\batchmode

\documentclass[10pt]{report}
\RequirePackage{ifthen}



\usepackage[latin1]{inputenc}
\usepackage{times}
\usepackage{helvet}
\usepackage{courier}
\usepackage{ltxtable}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[round]{natbib}
\usepackage{schuster}
\usepackage{chappg}
\usepackage{algorithmic}
%
\renewcommand{\algorithmiccomment}[1]{\textbf{// #1}}\usepackage{listings}

\lstset{stringspaces=false,language=C++,basicstyle=\ttfamily\footnotesize ,lineskip=-1pt,keywordstyle=\bfseries\green,commentstyle=\bfseries\green,stringstyle=\bfseries\green,indent=3mm,tabsize=4,morekeywords={Coord,Id,Node,Plan,Nodes,ifstream,string,Len,Spd,Cap,Link,Links,VLinks,Veh,Time,LinkQueue,Vehs,VehQueue,iterator,cout,cerr,Cells}}

\hyphenation{si-mu-la-tion si-mu-la-tions}
\usepackage{fancyhdr}
\pagestyle{fancy}

\lhead{}
\chead{}
\rhead{\nouppercase\rightmark}

\lfoot{{\tt\ttt$RCSfile: images.tex,v $, p.\thepage }}
\cfoot{}
\rfoot{\texttt{\today}}
\usepackage{mycolor-prn}
\usepackage{sf-blue}
\usepackage{mydefs}
\usepackage{geometry}
\geometry{a4paper,tmargin=25mm,lmargin=23mm,bmargin=20mm,rmargin=63mm,twoside=false}
\parindent0pt
\parskip0.3\baselineskip

\newtheorem{task}{Task}[chapter]\newtheorem{mytable}{Table}[chapter]\let\ptmp=\ptmp{\sf\blue
 }
\let\stmp=\stmp{\sf\blue
 }


\usepackage[dvips]{color}


\pagecolor[gray]{.7}

\usepackage[latin1]{inputenc}



\makeatletter
\AtBeginDocument{\makeatletter
\input /home/nagel/4cvs/tex/book/book/html/book.aux
\makeatother
}

\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
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\catcode`\<=12\catcode`\_=\count@
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\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
\let\newedcommand\renewedcommand
\let\renewedenvironment\newedenvironment
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\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
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\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
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\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
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\def\liih@math{\ifmmode$\else\bad@math\fi}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
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\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
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\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
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\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize %
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\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
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\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
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\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
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\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
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\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
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\newcommand\lthtmlindisplaymathZ{\egroup %
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\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
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\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
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\def\centerinlinemath{%
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\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize 
  \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
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\providecommand{\selectlanguage}[1]{}%
\makeatletter \tracingstats = 1 


\begin{document}
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
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\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\lthtmltypeout{}%
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\onecolumn

% !!! IMAGES START HERE !!!

