On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Experimental queueing analysis with long-range dependent packet traffic
IEEE/ACM Transactions on Networking (TON)
Heavy-tailed probability distributions in the World Wide Web
A practical guide to heavy tails
Macroscopic models for long-range dependent network traffic
Queueing Systems: Theory and Applications
An overview of Brownian and non-Brownian FCLTs for the single-server queue
Queueing Systems: Theory and Applications
LIMITS FOR CUMULATIVE INPUT PROCESSES TO QUEUES
Probability in the Engineering and Informational Sciences
Heavy traffic steady state approximations in stochastic networks with Lévy inputs
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Heavy traffic approximation for the stationary distribution of stochastic fluid networks
Queueing Systems: Theory and Applications
Mathematics of Operations Research
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We consider a Lévy stochastic network as a regulated multidimensional Lévy process. The reflection direction is constant on each boundary of the positive orthant and the corresponding reflection matrix corresponds to a single-class network. We use the representation of the Lévy process and Itô's formula to arrive at some equations for the steady-state process; the latter is shown to exist, under natural stability conditions. We specialize first to the class of Lévy processes with non-negative jumps and then add the assumption of self-similarity. We show that the stationary distribution of the network corresponding the the latter process does not has product form (except in trivial cases). Finally, we derive asymptotic bounds for two-dimensional Lévy stochastic network.