Deterministic Network Calculus

From Theory to Practical Implementation

Deterministic Network Calculus

Anne Bouillard, Nokia-Bell Labs, France
Marc Boyer, ONERA, France
Euriell Le Corronc, Paul Sabatier University, France

ISBN : 9781848218529

Publication Date : October 2018

Hardcover 350 pp

165.00 USD



Deterministic network calculus is a theory based on the (min,plus) algebra. Its aim is to compute worst-case performance bounds in communication networks. Our goal is to provide a comprehensive view of this theory and its recent advances, from its theoretical foundations to its implementations.

The book is divided into three parts. The first part focuses on the (min,plus) framework and its algorithmic aspects. The second part defines the network calculus model and analyzes one server in isolation. Different service and scheduling policies are discussed, particularly when data is packetized. The third part is about network analyses. Pay burst only once and pay multiplexing only once phenomena are exhibited, and different analyses are proposed and compared. This includes the linear programming approaches that compute tight performance bounds. Finally, some partial results on the stability are detailed.


1. Basic Model: Single Server, Single Flow.

Part 1. (min,plus) Functions and Algorithms
2. The (min,plus) Functions Semi-ring.
3. Sub-classes of Functions.
4. Efficient Computations for (min,plus) Operators.

Part 2. Network Calculus: Local Analysis
5. Network Calculus Basics: a Server Crossed by a Single Flow.
6. Single Flow Crossing Several Servers.
7. Multiple Flows Crossing One Server.
8. Packets.
9. A Hierarchy of Service Curves.

Part 3. NetworkCalculus: Global Analysis
10. Modular Analysis: Computing with Curves.
11. Tight Worst-case Performances.
12. Stability in Networks with Cyclic Dependencies.

About the authors

Anne Bouillard is a Research Engineer at Nokia-Bell Labs, France. From 2006 to 2010, she was Associate Professor at ENS Paris-Saclay, France. Her main research interests are discrete event systems, performance evaluation and probabilities.

Marc Boyer is a Researcher at ONERA, France, and he regularly cooperates with Airbus on research projects. Previously, he was Assistant Professor at INPT, France, and his main research focuses on worst-case performance in avionic embedded networks.

Euriell Le Corronc is Assistant Professor at Paul Sabatier University, France. Her main research interests are discrete event systems, (max,plus) algebra and network diagnosis.