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16938}%
$p_{noise} = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16941}%
$v_{max}=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16943}%
$p_{noise}=0.25$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16947}%
$gap > 3 \cdot v_{oncoming}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16949}%
$v_{max}=3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16951}%
$gap \ge 3 \cdot v_{oncoming}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16962}%
$N_{spl} \sim \sqrt  {p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16964}%
$p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16966}%
$p \to N_{links}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16968}%
$N_{spl}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16974}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16977}%
$t_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16979}%
$t_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16981}%
$t1 + t_{rct}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16983}%
$t_2 + t_{rct}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline16985}%
$t_1 + t_{rct}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17008}%
$v(q)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17010}%
$T(q)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17012}%
$v(\rho )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17014}%
$q(\rho )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17020}%
$z(\@mathbf {q})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17023}%
$\left \delimiter "426830A U_A\right \delimiter "526930B =3$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17025}%
$\left \delimiter "426830A U_B\right \delimiter "526930B =9$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17027}%
$U_B$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17029}%
$U_A$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17035}%
$x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17045}%
$U_C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17060}%
$gap$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17062}%
$weight2 = v - gap_o = 3 - 10 = -7 < 1 = weight1$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17064}%
$weight3 = v_{max} - gap_b = 5 - 6 = -1 < 1 = weight1$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17066}%
$weight4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17082}%
$=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17099}%
$v_{max}=2$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17101}%
$gap > v_{oncoming}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17103}%
$gap > v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline17122}%
$80\%$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline124}%
$RCSfile: images.tex,v $%
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$n$%
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{\newpage\clearpage
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$n \times n$%
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17146}%
\includegraphics[angle=-90,width=0.6\hsize]{gz/5actshusband.eps.gz}%
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$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1591}%
$t+1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17169}%
\includegraphics[width=\hsize]{gz/traffic1.eps.gz}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1593}%
$\vdots$%
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17191}%
\includegraphics[width=0.3\textwidth]{gz/traffic2.eps.gz}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath1549}%
\begin{displaymath} 
N_{cells} = L/\ell ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1609}%
$L$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1611}%
$\ell$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
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\stepcounter{chapter}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1613}%
$s$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1550}%
\begin{displaymath} 
\vec r_{st} 
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1617}%
$\theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1619}%
$\vec r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1551}%
\begin{displaymath} 
\tan \theta = \frac{y}{x} 
\hbox{\ \ or \ \ }
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1633}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1635}%
$(i+1) \, \ell$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1552}%
\begin{displaymath} 
\left[\begin{array}{c}x\\y\\\end{array}\right]
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1553}%
\begin{displaymath} 
\left[\begin{array}{c}+ w \, \sin \theta \\- w \, \cos \theta \\
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1639}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17274}%
\includegraphics[width=0.8\hsize]{gpl-tif.eps}%
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\stepcounter{section}
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1643}%
$=$%
\lthtmlinlinemathZ
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\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
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{\newpage\clearpage
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\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1645}%
$10^4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1647}%
$10^3$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$10^4 \times 10^3 = 10^7$%
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{\newpage\clearpage
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$10^6$%
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\begin{displaymath} 
{\tt tmpArrivalTime = now + outLinkTravelTime \ ,}
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\lthtmlinlinemathA{tex2html_wrap_inline1655}%
$U_{trip}(T_{trip})$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1657}%
$T_{trip}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1659}%
$U_{early}(T_{early})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1661}%
$U_{late}(T_{late})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1556}%
\begin{displaymath} 
U_{dep} = U_{trip}(T_{trip}) + U_{early}(T_{early}) +
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1138}%
\begin{displaymath}
U_{dep} = - \frac{0.4}{60~sec} \, T_{trip} - \frac{0.25}{60~sec} \, T_{early} - \frac{1.5}{60~sec} \, T_{late}\ .
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\lthtmlinlinemathA{tex2html_wrap_inline1663}%
$t_{des}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1557}%
\begin{displaymath} 
T_{early}(t_{dep}) 
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1667}%
$t_{dep}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1558}%
\begin{displaymath} 
T_{early}(t_{dep}) 
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1669}%
$T_{early}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1675}%
$t_{des} = 8:00$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1679}%
$T_{trip}(t_{dep})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1681}%
$T_{early}(t_{dep})$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17401}%
\includegraphics[width=0.6\hsize]{dep-time-fig.eps}%
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\begin{displaymath} 
p_i \propto e^{ \beta U_i } \ .
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1689}%
$p_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1691}%
$\sum_i p_i = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1560}%
\begin{displaymath} 
p_i = \frac{ e^{\beta U_i} }{ \sum_j e^{\beta U_j} } \ ,
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1695}%
$U_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1699}%
$\beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1701}%
$\beta \to 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1703}%
$U_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1705}%
$\beta \to \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1707}%
$U_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1711}%
$U_i < U_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1561}%
\begin{displaymath} 
p_i = \frac{e^{\beta U_i}}{e^{\beta U_{max}} 
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1713}%
$U_j = U_{max}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1562}%
\begin{displaymath} 
e^{\beta (U_i - U_{max})}  
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1715}%
$U_i - U_{max} < 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1717}%
$k$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1719}%
$U_k = U_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1563}%
\begin{displaymath} 
p_k 
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\stackrel{\beta \to \infty}{\too}
\frac{1}{1 + 0} \ ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1721}%
$U_j - U_{max} < 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1723}%
$j \ne k$%
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1725}%
$\beta = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1731}%
$f(t_{dep}) = e^{U(t_{dep})}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1733}%
$\Sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1564}%
\begin{displaymath} 
p(t_{dep}) = \frac{f(t_{dep})}{\Sigma} \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17437}%
\includegraphics[width=0.9\hsize]{fb2-dataflow-fig.eps}%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1737}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1739}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1741}%
$S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1743}%
$T \times R \times S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1751}%
$t_{arr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1753}%
$T_{early} = \max[ 0, t_{des}-t_{arr} ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1755}%
$T_{late} = \max[ 0, t_{arr} - t_{des} ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1565}%
\begin{displaymath} 
U_{dep} = - \frac{0.4}{60~sec} \, T_{trip} - \frac{0.25}{60~sec} \, T_{early} - \frac{1.5}{60~sec} \, T_{late}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1566}%
\begin{displaymath} 
\pi_i = e^{U_{dep}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1567}%
\begin{displaymath} 
\Pi := \sum_i \pi_i \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1568}%
\begin{displaymath} 
p_i := \pi_i / \Pi \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1757}%
$\pm 150$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1759}%
$p[i]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
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\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath4631}%
\begin{displaymath} 
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4675}%
