# Survey of deterministic and stochastic service curve models in the network calculus

@article{Fidler2010SurveyOD, title={Survey of deterministic and stochastic service curve models in the network calculus}, author={Markus Fidler}, journal={IEEE Communications Surveys \& Tutorials}, year={2010}, volume={12} }

In recent years service curves have proven a powerful and versatile model for performance analysis of network elements, such as schedulers, links, and traffic shapers, up to entire computer networks, like the Internet. The elegance of the concept of service curve is due to intuitive convolution formulas that determine the data departures of a system from its arrivals and its service curve. This fundamental relation constitutes the basis of the network calculus and relates it to systems theory…

## Figures and Topics from this paper

## 195 Citations

A temporal network calculus approach to service guarantee analysis of stochastic networks

- Computer ScienceVALUETOOLS
- 2011

The time-domain SNC traffic and service models are concretized by linking some well-known stochastic processes to them by investigating the delay performance of a Gilbert-Elliott channel and it is shown that the delay bound can be improved under the independence condition.

Advances in Theory and Applicability of Stochastic Network Calculus

- Mathematics
- 2016

Stochastic Network Calculus (SNC) emerged from two branches in the late 90s:
the theory of effective bandwidths and its predecessor the Deterministic Network
Calculus (DNC). As such SNC’s goal is…

A Temporal Network Calculus for Performance Analysis of Computer Networks

- Computer Science
- 2011

On the basis of the proposed models, the five basic properties of stochastic network calculus are proved, which implies broad applicability ofThe proposed time-domain approach.

A Temporal Approach to Stochastic Network Calculus

- Computer ScienceArXiv
- 2011

A temporal approach to stochastic network calculus is presented, to develop models and derive results from the time perspective and prove the basic properties of the proposed models, such as delay bound and backlog bound, output characterization, concatenation property and superposition property.

Applying Stochastic Network Calculus In Scenarios With Incomplete Knowledge

- 2013

The deterministic network calculus (DNC) and its probabilistic counterpart stochastic network calculus (SNC) are promising theories which provide methodologies to analyse and design networked…

A Guide to the Stochastic Network Calculus

- Computer ScienceIEEE Communications Surveys & Tutorials
- 2015

An intuitive approach to the stochastic network calculus is contributed, where the method uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service.

Duality of the Max-Plus and Min-Plus Network Calculus

- Computer ScienceFound. Trends Netw.
- 2017

It is shown that there exists a one-to-one correspondence between the min-plus and max-plus network calculus, as long as traffic and service are described by functions with real-valued domains and ranges.

On applying stochastic network calculus

- Computer ScienceFrontiers of Computer Science
- 2013

The aim of this paper is to provide a tutorial on the new theoretical tool SNC, for which, four critical steps are formalized and discussed and a list of SNC application topics/areas, where there may exist huge research potential, is presented.

Modeling and Performance Analysis of Networks with Flow Transformations

- Computer Science
- 2015

This thesis addresses an extension of the network calculus to deal with the random flow transformations and provides the performance evaluation.

On deriving stable backlog bounds by stochastic network calculus

- Computer ScienceProceedings of the 2013 25th International Teletraffic Congress (ITC)
- 2013

This work model an network element as a single server with impairment service based on two best-known models in stochastic network calculus and finds that they actually derive equivalent Stochastic service curves and backlog bounds.

## References

SHOWING 1-10 OF 222 REFERENCES

A network service curve approach for the stochastic analysis of networks

- Computer ScienceSIGMETRICS '05
- 2005

The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions and is shown to be bounded by O(Hlog H), where H is the number of nodes traversed by a flow.

An Algebra for Queueing Networks with Time-Varying Service and Its Application to the Analysis of Integrated Service Networks

- Mathematics, Computer ScienceMath. Oper. Res.
- 2004

A network model that allows to capture the time-varying service delivered to a traffic stream due to the presence of random perturbations is introduced and contains several earlier discrete event models pertaining to stochastic Petri nets, service curves, and fork-join networks and shows how the present model unifies them in a single algebraic structure.

A basic stochastic network calculus

- Computer ScienceSIGCOMM
- 2006

Stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server to perform independent case analysis and provides a convenient way to find the stochastic service curve of a serve.

Scaling properties in the stochastic network calculus

- Mathematics
- 2007

Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone…

Scaling properties of statistical end-to-end bounds in the network calculus

- Computer ScienceIEEE Transactions on Information Theory
- 2006

The presented network service curve permits the calculation of statistical end-to-end delay and backlog bounds for broad classes of arrival and service distributions and is shown to be bounded by /spl Oscr/(H log H), where H is the number of nodes traversed by a flow.

An End-to-End Probabilistic Network Calculus with Moment Generating Functions

- Computer Science, Mathematics200614th IEEE International Workshop on Quality of Service
- 2006

A concise, probabilistic network calculus with moment generating functions that achieve the objective of scaling linearly in the number of servers in series is established.

A Min-Plus Calculus for End-to-End Statistical Service Guarantees

- Computer ScienceIEEE Transactions on Information Theory
- 2006

The network calculus is extended to a probabilistic framework with statistical service guarantees and it is argued that many practically relevant service curves may be compliant to this description.

The DISCO Network Calculator

- Computer ScienceMMB
- 2008

Network calculus aims to be a system theory for deterministic queuing, allowing to derive deterministic guarantees on throughput and delay, as well as find bounds on buffer sizes and thereby allow for loss-free transfer.

Network Calculus Made Easy

- Mathematics
- 1996

We deene general concepts that extend, and simplify, the network calculus developed by Cruz 1, 2, 3] for guaranteed quality of service networks. We introduce a deenition of service curve, the…

Stochastic Network Calculus

- Computer Science
- 2004

A stochastic network calculus is proposed to systematically analyze the end-to-end Stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastics servers.