Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
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
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions
Queueing Systems: Theory and Applications
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions
Operations Research Letters
Limits and approximations for the M/G/1 LIFO waiting-time distribution
Operations Research Letters
The M/G/1 queue with heavy-tailed service time distribution
IEEE Journal on Selected Areas in Communications
On maximizing service-level-agreement profits
Proceedings of the 3rd ACM conference on Electronic Commerce
User-level performance of elastic traffic in a differentiated-services environment
Performance Evaluation
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
Queueing systems with long-range dependent input process and subexponential service times
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
The Maximum Queue Length for Heavy-Tailed Service Times in the M/G/1 FB Queue
Queueing Systems: Theory and Applications
Classifying scheduling policies with respect to higher moments of conditional response time
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Sojourn Times in the M/PH/1 Processor Sharing Queue
Queueing Systems: Theory and Applications
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
A sample path relation for the sojourn times in G/G/1-PS systems and its applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Sojourn time asymptotics in processor-sharing queues
Queueing Systems: Theory and Applications
A survey on discriminatory processor sharing
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
Provisioning servers in the application tier for e-commerce systems
ACM Transactions on Internet Technology (TOIT)
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
Sojourn time asymptotics in Processor Sharing queues with varying service rate
Queueing Systems: Theory and Applications
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Power-law vs exponential queueing in a network traffic model
Performance Evaluation
Throughputs in processor sharing models for integrated stream and elastic traffic
Performance Evaluation
The Foreground-Background queue: A survey
Performance Evaluation
The M/G/1 processor-sharing queue with disasters
Computers & Mathematics with Applications
Is fair resource sharing responsible for spreading long delays?
ACM SIGMETRICS Performance Evaluation Review
Self-adaptive admission control policies for resource-sharing systems
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Explicit formulas for the variance of conditioned sojourn times in M/D/1-PS
Operations Research Letters
Analysis of the M/G/1 processor-sharing queue with bulk arrivals
Operations Research Letters
Queueing Systems: Theory and Applications
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We show for the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer, iff the sojourn time distribution is regularly varying of index -ν. This result is derived from a new expression for the Laplace–Stieltjes transform of the sojourn time distribution. That expression also leads to other new properties for the sojourn time distribution. We show how the moments of the sojourn time can be calculated recursively and prove that the kth moment of the sojourn time is finite iff the kth moment of the service time is finite. In addition, we give a short proof of a heavy traffic theorem for the sojourn time distribution, prove a heavy traffic theorem for the moments of the sojourn time, and study the properties of the heavy traffic limiting sojourn time distribution when the service time distribution is regularly varying. Explicit formulas and multiterm expansions are provided for the case that the service time has a Pareto distribution.