$g_t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4677}%
$v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4632}%
\begin{displaymath} \displaystyle
v_{t+1} = \cases{%%
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}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4633}%
\begin{displaymath} 
x_{t+1} = x_{t} + v_{t+1} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4685}%
$p_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4687}%
$v_{max} -1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4691}%
$v_{safe}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4707}%
$g_t < v_{max} - 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4713}%
$v_{t+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4721}%
$v_{lead} < v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4723}%
$g_t = v_{lead}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4725}%
$0\to1\to2\to3\to\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4727}%
$0\to0\to1\to2\to2\to3\to\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4729}%
$g_t = v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4735}%
$\ell = 1/\rho_{jam} \approx 7.5~m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4737}%
$v=5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4741}%
$1/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4743}%
$p_n = 0.2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4745}%
$\ell =
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4747}%
$\Delta t = 1~sec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4749}%
$7.5~m/sec = 27~km/h = 16.875~mph$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4751}%
$(1 - p_{noise}) \, v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4757}%
$v_{max} - p_{noise}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4759}%
$m/sec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4761}%
$km/h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4763}%
$mph$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4765}%
$N_q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4769}%
$q_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4634}%
\begin{displaymath} 
q_T = \frac{N_q}{T} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4775}%
$N_\rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4635}%
\begin{displaymath} 
\rho_T = \frac{N_\rho}{T \, v_{max}} \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4779}%
$1000/7.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4781}%
$2000~veh/h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4783}%
$p_{noise}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17588}%
\includegraphics[width=0.45\hsize]{gz/fdiag-1lane.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4793}%
$min[v+1,v_{max},gap_{other}] >
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4795}%
$\min[v+1,v_{max}]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4797}%
$gap_{other,back} > v_{back}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4799}%
$v_{back}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17598}%
\includegraphics[width=0.8\textwidth]{gz/passing.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4801}%
$v \ge v_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4803}%
$v \ge
v_l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4805}%
$v_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4807}%
$v_l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4809}%
$v < v_r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4811}%
$v < v_l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4817}%
$d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4821}%
$d=16$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17619}%
\includegraphics[width=\hsize]{gz/nagel-twolane-basic1.eps.gz}%
\lthtmlpictureZ
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{\newpage\clearpage
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$a$%
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$v_{0,a}$%
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{\newpage\clearpage
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$L_a$%
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$C_a$%
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$n_{lanes,a}$%
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$T_{0,a}={L_a / v_{0,a}}$%
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$t_0$%
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$t_0 + T_{0,a}$%
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$T_{0,a}$%
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$int(C_a)$%
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$fr(C_a)$%
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$rnd$%
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$\lceil C_a \rceil$%
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$15~km/h$%
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$T_j$%
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$j$%
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$0.5$%
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$0.25$%
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$1/3$%
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{\newpage\clearpage
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$i=1..N$%
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$V_{a,i}$%
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{\newpage\clearpage
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$U$%
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$x_{a,j}, j \le k$%
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$x_{i,j},
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$\eta$%
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\lthtmlinlinemathA{tex2html_wrap_inline4959}%
$\vec x_{i,a}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4961}%
$V$%
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$V = \vec \beta \cdot \vec x$%
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\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4969}%
$\gamma$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$\mu$%
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\lthtmlinlinemathA{tex2html_wrap_inline4973}%
$t_b$%
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$t_c$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4977}%
$\beta_b$%
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{\newpage\clearpage
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$\beta_c$%
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{\newpage\clearpage
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$\beta_b >
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{\newpage\clearpage
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$\beta_x$%
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$10^5 \times 10^5 = 10^{10}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4991}%
$10^7$%
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$c_a(x_a)$%
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{\newpage\clearpage
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$37.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17823}%
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\lthtmlpictureA{tex2html_wrap17827}%
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\stepcounter{section}
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$N_{spl} = 250 \,
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5019}%
$N_{spl} =
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5025}%
$\sim p^{0.5}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5029}%
$p^{\alpha}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5031}%
$\alpha > 0.5$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5035}%
$p=1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5039}%
$A \,
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$T_{cmp}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5053}%
$T_{cmm}$%
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{\newpage\clearpage
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{\newpage\clearpage
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\lthtmldisplayZ
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{\newpage\clearpage
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$T_1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5061}%
$f_{ovr}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5063}%
$f_{dmn} =
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{\newpage\clearpage
\lthtmldisplayA{displaymath4643}%
\begin{displaymath} 
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\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5065}%
$T_{lt}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5067}%
$S_{msg}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5069}%
$b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5071}%
$b_{net} = 100$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5073}%
$b_{nd} = 40$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5075}%
$100/5 = 20$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5077}%
$b_{net}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmldisplayA{displaymath4644}%
\begin{displaymath} 
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{\newpage\clearpage
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$N_{sub}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5081}%
$N_{sub}=2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5083}%
$n_{nb}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5089}%
$p=2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5091}%
$p \to \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4645}%
\begin{displaymath} 
n_{nb}(p) = 2 \, (3 \sqrt{p} - 1) \, (\sqrt{p} - 1) / p \ ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5093}%
$n_{nb}(1) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5095}%
$n_{nb} \to 6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5103}%
$N_{spl}(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5105}%
$N_{spl}(p)/p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5107}%
$S_{bnd}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5109}%
$b_{nd}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4646}%
\begin{displaymath} 
T(p) = {T_1 \over p} \Big( 
1 + f_{ovr}(p) + f_{dmn}(p) \Big) +
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4647}%
\begin{displaymath} 
N_{sub} \cdot \left(
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+ N_{spl}(p) \,  {S_{bnd} \over b_{net}} \right) \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5115}%
$n_{nb} \sim const$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5121}%
$f_{dmn}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4648}%
\begin{displaymath} 
T(p) \sim {1 \over p} + 1 + {1 \over \sqrt{p}} + \sqrt{p}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5125}%
