Network Calculus

Network Calculus is a set of recent developments that provide deep insights into flow problems encountered in the Internet and in intranets. Network Calculus : A Theory of Deterministic Queuing Systems for the Internet is a self-contained, introductory course on network calculus.

Book Description

The foundation of network calculus lies in the mathematical theory of dioids, and in particular,the Min-Plus dioid (also called Min-Plus algebra). With network calculus, we are able to understand some fundamental properties of integrated services networks, window flow control, scheduling and buffer or delay dimensioning.

Network calculus belongs to what is sometimes called “exotic algebras” or “topical algebras”. This is a set of mathematical results, often with high description complexity, that give insights into man-made systems such as concurrent programs, digital circuits and, of course, communication networks. Petri nets fall into this family as well.
We hope to convince many readers that there is a whole set of largely unexplored, fundamental relations that can be obtained with the methods used in this book. Results such as “shapers keep arrival constraints” or “pay bursts only once”, derived in Chapter 1 have physical interpretations and are of practical importance to network engineers.

Table of Contents

• 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

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