1. Buffered Link

2. Buffered Link Standard model of an output buffer at a switch
Link rate of output is C
Scheduler is work-conserving (always transmitting when there is a backlog)
Transmission order is FIFO
Infinite Buffers (no buffer overflows)

3. Arrivals of packets to a buffered link
Backlog at the buffered link
slope -C

4. Definitions We write: \documentclass[10pt]{article}
\usepackage{color} %used for font color
\usepackage{amssymb} %maths
\usepackage{amsmath} %maths
\usepackage[utf8]{inputenc} %useful to type directly diacritic characters
\begin{document}
{\sf
\begin{tabbing}
xx \=xxxxxxx\= \kill
\> {\color{blue} $A(t)$ } \> Arrivals in $[0, t)$, with $ A(t) = 0$ if $t \leq 0$ \\[10pt]
\> {\color{blue}$D(t)$ } \> Departures in $[0, t)$, with $D(t) \leq A(t)$ \\[10pt]
\> {\color{blue} $B(t)$} \> Backlog at $t$. \\
\> \> {\color{blue} $B(t) = A (t) - D(t)$} \\[10pt]
\> {\color{blue} $W(t)$} \> (Virtual) delay at $t$: \\
\> \>
{\color{blue} $ W(t) = \inf \left\{ y > 0 \;|\; D(t+y) \geq A(t) \right\} $}
\end{tabbing} }
\end{document}
We write:

6. Reich's Backlog Equation (1958)
\documentclass[10pt]{article}
\usepackage{color} %used for font color
\usepackage{amssymb} %maths
\usepackage{amsmath} %maths
\usepackage[utf8]{inputenc} %useful to type directly diacritic characters
\begin{document}
{\sf
\fbox{\parbox[t]{3in}{
{\sc Reich's backlog equation:}
Given a left-continuous arrival function $A$ and a buffered link with capacity $C$.
Then for all $t \geq 0$ it holds that \[
\label{eq:reich-backlog}
B(t) = \sup_{0\leq s \leq t} \left\{ A(t) - A(s) - C(t-s) \right\} \ . \]
}}}
\end{document}

8. Introduction to Network Calculus (min, +) Algebra

9. Traffic process: Non-decreasing and and one-sided process

11. Burst and Delay Functions