$b_{net} = \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4649}%
\begin{displaymath} 
T(p) \sim {1 \over p} + 1 + {1 \over \sqrt{p}} 
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5129}%
$T(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4650}%
\begin{displaymath} 
rtr(p) := {\Delta t \over T(p)} = {1~sec \over T(p)} \ ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5131}%
$\Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5133}%
$1~sec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5137}%
$T_{lt} = 0.8$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5139}%
$b_{nd} =
50$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5143}%
$N_{spl}(p) = 140 \cdot p^{0.59} - 140$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5145}%
$S_{bnd} = 200~Bytes$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5149}%
$t_{lat}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17956}%
\includegraphics[width=0.8\hsize]{cars-time-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17957}%
\includegraphics[width=0.8\hsize]{cars-rtr-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17961}%
\includegraphics[width=0.8\hsize]{nocars-time-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17962}%
\includegraphics[width=0.8\hsize]{nocars-rtr-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17966}%
\includegraphics[width=0.7\hsize]{other-rtr-gpl.eps}%
\lthtmlpictureZ
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17967}%
\includegraphics[width=0.7\hsize]{ten-rtr-gpl.eps}%
\lthtmlpictureZ
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\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath4651}%
\begin{displaymath} 
S(p) := {T(1) \over T(p)}  \ ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5159}%
$T(1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5169}%
$
rtr(p) = {1~sec / T(p)} \ .
$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5171}%
$T(1)/(1~sec)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4652}%
\begin{displaymath} 
E(p) := {T(1)/p \over T(p)} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5173}%
$E(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5175}%
$p \, T(1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17986}%
\includegraphics[width=0.8\hsize]{eff-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{chapter}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17995}%
\includegraphics[height=0.3\hsize]{load-bal-repl-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap17996}%
\includegraphics[height=0.3\hsize]{plans-server-timing-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{part}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6383}%
$T=60~sec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6385}%
$T=5~min$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath6071}%
\begin{displaymath}
v_L = {1 \over N_L} \, \sum_{i=1}^{N_L} v_i \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6389}%
$N_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6078}%
\begin{displaymath}
\tilde v_T = {1 \over N_T} \sum v_i \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6391}%
$(v_i)_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6393}%
$v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6401}%
$w_i=v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6082}%
\begin{displaymath}
v_{spot} = {\sum w_i v_i \over \sum w_i}
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= {N \, \sigma^2 + N \overline{v}^2 \over N \overline{v}}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6403}%
$\sigma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6405}%
$v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6407}%
$L/v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6411}%
$q = \rho \, v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath6096}%
\begin{displaymath}
q_T = {N_T \over T \, N_{lanes}} \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6417}%
$q = \rho v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6102}%
\begin{displaymath}
q_L = \rho_L \, v_L
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6419}%
$\rho_L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath6108}%
\begin{displaymath}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6425}%
$\rho_T =
q_T/v_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6427}%
$\ell_i/v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6114}%
\begin{displaymath}
\rho_T = {1 \over T} \sum \ell_i/v_i \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6429}%
$\ell_i = const =1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6431}%
$\ell_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18045}%
\includegraphics[width=0.8\hsize]{gz/synchronized_time.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18050}%
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\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18055}%
\includegraphics[width=0.5\hsize]{rct-time-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18056}%
\includegraphics[width=0.5\hsize]{rct-time-2-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6447}%
$v_{t+1} = \min[ g , v_t + 1, v_{max} ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6449}%
$x_{t+1} = x_{t} + v_{t+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6451}%
$g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6463}%
$v_{max}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6469}%
$q = \rho \, v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6473}%
$\sum v_i = \sum g_i = N_{veh} \times \left\langle g\right\rangle $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6475}%
$\rho = 1/(\left\langle g\right\rangle +1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6182}%
\begin{displaymath}
q = \rho \, v = 1 - \rho \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6477}%
$\rho \, v_{max} = 1 - \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6187}%
\begin{displaymath}
\rho_* = \frac{1}{v_{max}+1} \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6191}%
\begin{displaymath}
q_{max} = \frac{v_{max}}{v_{max}+1} \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18096}%
\includegraphics[width=0.6\textwidth]{184tty-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18100}%
\includegraphics[width=0.6\hsize]{fdiag-184-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6481}%
$v_{t+1} = \max[ v_{t+1} - 1 , 0 ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6483}%
$p_{noise}=0.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6487}%
$2000~veh/hr$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6493}%
$5~veh/6~sec =
3000~veh/hr$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6497}%
$\rho_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6499}%
$\rho < \rho_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6503}%
$\Big( v_t=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6505}%
$g_t \le 1 \Big)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6507}%
$v_{t+1} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6509}%
$v_{t+1} = \min[ g_t , v_t + 1, v_{max} ]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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..4............4......5..........4........5..........5................
......5............4.......5.........5.........4..........4...........
...........5...........5........4.........4........5..........4.......
................4...........4.......5.........5.........4.........5...
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.....4..................4...........5.........5........5.........4....
.........4..................5............5.........5........4........5
....4........5...................5............5.........4.......5.....
........4.........4...................5............5........4........4
...4........5.........5....................5............4.......5.....
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....4......4.........4.........5.....................5..........5.....
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...........01.....1..2..3.......4..........5...............5.......4..
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......4.....1..2.....3...2....3..........5..........5...............4.
..5.......2..1...2......1..2.....4............4..........5............
.......3....1.2....2.....1...2.......4............4...........5.......
..........1..1..3....2....1....2.........5............4............4..
.4.........1..2....2...3...2.....3............4...........4...........
.....5......2...2....3....1..3......4.............5...........4.......
..........3...3...3.....1..1....4.......4..............5..........4...
4............3...2...3...2..1.......5.......4...............4.........
....4...........2..2....1..1.1...........4......5...............4.....
........4.........1..2...2..1.2..............5.......4..............4.
..4.........4......2...3...1.1..2.................4......4............
......5.........4....2....1.0.2...2...................4......4........
...........5........2..3...01...2...2.....................4......5....
5...............4.....2...00.1....3...3.......................4.......
.....4..............2...0.01..2......3...3........................5...
.5.......4............1.0.0.1...3.......3...3.........................
......5......5.........00.1..2.....3.......3...4......................
...........5......3....00..1...3......3.......4....4..................
................4....0.01...1.....4......4........4....5..............
....................01.0.1...2........4......5........4.....4.........
....................1.00..1....3..........4.......4.......5.....5.....
.....................000...2......3...........5.......4........5.....5
....5................000.....3.......3.............5......4.........4.
..4......5...........001........3.......4...............5.....4.......
......5.......4......00.1..........3........5................4....4...
5..........5......1..01..2............3..........5...............4....
.....5..........2..1.0.2...3.............3............5..............4
...4......4.......1.00...2....3.............3..............4..........
.......4......3....001.....2.....3.............3...............5......
...........5.....1.00.1......3......4.............4.................4.
..4.............1.000..1........3.......5.............5...............
......5..........0000...1..........3.........4.............4..........
...........4.....0001....2............4..........5.............5......
...............1.001.2.....2..............5...........4.............5.
...5............001.2..3.....2.................5..........4...........
........5.......00.2..3...4....2....................5.........4.......
.............2..00...3...3....2..2.......................5........5...
.4.............000......3...3...2..2..........................4.......
