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)
Internet Web servers: workload characterization and performance implications
IEEE/ACM Transactions on Networking (TON)
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
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
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
Tandem queues with subexponential service times and finite buffers
Queueing Systems: Theory and Applications
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We investigate the tail distribution of the virtual waiting times in a LRD/GI/1 queue where the arrival process is long-range dependent (LRD) and the service times are independent and identically distributed (i.i.d.) random variables. We present two lower bounds on the stationary waiting time tail asymptotics, which illustrate the different dominating components that influence server performance under various conditions. In particular, we show that the tail distribution of the stationary waiting time is bounded below by that of the associated LRD/D/1 queues resulting from replacing all random service times by the mean. This shows the performance impact purely due to the long-range dependency of the arrival process. On the other hand, when the service times are subexponential, we show that the tail distribution of the stationary waiting time is bounded below by that of the corresponding D/GI/1 queue by replacing the dependent arrival process with its associated independent version. This shows the minimum performance impact due to the tail distribution of the service times. The above two lower bounds indicate that the performance of LRD/GI/1 queues will be dominated by the heavier tail of the corresponding LRD/D/1 and D/GI/1 queues. These features are further illustrated and quantified through examples and via numerous simulation experiments.