How large delays build up in a GI/G/1 quqe
Queueing Systems: Theory and Applications
Heavy-traffic analysis of a data-handling system with many sources
SIAM Journal on Applied Mathematics
Effective bandwidths for multiclass Markov fluids and other ATM sources
IEEE/ACM Transactions on Networking (TON)
Quick simulation of ATM buffers with on-off multiclass Markov fluid sources
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Transient analysis of fluid model for ATM statistical multiplexer
Performance Evaluation - Special issue: performance models for information communication networks
Broadband integrated networks
Conditioned asymptotics for tail probabilities in large multiplexers
Performance Evaluation
Efficient simulation of a tandem Jackson network
Proceedings of the 31st conference on Winter simulation: Simulation---a bridge to the future - Volume 1
Optimal trajectory to overflow in a queue fed by a large number of sources
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
FAST SIMULATION OF A QUEUE FED BY A SUPERPOSITION OF MANY (HEAVY-TAILED) SOURCES
Probability in the Engineering and Informational Sciences
Large-deviations analysis for energy-saving mechanisms in wireless networks
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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This article analyzes the transient buffer content distribution of a queue fed by a large number of Markov fluid sources. We characterize the probability of overflow at time t, given the current buffer level and the number of sources in the on-state. After scaling buffer and bandwidth resources by the number of sources n, we can apply large deviations techniques. The transient overflow probability decays exponentially in n. In case of exponential on/off sources, we derive an expression for the decay rate of the rare event probability under consideration. For general, Markov fluid sources, we present a plausible conjecture. We also provide the "most likely path" from the initial state to overflow (at time t). Knowledge of the decay rate and the most likely path to overflow leads to (i) approximations of the transient overflow probability, and (ii) efficient simulation methods of the rare event of buffer overflow. The simulation methods, based on importance sampling, give a huge speed-up compared to straightforward simulations. The approximations are of low computational complexity, and accurate, as verified by means of simulation experiments.