.....4.........000.........2...2..2..2............................5...
.5.......5.....001...........3...1..2..2..............................
......4.......001.2.............0.1...2..2............................
..........3...00.2..3...........1..2....2..2..........................
.............000...2...3.........1...2....1..3........................
.............000.....3....4.......1....2...1....4.....................
\end{center}
\par  \end{center}
\end{figure}%
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\begin{figure}
% latex2html id marker 6330
<tex2html_file>#./krauss-hl.tex#
\begin{center}
\par\frame{
\parbox{0.8\linewidth}{%%
\footnotesize
{\noindent \bf \strut Derivation of the safe velocity}
\par
Let us first Taylor-expand the function $d(v)$\  describing the braking
distance around the operating point $\overline v := (v + \tilde v)/2$,
where $v$\  and $\tilde v$\  are again the velocity of the follower and
leader, respectively:
\begin{displaymath}
d(v) = d(\overline v) + (v - \overline v) \, d'(\overline v)
+ {(v - \overline v)^2 \over 2} \, d''(\overline v) 
+ O\big( (v - \overline v)^3 \big) \ .
\end{displaymath}
\par
Inserting this into Eq.~\ref{no-collision}, one obtains first
\begin{displaymath}
(v - \overline v) \, d'(\overline v) 
+ v \, \tau
\le (\tilde v - \overline v) \, d'(\overline v) \, \tilde v + g
\end{displaymath}
and then
\begin{displaymath}
v \, d'(\overline v) + v \, \tau
\le \tilde v \, d'(\overline v) \, \tilde v + g \ .
\qquad (*)
\end{displaymath}
Note that this is correct up to and including second order, since the
second order terms cancel out.
\par
Next, we note the kinematic relation
\begin{displaymath}
d'(\overline v) \equiv {d \over dv} d (\overline v) = {\overline v \over 
b(\overline v)}  \ ,
\end{displaymath}
where $b(v)$\  is the deceleration of the car.  This relation can be
easily derived when one assumes a constant $b$\  until the car is
stopped, but is also true for an arbitrary braking profile $b(v)$. 
\par
Inserting this into Eq.~($*$) and rearranging terms yields
\begin{displaymath}v \le \tilde v 
+ {g - \tilde v \, \tau \over \tau + \overline v/b(\overline v)} 
\ .
\end{displaymath}
\par
{\noindent \bf Showing the collision freeness}
\par
In continuous time and after the assumptions made, the above is the
condition for collision-free driving. This is true also for the
discrete analogue of this formula, provided the step-size $h$\  is
smaller than $\tau$: First, in general one obtains for the gap
\begin{displaymath}
g_{t+h} = g_t + h \, 
\Big( \tilde v_{t+h} - v_{t+h} \Big) \ .
\end{displaymath}
After using Eq.~(\ref{eq:SK_vSafe}) of the main text, rearranging
terms, and using the notation $\xi_t := g_t - h \, \tilde v_t$\  one
gets
\begin{displaymath}
\xi_{t+h} 
\ge \xi_t \Big( 1 - {h \over \tau + \overline v /b} \Big)
+ h \, \tilde v \, {\tau -  h
\over \tau + \overline v / b} \ ,
\end{displaymath}
a map $\xi_t \to \xi(t + h)$. Thus, $h \le \tau$\  is a sufficient
condition to ensure that if $\xi_t \ge 0$, then $\xi{t+h} \ge 0$,
meaning that $\xi_t \ge 0$\  for all $t$\  if $\xi_{t=0} \ge 0$.  Because
of the definition of $\xi$, this ensures that $g_t \ge 0$\  for all $t
\ge 0$.\strut 
\par
}}
\end{center}
<tex2html_endfile>#./krauss-hl.tex#
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8108}%
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{\newpage\clearpage
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$x=0$%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7894}%
\(
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8118}%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\lthtmlpictureA{tex2html_wrap18269}%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7926}%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7895}%
\(
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$dq/d\rho = v_{max}$%
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{\newpage\clearpage
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$dq/d\rho = -1$%
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{\newpage\clearpage
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$\rho=1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8140}%
$v=0$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8142}%
$q=0$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8144}%
$v=v_{max}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8146}%
$\rho = 1/(v_{max}+1)$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath6938}%
\begin{displaymath}
{\Delta q \over \Delta \rho}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8148}%
$c =
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{\newpage\clearpage
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$(\rho=0,q=0)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8152}%
$-1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8154}%
$1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8156}%
$q_{out}=0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8158}%
$c_{in} = q_{in}/(\rho_{in}-1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8162}%
$c_{in}$%
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{\newpage\clearpage
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\includegraphics[width=0.6\hsize]{tr-light-fig.eps}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath6966}%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8164}%
$c=dq/d\rho$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6972}%
\begin{displaymath}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8170}%
$Dv/Dt$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8172}%
$\partial_t v + v \, \partial_x v$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath6976}%
\begin{displaymath}
\partial_t v + v \, \partial_x v 
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8174}%
$V(\rho)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8176}%
$V(\Delta x)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath6979}%
\begin{displaymath}
V(\rho(\Delta x/2)) = V(\rho(0)) 
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{\newpage\clearpage
\lthtmldisplayA{displaymath6983}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath6988}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8182}%
$\partial_x \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8184}%
$\nu \, \partial_x^2
v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7896}%
\( \partial_t v
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8194}%
$v = V(\rho)$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
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\lthtmlpictureA{tex2html_wrap18339}%
\includegraphics[width=0.5\textwidth]{cap-fig.eps}%
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\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8196}%
$U=RI$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8202}%
$I$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8210}%
$T(q) = L/v(q)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18352}%
\includegraphics[width=0.7\hsize]{3d-assign-fig.eps}%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8222}%
$T_{link}(q)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18371}%
\includegraphics[width=0.6\textwidth]{q-v-fig.eps}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8226}%
$cap$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8228}%
$q > cap$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8230}%
$q=cap$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18378}%
\includegraphics[width=0.8\textwidth]{bottleneck-fig.eps}%
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\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8232}%
$q_a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8240}%
$\vec q = (q_1, q_2, ...)$%
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{\newpage\clearpage
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$t_a = t_a(q_a)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8244}%
$Q^{rs}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8246}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8256}%
$f^{rs,p}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7062}%
\begin{displaymath}
\sum_p f^{rs,p} = Q^{rs} \ .
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{\newpage\clearpage
\lthtmldisplayA{displaymath7066}%
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8260}%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8262}%
$rs,p$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7077}%
\begin{displaymath}
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7082}%
\begin{displaymath}
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8266}%
$c^{rs,p}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7095}%
\begin{displaymath}
c^{rs,p} = \sum_a \, t_a \, \delta_a^{rs,p} \ .
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{\newpage\clearpage
\lthtmldisplayA{displaymath7100}%
\begin{displaymath}
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\lthtmldisplayZ
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\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath7106}%
\begin{displaymath}
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7110}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8282}%
$z(\vec q)$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8286}%
$\vec q$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8292}%
$\vec q^*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8294}%
$\nabla z \, (\vec q^*) = \vec 0$%
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{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18433}%
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\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8302}%
$> 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8306}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8308}%
$\vec v \cdot H \vec v > 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8310}%
$\vec v \ne \vec 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8316}%
$\nabla z \,
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8320}%
$\nabla z(\vec q) \equiv \vec 0$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath7928}%
\begin{displaymath} 
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7929}%
\begin{displaymath} 
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8342}%
$X_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8344}%
$X_2$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7144}%
\begin{displaymath}
X_3 := \alpha \, X_1 + (1-\alpha) \, X_2
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8346}%
$\alpha \le 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8348}%
$f^{rs,p} \ge 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8350}%
$\sum_p f^{rs,p} = Q^{rs}$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8354}%
