On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
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
IEEE/ACM Transactions on Networking (TON)
Long-tail buffer-content distributions in broadband networks
Performance Evaluation
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Internet Web servers: workload characterization and performance implications
IEEE/ACM Transactions on Networking (TON)
Performance Guarantees in Communication Networks
Performance Guarantees in Communication Networks
Self-Similar Network Traffic and Performance Evaluation
Self-Similar Network Traffic and Performance Evaluation
Traffic model and performance evaluation of Web servers
Performance Evaluation
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
The Structural Cause of File Size Distributions
MASCOTS '01 Proceedings of the Ninth International Symposium in Modeling, Analysis and Simulation of Computer and Telecommunication Systems
LOWER BOUNDS FOR LRD/GI/1 QUEUES WITH SUBEXPONENTIAL SERVICE TIMES
Probability in the Engineering and Informational Sciences
Tail probabilities for a multiplexer with self-similar traffic
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 3
Web traffic modeling at finer time scales and performance implications
Performance Evaluation - Long range dependence and heavy tail distributions
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We analyze the asymptotic tail distribution of stationary waiting times and stationary virtual waiting times in a single-server queue with long-range dependent arrival process and subexponential service times. We investigate the joint impact of the long range dependency of the arrival process and of the tail distribution of the service times. We consider two traffic models that have been widely used to characterize the long-range dependence structure, namely, the M/G/8 input model and the Fractional Gaussian Noise (FGN) model. We focus on the response times of the customers in a First-Come First-Serve (FCFS) queueing system, although the results carry through to the backlog distribution of the system with any arbitrary queueing discipline. When the arrival process is driven by an M/G/8 input model we show that if the residual service time tail distribution Fe is lighter than the residual session duration Ge, then the stationary waiting time is dominated by the long-range dependence structure, which is determined by the residual session duration Ge. If the residual service time distribution Fe is heavier than the residual session duration Ge, then the tail distribution of the stationary waiting time is dominated by that of the residual service time. When the arrival process is modeled by an FGN, we show that the waiting time tail distribution is asymptotically equal to the tail distribution of the residual service time if the latter is asymptotically heavier than Weibull distribution with shape parameter 2-2H, where H is the Hurst parameter of the FGN. If, however, this residual service time is asymptotically lighter than Weibull distribution with shape parameter 2-2H, then the waiting time tail distribution is dominated by the dependence structure of the arrival process so that it is asymptotically equal to Weibull distribution with shape parameter 2-2H.