File:MM1 queue state space.svg

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

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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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I, the copyright holder of this work, hereby publish it under the following license:
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Code used to produce this image[edit]

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

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