$\vec q^n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8358}%
$z(\vec q)
\equiv z(\vec q^n + y)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7153}%
\begin{displaymath}
z(\vec q^n) + \vec y \cdot \nabla z \, (\vec q^n) \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8362}%
$z(\vec q^n)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8366}%
$\vec x^n = \vec q^n +
\vec y^n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8370}%
$\vec x^n$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath7930}%
\begin{displaymath} 
\vec q^{n+1} = \alpha \, \vec q^n + (1-\alpha) \, \vec x^n \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8372}%
$\nabla z$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8376}%
$(\nabla z)_b \equiv \partial_b \equiv
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8380}%
$q_b$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath7931}%
\begin{displaymath} 
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\lthtmldisplayZ
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{\newpage\clearpage
\lthtmldisplayA{displaymath7166}%
\begin{displaymath}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8382}%
$\tilde z$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8384}%
$\vec q^n + \vec
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7932}%
\begin{displaymath} 
\hat z := \sum_a (\vec q^n + \vec y) \, t_a(\vec q^n) \ .
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8388}%
$\hat z$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8390}%
$\vec x = \vec
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8400}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8406}%
$\alpha^n =
1/n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8408}%
$\sum_{n=m}^\infty 1/n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8410}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8424}%
$U_X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8426}%
$V_X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8428}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7183}%
\begin{displaymath}
P_A \propto e^{V_A} \ ,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8430}%
$V_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8434}%
$e^{V_A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8436}%
$\leadsto$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7897}%
\(
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8448}%
$\epsilon_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8452}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7192}%
\begin{displaymath}
Pr(A) = Pr( U_A > U_B) = Pr( V_A + \epsilon_A > V_B + \epsilon_B)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7196}%
\begin{displaymath}
= Pr( \epsilon_B - \epsilon_A < V_A - V_B )
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8454}%
$\left\langle U_A\right\rangle =3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8456}%
$\left\langle U_B\right\rangle =9$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18543}%
\includegraphics[width=0.8\hsize]{overlap-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8464}%
$V_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7206}%
\begin{displaymath}
V_A = \beta_1 \, x_{A,1} + \beta_2 \, x_{A,2} + ...
= \vec\beta \cdot \vec x_{A}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7211}%
\begin{displaymath}
V_B = ... = \vec\beta \cdot \vec x_{B} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8466}%
$x_{X,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7216}%
\begin{displaymath}
\begin{tabular}{|c|c|c|}
\hline
Car & Bus & Coeff \\
\hline
1 & 0 & -1.4 \\
time with car[min] & time with bus[min] & -0.1 \\
cost with car[cent] & cost with bus[cent] & -0.012 \\
\hline
\end{tabular}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7221}%
\begin{displaymath}
V_{car} = -1.4 - \frac{0.1}{min} \times \hbox{time w/ car} 
- \frac{0.012}{cents} \times \hbox{cost w/ car} \ ;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7230}%
\begin{displaymath}
V_{bus} = 0 - \frac{0.1}{min} \times \hbox{time w/ bus}
- \frac{0.012}{cents} \times \hbox{cost w/ bus} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7239}%
\begin{displaymath}
V_{car} = -1.4 - 1 - 2.4 = - 4.8 \ ;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7242}%
\begin{displaymath}
V_{bus} = 0 - 2 - 1.2 = - 3.2 \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7245}%
\begin{displaymath}
P_{car} = \frac{e^{V_{car}}}{e^{V_{car}} + e^{V_{bus}}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7251}%
\begin{displaymath}
P_{bus} = \frac{e^{V_{bus}}}{e^{V_{car}} + e^{V_{bus}}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8468}%
$\eps_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7264}%
\begin{displaymath}
f(x) 
= \frac{1}{\sqrt{2\pi} \, \sigma} 
\, \exp\left( - \frac{1}{2} \, \left(\frac{x}{\sigma}\right)^2 \right)  \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7934}%
\begin{displaymath} 
\int_x^{x+\Delta x} f(x)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8474}%
$x + \Delta x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8476}%
$F(x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7935}%
\begin{displaymath} 
f(x) = F'(x) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8478}%
$X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7936}%
\begin{displaymath} 
Pr(x < X) = \int_{-\infty}^X f(x)
= F(X) - F(-\infty) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7276}%
\begin{displaymath}
Pr(A) = Pr( U_A > U_B) = Pr( \epsilon_B - \epsilon_A < V_A - V_B ) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8480}%
$Pr(A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8482}%
$\eps_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8484}%
$\eps_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8486}%
$\epsilon := \epsilon_B - \epsilon_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7278}%
\begin{displaymath}
f(\eps) 
= \frac{1}{\sqrt{2\pi} \, \sigma} 
\, \exp\left( - \frac{1}{2} \, \left(\frac{\epsilon}{\sigma}\right)^2 \right)  \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18599}%
\includegraphics[height=0.4\hsize,width=0.6\hsize]{erf-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18605}%
\includegraphics[height=0.4\hsize,width=0.6\hsize]{gz/gauss.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8492}%
$Pr( \epsilon < C )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8494}%
$C := V_A - V_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7296}%
\begin{displaymath}
Pr( \epsilon < C ) = \frac{1}{\sqrt{2\pi} \, \sigma} \, \int_{-\infty}^C
\, \exp\left( - \frac{1}{2} \, \left(\frac{\epsilon}{\sigma}\right)^2 \right) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7308}%
\begin{displaymath}
F(\epsilon) = \exp[ - e^{ - \mu \, (\epsilon - \eta) } ] \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7311}%
\begin{displaymath}
f(\epsilon) = F'(\epsilon) = \mu \, e^{- \mu \, (\epsilon - \eta)}
\, \exp[ - e^{- \mu \, (\epsilon - \eta)} ] \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8500}%
$\frac{\pi^2}{6 \mu^2} \sim \frac{1}{\mu^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8502}%
$\mu =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8506}%
$\epsilon_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8508}%
$\epsilon_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8512}%
$\max(\epsilon_1,\epsilon_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7320}%
\begin{displaymath}
\mu^{-1} \, \ln[ e^{\mu \eta_1} + e^{\mu \eta_2} ] \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8524}%
$\epsilon = \epsilon_1 - \epsilon_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7325}%
\begin{displaymath}
F(\epsilon) = \frac{1}{1 + e^{\mu \, (\eta_2 - \eta_1 - \epsilon)}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7898}%
\(
F(\epsilon) = \frac{1}{1 + e^{-\mu \, \epsilon}} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7332}%
\begin{displaymath}
F(-\infty) = \frac{1}{1 + e^{\infty}}
= \frac{1}{\infty} = 0 \ ; \ \ 
F(+\infty) = \frac{1}{1+e^{-\infty}} = 1 \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7899}%
\( 
f(\epsilon) = \frac{\mu \, e^{-\mu \, \epsilon}}%%
{(1+e^{-\mu \, \epsilon})^2} \ .  
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18640}%
\includegraphics[width=0.6\hsize]{logistic-vs-gauss-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18641}%
\includegraphics[width=0.6\hsize]{logistic-vs-gauss-logscale-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8532}%
$\epsilon_B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8534}%
$\epsilon =
\epsilon_B - \epsilon_A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7350}%
\begin{displaymath}
\int_{-\infty}^C \, f(\epsilon) \, d\epsilon
= F(C) - F(-\infty)
= \frac{1}{1 + e^{-\mu \, C}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7900}%
\(
Pr(A) = \frac{1}{1 + e^{-\mu \, V_A + \mu \, V_B}}
= \frac{e^{\mu \, V_A}}{e^{\mu \, V_A} + e^{\mu \, V_B}} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18668}%
\includegraphics[width=0.8\hsize]{overlap-multi-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7367}%
\begin{displaymath}
P_1 = Pr(U_1 > U_j, \forall j \ne 1)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7370}%
\begin{displaymath}
= Pr( V_1 + \epsilon_1 > V_j + \epsilon_j, \forall j \ne 1)
= Pr( \epsilon_j < \Delta V_{1j} + \epsilon_1, \forall j \ne 1) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7373}%
\begin{displaymath}
P_1 = Pr\left[
\epsilon_1 > \max_{j \ne 1}[ \Delta V_{1j} + \epsilon_j ]
\right] \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8562}%
$\epsilon_j \ (j \ne 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8564}%
$\Rightarrow$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8566}%
$
\epsilon_* := \max_{j \ne 1}[ \Delta V_{1j} + \epsilon_j ]
$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8570}%
$\epsilon_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8574}%
$\epsilon_* - \epsilon_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7901}%
\(
\frac{1}{1 + e^{\mu \, (V_* - V_1)}}
= \frac{e^{\mu \, V_1}}{e^{\mu \, V_1} + e^{\mu \, V_*}} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8580}%
$V_*$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7902}%
\(
= \frac{e^{\mu \, V_1}}{\sum_{j} e^{\mu V_j}} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7397}%
\begin{displaymath}
\frac{p_i}{p_j} = \frac{e^{\mu \, V_i}}{e^{\mu \, V_j}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8584}%
$50\%$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8586}%
$25\%$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8590}%
$2:1:1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8594}%
$2:1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8596}%
$2/3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8600}%
$\max_j[\Delta
