Buffered Link

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)

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

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:

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}

Introduction to Network Calculus (min, +) Algebra

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

Burst and Delay Functions