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

@article{Zwart2000ExactAF, title={Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows}, author={Bert Zwart and Sem C. Borst and Michel Mandjes}, journal={Industrial \& Engineering Chemistry Research}, year={2000} }

We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a “dominant” subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation.
The dominant set consists of a… Expand

#### 53 Citations

Exact queueing asymptotics for multiple heavy-tailed on-off flows

- Mathematics, Computer Science
- Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213)
- 2001

A fluid queue fed by multiple on-off flows with heavy-tailed (regularly varying) on-periods is considered, and it is proved that the workload distribution is asymptotically equivalent to that in a reduced system. Expand

A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows

- Computer Science, Chemistry
- Advances in Applied Probability
- 2003

Under mild assumptions, it is proved that the workload distribution is asymptotically equivalent to that in a somewhat ‘dual’ reduced system, multiplied by a certain prefactor. Expand

Fluid queues with heavy-tailed M/G/infinity input

- Mathematics, Chemistry
- 2001

We consider a fluid queue fed by several heterogeneous M / G / 00 input processes with regularly varying session lengths. Under fairly mild assumptions, we derive the exact asymptotic behavior of the… Expand

Fluid Queues with Heavy-Tailed M/G/ Input

- Mathematics, Computer Science
- Math. Oper. Res.
- 2005

A fluid queue fed by several heterogeneous M/G/∞ input processes with regularly varying session lengths is considered, and the exact asymptotic behavior of the stationary workload distribution is derived. Expand

Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations

- Computer Science, Mathematics
- Math. Oper. Res.
- 2018

This work introduces a novel class of Lyapunov functions (piecewise linear and nonincreasing in the length of heavy-tailed queues), whose drift analysis provides exponentially decaying upper bounds to queue-length tail asymptotics despite the presence of heavy tails. Expand

Delay analysis of the Max-Weight policy under heavy-tailed traffic via fluid approximations

- Computer Science, Mathematics
- 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2013

A single-hop switched queueing network with a mix of heavy-tailed and light-tailed traffic is considered, and how fluid approximations and stochastic Lyapunov theory can be combined with renewal theory in order to prove delay instability results are shown. Expand

Generalized processor sharing queues with heterogeneous traffic classes

- Geography, Mathematics
- Advances in Applied Probability
- 2003

This work derives the asymptotic workload behaviour of the light-tailed traffic flow under the assumption that its GPS weight is larger than its traffic intensity, and shows that the workload distribution is asymPTotically equivalent to that in the isolated system, multiplied by a certain prefactor which accounts for the interaction with the heavy-tailed flow. Expand

Two-node fluid network with a heavy-tailed random input: the strong stability case

- Mathematics
- Journal of Applied Probability
- 2014

We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a… Expand

Asymptotic Loss Probability in a Finite Buffer Fluid Queue with Heterogeneous Heavy-Tailed On-Off Pr

- Computer Science
- INFOCOM 2000
- 2000

This work derives explicit and asymptotically exact formulas for approximating the stationary overflow probability and loss rate of a fluid queue with a finite buffer B and capacity c fed by a superposition of N independent On–Off processes. Expand

On Large Delays in Multi-Server Queues with Heavy Tails

- Mathematics, Computer Science
- Math. Oper. Res.
- 2012

We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the… Expand

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