V_{1j} + \eps_j]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8602}%
$\eps_* - \eps_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8604}%
$n=1..N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8610}%
$x_{n,A,1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8612}%
$x_{n,A,2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8614}%
$= \vec x_{n,A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8616}%
$x_{n,B,1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8618}%
$x_{n,B,2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8620}%
$= \vec x_{n,B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7413}%
\begin{displaymath}
V_A = \beta_1 \, x_{A,1} + \beta_2 \, x_{A,2} + ... 
= \vec \beta \cdot \vec x_A \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8624}%
$\beta_1,...,\beta_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8628}%
$y_{n,A} = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8634}%
$y_{n,B} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8636}%
$(1,2,3,4,...)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8638}%
$(A,B,A,A,...)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7420}%
\begin{displaymath}
P_{A,B,A,A,...} = P_{1,A} \, P_{2,B} \, P_{3,A} \, P_{4,A} \, ... \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8640}%
$y_{n,B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7428}%
\begin{displaymath}
P_{survey} = \prod_n P_{n,A}^{y_{n,A}} \, P_{n,B}^{y_{n,B}} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8642}%
$(\beta_1,...,\beta_k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7436}%
\begin{displaymath}
L = \log P_{survey}
= \sum_n [ y_{n,A} \, \log P_{n,A} + y_{n,B} \, \log P_{n,B} ] \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8644}%
$P_{n,X}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7449}%
\begin{displaymath}
P_{n,X} = \frac{e^{\vec \beta \cdot \vec x_X}}%%
{e^{\vec \beta \cdot \vec x_A} + e^{\vec \beta \cdot \vec x_B}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8648}%
$P_{survey}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8652}%
$\beta_0, \beta_1, ...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7903}%
\(
\vec \xi_n = \vec x_{n,A} - \vec x_{n,B} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7904}%
\(
P_{n,A} = \frac{1}{1 + e^{- \vec\beta \cdot \vec\xi_n}}
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7905}%
\(
P_{n,B}
= \frac{e^{-\vec\beta \cdot \vec\xi_n}}{1 + e^{- \vec\beta \cdot \vec\xi_n}}
= \frac{1}{1 + e^{+ \vec \beta \cdot \vec\xi_n}} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8654}%
$\log P_{n,A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7473}%
\begin{displaymath}
\frac{\partial \log P_{n,A}}{\partial \beta_k}
= - \frac{\partial }{\partial \beta_k} \log( 1 + e^{-...} )
= - \frac{1}{(1 + e^{-...})} \, e^{-...} \, (- \xi_{n,k})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7906}%
\(
\frac{\partial \log P_{n,A}}{\partial \beta_k}
= \xi_{n,k} \, P_{n,B} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7907}%
\(
\frac{\partial \log P_{n,B}}{\partial \beta_k}
= - \xi_{n,k} \, P_{n,A} \ .
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7492}%
\begin{displaymath}
\frac{\partial P_{n,A}}{\partial \beta_k}
= (-1) \, \frac{1}{(1 + e^{-...})^2} \, e^{-...} \, (-\xi_k) 
= P_{n,B} \, P_{n,A} \, \xi_k \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7502}%
\begin{displaymath}
\frac{\partial L}{\partial \beta_k}
= \sum_n \Big(
y_{n,A} \, P_{n,B} \, \xi_{n,k} - y_{n,B} \, P_{n,A} \, \xi_{n,k}
\Big)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7512}%
\begin{displaymath}
= \sum_n 
\Big( y_{n,A} \, (1\!-\!P_{n,A}) - (1\!-\!y_{n,A}) \, P_{n,A}\Big) \,
\xi_{n,k}
= ...
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7519}%
\begin{displaymath}
= \sum_n \Big( y_{n,A} - P_{n,A} \Big) \, \xi_{n,k} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8656}%
$P_{n,A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7908}%
\(
= \sum_n \Big( y_{n,A} - \frac{1}{1+e^{-\vec\beta\cdot\vec\xi_n}} \Big)
\, \xi_{n,k} \ .  
\)%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8660}%
$\vec\beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8664}%
$M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8666}%
$x^T C x > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8670}%
$C = M^T \, M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8672}%
$x^T M^T M x = (M x)^T \, (M x) >
0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8676}%
$M x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7531}%
\begin{displaymath}
(\nabla^2 L)_{kl} = \frac{\partial^2 L}{\partial \beta_k \, \partial \beta_l}
\sum_n \Big( ... \Big)
= - \sum_n P_{n,A} \, P_{n,B} \, \xi_{n,k} \, \xi_{n,l} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7540}%
\begin{displaymath}
M_{n,k} = \Big( P_{n,A} \, P_{n,B} \Big)^{1/2} \, \xi_{n,k} \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7547}%
\begin{displaymath}
\nabla^2 L = - M^T \, M \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8680}%
$M^T \, M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8682}%
$- M^T \, M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7937}%
\begin{displaymath} 
p_X \propto e^{\mu \, V_X}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7938}%
\begin{displaymath} 
V_X = \sum_k \beta_k \, x_{X,k} \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7939}%
\begin{displaymath} 
\tilde \beta_k := \mu \, \beta_k \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8702}%
$\tilde \beta_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8708}%
$P_A \propto e^{V_A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8720}%
$0.99^{100} \approx 0.366$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18796}%
\includegraphics[width=0.7\hsize]{gz/sumtt-by-iteration.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7592}%
\begin{displaymath}
p_i \propto e^{-\beta \, T_i} \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8724}%
$T_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8728}%
$1/360~sec$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8730}%
$O(N_{people} \times N_{trips} \times
N_{links} \times N_{options})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8732}%
$N_{people}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8734}%
$N_{trips}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8736}%
$N_{links}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8738}%
$N_{options}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8740}%
$N_{people} \sim
7.5~\hbox{mio}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8742}%
$N_{trips} \sim 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8744}%
$N_{links} \sim 50$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8746}%
$N_{options} \sim 5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7617}%
\begin{displaymath} 
7.5 \cdot 10^6~\hbox{persons} ~\times~ 3~\hbox{trips per person}
~\times~ 50~\hbox{links per trip}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7622}%
\begin{displaymath}
\times~ 5~\hbox{options}
\times~ 4~\hbox{bytes per link} ~=~ 22.5~\hbox{GByte}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8748}%
$O(N_{nodes} \times
N_{destinations} \times N_{options})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8750}%
$N_{nodes}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8752}%
$N_{destinations}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7636}%
\begin{displaymath}
    1\,000~\hbox{destinations} ~\times~ 10\,000~\hbox{nodes} 
~\times~ 5~\hbox{options per destination} ~\times~ 4~\hbox{bytes per
  node}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8758}%
$=~ 200~\hbox{MByte}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7644}%
\begin{displaymath}
30\,000~\hbox{links} ~\times~ 10\,000~\hbox{nodes} 
~\times~ 100~\hbox{time slices}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7649}%
\begin{displaymath}
\times~ 5~\hbox{options} ~\times~ 4~\hbox{bytes per entry} \approx
600~\hbox{GByte} \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18828}%
\includegraphics[width=0.7\hsize]{gz/individualization.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8762}%
$X_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8766}%
$n+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8768}%
$\Phi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7665}%
\begin{displaymath}
X_{n+1} = \Phi(X_n) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18842}%
\includegraphics[width=0.8\hsize]{mapping-fig.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7680}%
\begin{displaymath}
X_* = \Phi(X_*) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7683}%
\begin{displaymath}
X_{n+k} = X_n
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8782}%
$p(X)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7694}%
\begin{displaymath}
p_* = \Phi(p_*) \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8786}%
$\Phi(X)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8788}%
$\Phi(p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8794}%
$X_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8796}%
$p(X) = \delta(X - X_0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8800}%
$p_*(X)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath7707}%
\begin{displaymath}
\frac{df}{dt} = - f \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8802}%
$df/dt=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8804}%
$f = 0 \ .$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath7711}%
\begin{displaymath}
f(t) = f_0 \, e^{-t} \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8806}%
$f_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8818}%
$f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap18882}%
\includegraphics[width=0.6\hsize]{gz/reroute-unpredict.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{part}
\stepcounter{chapter}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10430}%
$= 1 / \rho_{jam} =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10432}%
$\rho_{jam} =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10438}%
$= 5 \cdot 7.5~\hbox{m} /
\hbox{sec} = 135 \hbox{km/h} \approx 85 \hbox{mph}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10440}%
$3.5 \cdot 7.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10442}%
$\approx$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10444}%
$4.49999 \cdot 7.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10456}%
$v_i \ge gap_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline18913}%
$ possible$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\setcounter{footnote}{2}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10462}%
$\displaystyle v_i := \cases{ 
gap_i-1 & with probability $p_{noise}$\  if possible\footnotemark \cr
gap_i & else \cr }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10464}%
