\documentclass[a4paper]{article}

\usepackage{amsmath,amssymb,amsthm}
\usepackage{tikz}
\usetikzlibrary{arrows,automata,calc,positioning}

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}

\newcommand*{\ArcAngle}{220}%
\newcommand*{\ArcRadius}{1}%

\makeatletter 
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\inheritanchor[from=rectangle]{north} 
\inheritanchor[from=rectangle]{south} 
\inheritanchor[from=rectangle]{west} 
\inheritanchor[from=rectangle]{east} 
\inheritanchor[from=rectangle]{north east} 
\inheritanchor[from=rectangle]{south east} 
\inheritanchor[from=rectangle]{north west} 
\inheritanchor[from=rectangle]{south west} 
\inheritanchor[from=rectangle]{base} 
\backgroundpath{% 
\southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y  % south west is (xa,ya)
\northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y  % north east is (xb,yb)
%\pgfpathmoveto{\pgfpoint{\pgf@xa}{\pgf@ya}} 
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\pgfpathlineto{\pgfpoint{\pgf@xb}{\pgf@yb}} 
\pgfpathclose 
}% 
} 
\makeatother 
\tikzstyle{queueing area}=[queueing box,thick,draw=black,minimum size=1cm,left color=white]

\begin{document}

% Diagram inspired by those in 
% Levy, Hanoch, and Moshe Sidi. "Polling systems: Applications, modeling, and optimization." Communications, IEEE Transactions on 38.10 (1990): 1750-1760.
% https://dx.doi.org/10.1109/26.61446

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2.3cm,semithick]
  \tikzstyle{every state}=[fill=white,draw=black,text=black,minimum size=1.1cm]

\coordinate (Origin) at (0,0);

  % centre
  \node (C) {};

  % server
  \node[state] (S) [below right of=C,node distance=1cm] {};
  % server arc
  \draw [->] ($(C)+(\ArcRadius,0)$) arc (0:\ArcAngle:\ArcRadius);

  % queueing areas
  \node[queueing area] (Q1) [left of=C] {};
  \node[queueing area,rotate=315] (Q2) [left of=C] {};
  \node[queueing area,rotate=270] (Q3) [left of=C] {};
  \node[queueing area,rotate=225] (Q4) [left of=C] {};
  \node[queueing area,rotate=180] (Q5) [left of=C] {};
  \node[queueing area,rotate=135] (Q6) [left of=C] {};
  \node[rotate=90] (Q7) [left of=C] {$\vdots$};
  \node[queueing area,rotate=45] (Q8) [left of=C] {};

  \node (A1) [below left of=C] {};
  \node (A2) [left of=C] {};
  \node (A3) [above left of=C] {};
  \node (A4) [above of=C] {};
  \node (A5) [above right of=C] {};
  \node (A6) [right of=C] {};
  \node (A7) [below right of=C] {};

  \node (S1) [below left of=A1] {\Large $\lambda_6$};
  \node (S2) [left of=A2] {\Large$\lambda_5$};
  \node (S3) [above left of=A3] {\Large$\lambda_4$};
  \node (S4) [above of=A4] {\Large$\lambda_3$};
  \node (S5) [above right of=A5] {\Large$\lambda_2$};
  \node (S6) [right of=A6] {\Large$\lambda_1$};
  \node (S7) [below right of=A7] {\Large$\lambda_n$};
 
  \path (S1) edge ($(A1)+(-0.5,-0.5)$);
  \path (S2) edge ($(A2)+(-0.7,0)$);
  \path (S3) edge ($(A3)+(-0.5,0.5)$);
  \path (S4) edge ($(A4)+(0,0.7)$);
  \path (S5) edge ($(A5)+(0.5,0.5)$);
  \path (S6) edge ($(A6)+(0.7,0)$);
  \path (S7) edge ($(A7)+(0.5,-0.5)$);

\end{tikzpicture}

\end{document}