Telecommunication traffic, queueing models, and subexponential distributions
Queueing Systems: Theory and Applications
Modeling and analysis of power-tail distributions via classical teletraffic methods
Queueing Systems: Theory and Applications
Exact Buffer Overflow Calculations for Queues via Martingales
Queueing Systems: Theory and Applications
Performance Evaluation with Heavy Tailed Distributions
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Performance of correlated queues: the impact of correlated service and inter-arrival times
Performance Evaluation - Internet performance symposium (IPS 2002)
The Effect of Different Failure Recovery Procedures on the Distribution of Task Completion Times
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 16 - Volume 17
On unreliable computing systems when heavy-tails appear as a result of the recovery procedure
ACM SIGMETRICS Performance Evaluation Review - Special issue on the workshop on MAthematical performance Modeling And Analysis (MAMA 2005)
A general model for long-tailed network traffic approximation
The Journal of Supercomputing
On checkpointing and heavy-tails in unreliable computing environments
ACM SIGMETRICS Performance Evaluation Review
Analysis of round-robin variants: favoring newly arrived jobs
SpringSim '09 Proceedings of the 2009 Spring Simulation Multiconference
Probabilistic models for access strategies to dynamic information elements
Performance Evaluation
Dynamic resource allocation of computer clusters with probabilistic workloads
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Hyper-Erlang based model for network traffic approximation
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
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Power-tail distributions are those for which the reliability function is of the form x-α for large x. Although they look well behaved, they have the singular property that E(Xl) = infinity for all l ≥ α. Thus it is possible to have a distribution with an infinite variance, or even an infinite mean. As pathological as these distributions seem to be, they occur everywhere in nature, from the CPU time used by jobs on main-frame computers to sizes of files stored on discs, earthquakes, or even health insurance claims. Recently, traffic on the "electronic super highway" was revealed to be of this type, too. In this paper we first describe these distributions in detail and show their suitability to model self-similar behavior, e.g., of the traffic stated above. Then we show how these distributions can occur in computer system environments and develop a so-called truncated analytical model that in the limit is power-tail. We study and compare the effects on system performance of a GI/M/1 model both for the truncated and the limit case, and demonstrate the usefulness of these approaches particularly for Markov modeling with LAQT (Linear Algebraic Approach to Queueing Theory, Lipsky 1992) techniques.