$v_i < v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10468}%
$\displaystyle v_i := \cases{
v_i & with probability $p_{noise}$\  \cr
v_i + 1 & else \cr }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10470}%
$v_i = v_{max}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10472}%
$v_i < gap_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10476}%
$\displaystyle v_i := \cases{
v_{max}-1 & with probability $p_{noise}$\  \cr
v_{max} & else \cr }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10480}%
$x_i(t+1) = x_i(t) + v_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10482}%
$_{\it max\/}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10492}%
$0 \to 0 \to 1 \to 2 \to 2 \to 2 \to 3 \to
\ldots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10496}%
$1-p_{noise}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10512}%
$1/v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10516}%
$a(t)
\propto V[\Delta x(t)] - v(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10518}%
$v(t+\tau) \propto V[\Delta x(t)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10530}%
$x_o(i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10532}%
${\it gap_o\/}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10534}%
${\it gap_b\/}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10536}%
$<$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10540}%
$> gap(i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10542}%
$\;\;\;\;\;-\;\;\;$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10544}%
$weight1 = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10548}%
$weight1 = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10550}%
$weight2 = v(i) - gap_o(i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10552}%
$weight3 = v_{max} - gap_b(i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10554}%
$weight1 > weight2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10556}%
$weight1
> weight3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10560}%
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$gap_b$%
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$weight1$%
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$weight3$%
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$gap_o \ge v$%
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$v \le gap$%
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$weight1 + weight4 > weight2$%
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$d^*$%
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$d^*/v_{max}=14$%
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$weight4 = 0$%
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$weight4 = 1$%
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$t2$%
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$t_3$%
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$t_4$%
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$t_5 = t+1$%
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$L=5$%
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$=5 \times 7.5$%
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$=
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$k=180$%
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$\displaystyle {\it\rho\/} = \frac{\it N\/}{\it k * L}$%
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$x=501$%
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$x=900$%
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$x=500$%
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$gap=0$%
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$gap \ge 3 v_{oncoming}$%
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{\newpage\clearpage
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$gap > 3
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{\newpage\clearpage
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$N_{cns}(T)$%
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\stepcounter{section}
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$V_i$%
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{\newpage\clearpage
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$\eta_i$%
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{\newpage\clearpage
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$\beta U_i$%
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{\newpage\clearpage
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$N_{tr}(t)$%
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{\newpage\clearpage
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$N_{acs}(t)$%
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{\newpage\clearpage
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$f_{ch}(t)$%
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{\newpage\clearpage
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$f_{ch}$%
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{\newpage\clearpage
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$N_{acs}(t) =
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\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10796}%
$G$%
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{\newpage\clearpage
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$f_{ch}(.)$%
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{\newpage\clearpage
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$N_{acs}(t) = G[f_{ch}](t)$%
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{\newpage\clearpage
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$f_{act}$%
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{\newpage\clearpage
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$f_{ch}^{(n+1)}$%
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{\newpage\clearpage
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$G[.]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10820}%
$N_{cns}(t)$%
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{\newpage\clearpage
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$N_{tr}/N_{acs}$%
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{\newpage\clearpage
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$G[f_{ch}]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10826}%
$f_{ch}^{(n+1)}(t) = N_{cns}(t) / N_{acs}^{(n)}(t)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10830}%
$h$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10832}%
$t_{hw}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10834}%
$n_{wo}(w)$%
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{\newpage\clearpage
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{\newpage\clearpage
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$f_{ch}(T)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10846}%
$N_{wp}(i,T)$%
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{\newpage\clearpage
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{\newpage\clearpage
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$N_{wp}(T)$%
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{\newpage\clearpage
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$N_{acs}(T)$%
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$N_{acs}(i,T)$%
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$T^*$%
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{\newpage\clearpage
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$N_{acs}(i,T) \, f_{ch}(T)$%
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{\newpage\clearpage
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\stepcounter{section}
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$O(f \, N \, E \log\ K)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10876}%
$E \log\ K$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10878}%
$E$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$K$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10882}%
$O(F(\Delta T) \, M \, E \log\ K)$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$F(\Delta T)$%
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{\newpage\clearpage
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$\Delta T$%
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{\newpage\clearpage
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$O( F(\Delta T) \, E^2 \log\ K)$%
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{\newpage\clearpage
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$E \approx 20k$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10894}%
$N \approx 500\,000$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10896}%
$f =
0.1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10902}%
$80-85\%$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10906}%
$20\%$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19280}%
\includegraphics[width=\hsize]{gz/tot_travel_time.eps.gz}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19286}%
\includegraphics[width=\hsize]{ttdis_relaxed-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath10305}%
\begin{displaymath}
b_{abs,c} = (1/N_c) \, \sum_i (x_i - \xi_i) 
= (1/N_c) \, \Bigg(  \sum_i x_i - \sum_i \xi_i \Bigg)
\hbox{ ~~~and~~~ }
b_{rel,c} = b_{abs,c} \, / \, \langle\xi\rangle_c \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath10311}%
\begin{displaymath}
d_{abs,c} = (1/N_c) \,  \sum_i | x_i - \xi_i|
\hbox{ ~~~and~~~ }
d_{rel,c} = d_{abs,c} \, / \, \langle\xi\rangle_c \ ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath10317}%
\begin{displaymath}
var_c = \Bigg( (1/N_c) \,  \sum_i (x_i - \xi_i)^2 \Bigg)^{1/2}
\hbox{ ~~~and~~~ }
\sigma_c = var_c \, / \, \langle\xi\rangle_c \ .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10924}%
$<250$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10926}%
$>1500$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10928}%
$\pm 15-20\%$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19308}%
\includegraphics[width=0.45\textwidth]{scatter-100-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19309}%
\includegraphics[width=0.45\textwidth]{scatter-080-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19310}%
\includegraphics[width=0.45\textwidth]{scatter-e2-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10932}%
$250-500$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10934}%
$500-750$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10936}%
$750-1000$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10938}%
$1000-1500$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10966}%
$+$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap19492}%
\includegraphics[width=0.45\textwidth]{scatter-errors-gpl.eps}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{section}
\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline19979}%
$\!$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
