer Communications
Is Tail-Optimal Scheduling Possible?
Operations Research
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Over the past few decades, the Processor-Sharing (PS) discipline has attracted a great deal of attention in the queueing literature. While the PS paradigm emerged in the sixties as an idealization of round-robin scheduling in time-shared computer systems, it has recently captured renewed interest as a useful concept for modeling the flow-level performance of bandwidth-sharing protocols in communication networks. In contrast to the simple geometric queue length distribution, the sojourn time lacks such a nice closed-form characterization, even for exponential service requirements. In case of heavy-tailed service requirements however, there exists a simple asymptotic equivalence between the sojourn time and the service requirement distribution, which is commonly referred to as a reduced service rate approximation. In the present survey paper, we give an overview of several methods that have been developed to obtain such an asymptotic equivalence under various distributional assumptions. We outline the differences and similarities between the various approaches, discuss some connections, and present necessary and sufficient conditions for an asymptotic equivalence to hold. We also consider the generalization of the reduced service rate approximation to several extensions of the M/G/1 PS queue. In addition, we identify a relationship between the reduced service rate approximation and a queue length distribution with a geometrically decaying tail, and extend it to so-called bandwidth-sharing networks. The state-of-the-art with regard to sojourn time asymptotics in PS queues with light-tailed service requirements is also briefly described. Last, we reflect on some possible avenues for further research.