# Using fluid models to prove stability of adversarial queueing networks

@article{Gamarnik2000UsingFM, title={Using fluid models to prove stability of adversarial queueing networks}, author={David Gamarnik}, journal={IEEE Trans. Autom. Control.}, year={2000}, volume={45}, pages={741-746} }

A digital communication network can be modeled as an adversarial queueing network. An adversarial queueing network is defined to be stable if the number of packets stags bounded over time. A central question is to determine which adversarial queueing networks are stable under every work-conserving packet routing policy. Our main result is that stability of an adversarial queueing network is implied by stability of an associated fluid queueing network.

## 48 Citations

### Stability of adaptive and non-adaptive packet routing policies in adversarial queueing networks

- Computer ScienceSTOC '99
- 1999

A simple and checkable network flow-type load condition is formulated for adaptive adversarial queueing networks, and a policy is proposed which achieves stability under this new load condition.

### On Delivery Times in Packet Networks under Adversarial Traffic

- Computer Science, MathematicsSPAA '04
- 2004

It is shown that delivering all packets while maintaining stability can be done by an offline scheduler whenever the injection of packets is done at rate of at most 1, and that there is no online protocol that can achieve that property against all rate-1 adversaries.

### Stability of FIFO networks under adversarial models: State of the art

- Computer ScienceComput. Networks
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### Packet Scheduling Across Networks of Switches

- Computer ScienceICN
- 2005

It is shown how coordination over sequential timeslots by algorithms such as those based on a round robin can provide considerable advantages over a randomized scheme.

### Instability phenomena in underloaded packet networks with QoS schedulers

- BusinessIEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
- 2003

This paper studies with fluid models and with adversarial queueing theory possible underload instabilities due to strict-priority schedulers and to Generalized Processor Sharing (GPS) Schedulers.

### Underload Instabilities in Packet Networks With

- Business
- 2004

This paper studies possible underload instabilities due to flow Schedulers in packet networks, focusing on output queued switches with strict priority (SP) schedulers and Generalized Processor Sharing (GPS) schedULers, and results are rather surprising: SP scheduler appear to be more robust than GPS schedulering whenever exact information on the effective average packet flow rates is not available.

### Performance Analysis of Queueing Networks via Robust Optimization

- Computer Science, MathematicsOper. Res.
- 2011

This paper proposes a new performance analysis method, which is based on the robust optimization, and is able to obtain explicit upper bounds on some steady-state performance measures of queueing networks.

### Large bursts do not cause instability

- Computer ScienceIEEE Trans. Autom. Control.
- 2000

The purpose of this paper is to reduce the question of stability for networks with input traffic satisfying deterministic constraints in the sense of R.I. Cruz (1991) to a question of Stability for a fluid model.

### ON DECIDING STABILITY OF MULTICLASS QUEUEING NETWORKS UNDER BUFFER PRIORITY SCHEDULING POLICIES

- Mathematics
- 2009

One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key…

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