Large deviations of uniformly recurrent Markov additive processes
Advances in Applied Mathematics
How large delays build up in a GI/G/1 quqe
Queueing Systems: Theory and Applications
On the self-similar nature of Ethernet traffic
SIGCOMM '93 Conference proceedings on Communications architectures, protocols and applications
Effective bandwidths for multiclass Markov fluids and other ATM sources
IEEE/ACM Transactions on Networking (TON)
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
On-line call admission for high-speed networks
On-line call admission for high-speed networks
Fluid queues and regular variation
Performance Evaluation
Long-tail buffer-content distributions in broadband networks
Performance Evaluation
M|G|Infinity Input Processes: A Versatile Class of Models for Network Traffic
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
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
A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation
Performance Evaluation
Large Deviations for Small Buffers: An Insensitivity Result
Queueing Systems: Theory and Applications
Allocating commodity resources in aggregate traffic networks
Performance Evaluation
Queueing Systems: Theory and Applications
A highly efficient M/G/∞ generator of self-similar traces
Proceedings of the 38th conference on Winter simulation
Fluid Queues with Heavy-Tailed M/G/∞ Input
Mathematics of Operations Research
Using the Whittle Estimator for the Selection of an Autocorrelation Function Family
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
Performance analysis of a Poisson-Pareto queue over the full range of system parameters
Computer Networks: The International Journal of Computer and Telecommunications Networking
Snapshot simulation of internet traffic: queueing of fixed-rate flows
Proceedings of the 2nd International Conference on Simulation Tools and Techniques
Efficient On-Line Generation of the Correlation Structure of F-ARIMA Processes
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
On the flexibility of M/G/∞ processes for modeling traffic correlations
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
Fast simulation of self-similar and correlated processes
Mathematics and Computers in Simulation
Robustness of the whittle estimator applied to non-Gaussian long-range dependent processes
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Analysis of the distribution of the statistic of a test for discriminating correlated processes
NEW2AN'11/ruSMART'11 Proceedings of the 11th international conference and 4th international conference on Smart spaces and next generation wired/wireless networking
A note on queues with M/G/∞ input
Operations Research Letters
Model selection for long-memory processes in the spectral domain
Computer Communications
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We analyze the queue at a buffer with input comprising sessions whose arrival is Poissonian, whose duration is long-tailed, and for which individual session detail is modeled as a stochastic fluid process. We obtain a large deviation result for the buffer occupation in an asymptotic regime in which the arrival rate nr, service rate ns, and buffer level nb are scaled to infinity with a parameter n. This can be used to approximate resources which multiplex many sources, each of which only uses a small proportion of the whole capacity, albeit for long-tailed durations. We show that the probability of overflow in such systems is exponentially small in n, although the decay in b is slower, reflecting the long tailed session durations. The requirements on the session detail process are, roughly speaking, that it self-averages faster than the cumulative session duration. This does not preclude the possibility that the session detail itself has a long-range dependent behavior, such as fractional Brownian motion, or another long-tailed M/G/\infty process. We show how the method can be used to determine the multiplexing gain available under the constraint of small delays (and hence short buffers) for multiplexers of large aggregates, and to compare the differential performance impact of increased buffering as opposed to load reduction.