Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows.

DOI10.1214/105051604000000161zbMath1050.60091arXivmath/0406178OpenAlexW3104262590MaRDI QIDQ1879897

Bert Zwart, Sem C. Borst, M. R. H. Mandjes

Publication date: 15 September 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406178

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Large deviations (60F10)

Related Items (17)

Asymptotics for the partial sum and its maximum of dependent random variables ⋮ Sample path large deviations for Lévy processes and random walks with regularly varying increments ⋮ Sample-path large deviations for a class of heavy-tailed Markov-additive processes ⋮ Heavy loads and heavy tails ⋮ Scale-free graphs with many edges ⋮ Asymptotic loss probability in a finite buffer fluid queue with heterogeneous heavy-tailed on-off processes ⋮ Asymptotics of Hybrid Fluid Queues with Lévy Input ⋮ Heavy tails in multi-server queue ⋮ Subexponential asymptotics of hybrid fluid and ruin models ⋮ A note on queues with M/G/\(\infty\) input ⋮ Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations ⋮ Buffer content of a leaky-bucket system with long-range dependent input traffic ⋮ A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows ⋮ Generalized processor sharing queues with heterogeneous traffic classes ⋮ Tail behavior of negatively associated heavy-tailed sums ⋮ Two-node fluid network with a heavy-tailed random input: the strong stability case ⋮ Large deviations for stochastic fluid networks with Weibullian tails

Cites Work

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• Queueing at large resources driven by long-tailed \(M/G/\infty\)-modulated processes
• Asymptotic loss probability in a finite buffer fluid queue with heterogeneous heavy-tailed on-off processes
• Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
• Large deviations, the shape of the loss curve, and economies of scale in large multiplexers
• On a reduced load equivalence for fluid queues under subexponentiality
• Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues
• Subexponential loss rates in a GI/GI/1 queue with applications
• Overflow behavior in queues with many long-tailed inputs
• Loss asymptotics in large buffers fed by heterogeneous long-tailed sources
• The M / G /1 queue with two service speeds
• Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models
• Fluid queues and regular variation
• Analysis of separable Markov-modulated rate models for information-handling systems
• On the tails of waiting-time distributions
• Asymptotics of palm-stationary buffer content distributions in fluid flow queues
• Logarithmic asymptotics for steady-state tail probabilities in a single-server queue
• A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows
• A fluid queue with a finite buffer and subexponential input
• Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources
• Asymptotic results for multiplexing subexponential on-off processes
• Tail probabilities for non-standard risk and queueing processes with subexponential jumps
• Steady-state distribution of the buffer content for \(\text{M}/\text{G}/\infty\) input fluid queues
• Large deviations for Small buffers: An insensitivity result
• A note on queues with M/G/\(\infty\) input

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