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File:MM1 queue state space.svg

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Original file (SVG file, nominally 605 × 67 pixels, file size: 28 KB)

Summary

Description
English: State space diagram of an M/M/1 queue. The state space records the number of customers in the queueing system. The values lambda and mu represent the arrival and service rates of customers.
Date
Source Own work
Author Gareth Jones

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Code used to produce this image

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=2cm,semithick]
  \tikzstyle{every state}=[fill=white,draw=black,text=black,minimum size=1.1cm]

  \node[state] (A) {0};
  \node[state] (B) [right of=A] {$1$};
  \node[state] (C) [right of=B] {$2$};
  \node[state] (D) [right of=C] {$3$};
  \node[minimum size=1cm] (E) [right of=D] {$\cdots$};
  \node[state] (F) [right of=E] {$n-1$};
  \node[state] (G) [right of=F] {$n$};
  \node[state] (H) [right of=G] {$n+1$};
  \node[minimum size=1cm] (I) [right of=H] {$\cdots$};

  \path (A) edge [bend left] node {$\lambda$} (B);
  \path (B) edge [bend left] node {$\mu$} (A);
  \path (B) edge [bend left] node {$\lambda$} (C);
  \path (C) edge [bend left] node {$\mu$} (B);
  \path (C) edge [bend left] node {$\lambda$} (D);
  \path (D) edge [bend left] node {$\mu$} (C);
  \path (D) edge [bend left] node {$\lambda$} (E);
  \path (E) edge [bend left] node {$\mu$} (D);
  \path (E) edge [bend left] node {$\lambda$} (F);
  \path (F) edge [bend left] node {$\mu$} (E);
  \path (F) edge [bend left] node {$\lambda$} (G);
  \path (G) edge [bend left] node {$\mu$} (F);
  \path (G) edge [bend left] node {$\lambda$} (H);
  \path (H) edge [bend left] node {$\mu$} (G);
  \path (H) edge [bend left] node {$\lambda$} (I);
  \path (I) edge [bend left] node {$\mu$} (H);
\end{tikzpicture}

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1 November 2011

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Date/TimeThumbnailDimensionsUserComment
current22:42, 30 May 2013Thumbnail for version as of 22:42, 30 May 2013605 × 67 (28 KB)Gareth Jonesbetter fonts
20:31, 1 November 2011Thumbnail for version as of 20:31, 1 November 2011599 × 64 (48 KB)Gareth Jones

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