Stationary analysis of a fluid queue with input rate varying as an Ornstein-Uhlenbeck process
SIAM Journal on Applied Mathematics
Effective bandwidths for multiclass Markov fluids and other ATM sources
IEEE/ACM Transactions on Networking (TON)
Single Class Queueing Networks with Discrete and Fluid Customers on the Time Interval R
Queueing Systems: Theory and Applications
An invariance principle for semimartingale reflecting Brownian motions in an orthant
Queueing Systems: Theory and Applications
Optimal trajectory to overflow in a queue fed by a large number of sources
Queueing Systems: Theory and Applications
Moderate deviations for queues in critical loading
Queueing Systems: Theory and Applications
On–off fluid models in heavy traffic environment
Queueing Systems: Theory and Applications
A most probable path approach to queueing systems with general Gaussian input
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: Advances in modeling and engineering of Longe-Range dependent traffic
Properties of the Reflected Ornstein–Uhlenbeck Process
Queueing Systems: Theory and Applications
Queueing systems fed by many exponential on-off sources: an infinite-intersection approach
Queueing Systems: Theory and Applications
Large deviations approximation for fluid queues fed by a large number of on/off sources
IEEE Journal on Selected Areas in Communications
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
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We consider the superposition of the cumulative fluid generated by an increasing number of stationary iid on-off sources with exponential iid on- and off-time distributions. We establish a family of sample path large deviation principles when the fluid is centered and then scaled with a factor between the inverse of the number of sources and its square root. The common rate function in this family also appears in a large deviation principle for the tail probabilities of an integrated Ornstein---Uhlenbeck process. When the produced fluid is centered and scaled with the square root of the inverse of the number of sources it converges to this integrated Ornstein---Uhlenbeck process in distribution. We discuss several representations of the rate function. We apply the results to queueing systems loaded with on-off traffic and approaching critical loading.