# Network Calculus

@inproceedings{Boudec2002NetworkC, title={Network Calculus}, author={Jean-Yves Le Boudec and Patrick Thiran}, booktitle={Lecture Notes in Computer Science}, year={2002} }

Network Calculus.- Application of Network Calculus to the Internet.- Basic Min-plus and Max-plus Calculus.- Min-plus and Max-plus System Theory.- Optimal Multimedia Smoothing.- FIFO Systems and Aggregate Scheduling.- Adaptive and Packet Scale Rate Guarantees.- Time Varying Shapers.- Systems with Losses.

## Figures and Tables from this paper

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## 918 Citations

A Max-plus Network Calculus

- Computer Science2009 Eighth IEEE/ACIS International Conference on Computer and Information Science
- 2009

This paper shows a novel network calculus that based on other dioids, that is max-plus algebra, that can be obtained by max- plus network calculus in performance analysis of network calculus.

Min-plus and Max-plus System Theory Applied to Communication Networks

- Computer SciencePOSTA
- 2003

It is shown how a simple but important fixed-point theorem (residuation theorem) in min-plus or max-plus algebra can be applied to window flow control.

Comparison of delay bounds for Ethernet networks based on simple Network Calculus algorithms

- Computer Science2014 IEEE Symposium on Computers and Communications (ISCC)
- 2014

This paper gives a simple introduction to Network Calculus (NC), a theory to calculate end-to-end delay bounds for packet-switched communication networks. It illustrates how various networking…

Max-plus : A network algebra

- Computer Science
- 2006

The goal of this paper is to improve the systematic use of the Max-Plus algebra in the formulation and derivation of NC results by analyzing the problem of optimizing the playback delay and the buffer size of an optimal video decoder with some look-ahead.

Stochastic network calculus for performance analysis of Internet networks — An overview and outlook

- Computer Science2012 International Conference on Computing, Networking and Communications (ICNC)
- 2012

This paper provides an overview of stochastic network calculus from the queueing principle perspective and presents an outlook by discussing crucial yet still open challenges in the area.

Dynamic Internet Congestion with Bursts

- Computer ScienceHiPC
- 2006

A novel model for dynamics based on concepts of network calculus is introduced, which features a limited form of amortization: after quiet times where the available bandwidth was roughly constant, the congestion may change more abruptly.

Packetization and packet curves in network calculus

- Computer Science6th International ICST Conference on Performance Evaluation Methodologies and Tools
- 2012

A new formalism for data packetization in Network Calculus, the packet curves is presented and a model for a wormhole switch is given and it is shown how the results can be used to get efficient delay bounds.

Network calculus: application to switched real-time networking

- Computer ScienceVALUETOOLS
- 2011

It is shown how Network Calculus can be used to determine whether a switched network may satisfy the time constraints of a real-time application and which kind of traffic inter-dependencies are problematic.

Applying stochastic network calculus to 802.11 backlog and delay analysis

- Computer Science2011 IEEE Nineteenth IEEE International Workshop on Quality of Service
- 2011

The derived bounds are very loose in comparison to ns-2 simulation results especially for heavy arriving traffic, indicating that improvements are needed for the current version of stochastic network calculus.

Elements of Probabilistic Network Calculus for Packet Scale Rate Guarantee Nodes

- Computer Science
- 2002

Packet Scale Rate Guarantee (PSRG) is a node model used by IETF for Expedited Forwarding, a priority service defined in the context of Differentiated Services. We review probabilistic performance…

## References

SHOWING 1-10 OF 120 REFERENCES

Determining end-to-end delay bounds in heterogeneous networks

- Computer ScienceMultimedia Systems
- 1997

A method for determining an upper bound on end-to-end delay bounds for sources conforming to Leaky Bucket and exponentially bounded burstiness is presented.

A Delay Bound for a Network with Aggregate Scheduling

- Computer Science
- 2000

A worst case bound is given that is valid for any network topology given the maximum hop count for every flow and the utilization at every link and is finite only for small utilization.

Analysis and simulation of a fair queueing algorithm

- Computer ScienceSIGCOMM 1989
- 1989

It is found that fair queueing provides several important advantages over the usual first-come-first-serve queueing algorithm: fair allocation of bandwidth, lower delay for sources using less than their full share of bandwidth and protection from ill-behaved sources.

A deterministic approach to the end-to-end analysis of packet flows in connection-oriented networks

- Computer ScienceTNET
- 1998

A worst-case bound is proven for the end-to-end queueing delay and buffer size needed to guarantee loss-free packet delivery, given that sources satisfy a given source rate condition.

Comments on “a deterministic approach to the end-to-end analysis of packet flows in connection oriented networks”

- Computer ScienceTNET
- 2000

It is proved that the buffer bound in the above paper, can be improved by using a modification of the proofs in the original paper together with so-called network calculus bounds.

A note on deterministic end-to-end delay analysis in connection oriented networks

- Computer Science, Business1999 IEEE International Conference on Communications (Cat. No. 99CH36311)
- 1999

This paper extends the results presented by Chlamtac, Farago, Zhang, and Fumagalli by obtaining a smaller upper bound of end-to-end delay in connection-oriented networks under the same source rate condition and investigates the tightness of this upper bound and proves that it is tight for multipoint- to-point trees.

Application of Network Calculus to Guaranteed Service Networks

- Computer ScienceIEEE Trans. Inf. Theory
- 1998

It is found that call acceptance regions based on deterministic criteria (loss or delay) are convex, in contrast to statistical cases where it is the complement of the region which is convex.

Delay bounds for a network of guaranteed rate servers with FIFO aggregation

- Computer ScienceComput. Networks
- 2002

Delay bounds for a network of guaranteed rate servers with FIFO aggregation

- Computer Science2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333)
- 2002

A network implementing guaranteed rate (GR) scheduling with first-in-first-out (FIFO) aggregation is studied and an upper bound on the worst case end-to-end delay for the network is derived.

Real-time calculus for scheduling hard real-time systems

- Computer Science2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353)
- 2000

A link between three areas, namely Max-Plus Linear System Theory as used for dealing with certain classes of discrete event systems, Network Calculus for establishing time bounds in communication networks, and real-time scheduling is established.