\documentclass{article}

\usepackage[usenames,dvipsnames]{color,xcolor}

\usepackage{tikz}
\usetikzlibrary{mindmap,backgrounds,shadows,trees,positioning,shapes,arrows,decorations,calc,shapes,intersections}


\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1mm}

\usepackage{fontspec}
\setmainfont[Scale=.7]{Linux Libertine}


\begin{document}
\begin{tikzpicture}



\draw[red, domain=0:4, samples=200,name path=c1] plot (\x+1, {.25*(\x)^2}) node[right,yshift=-8mm,xshift=-4mm] {\footnotesize $ q_{i,\tau}(t)$};
\draw[blue, domain=0:1.9, samples=200,name path=c2] plot (\x+2.5, {1.15*(\x)^2}) node[left,yshift=-5mm,xshift=-1mm] {\footnotesize $q_{i',\tau'}(t)$};

\draw[-latex](0,0)--(0,4) node[at end,sloped,above,xshift=-3mm] {priority};
\draw[-latex,name path=c3](0,0)--(6,0) node[at end,below] {t};

\draw[name intersections={of=c1 and c2},dashed,gray!90] (intersection-1)--(3.8,0);
\draw[draw=none,fill=Plum](intersection-1)circle(.5mm);



 \node at (1.15,-.16) [] {\footnotesize $\tau$};
  \node at (2.55,-.16) [] {\footnotesize $\tau'$};
  \node at (3.85,-.16) [] {\footnotesize $t_{0}$};

\end{tikzpicture}
\end{document}