67 lines
2.5 KiB
TeX
67 lines
2.5 KiB
TeX
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\documentclass{article}
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\usepackage{bbold}
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\usepackage{commath}
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\begin{document}
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\section{VLAN Introduction}
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For those unfamilliar with the concept of a VLAN (Virtual LAN) here is a shot
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formal specification of what such a thing does.
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A Switch is a 8-tuple \( \mathcal{S} = (\mathbb{A}, \mathbb{P}, \mathbb{V}, t, v, a, \beta, \epsilon) \)
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consisting of
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\begin{itemize}
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\item a finite set of (MAC) addresses \(\mathbb{A}\),
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\item a finite set of physical ports \(\mathbb{P}\),
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\item a finite set of VLANs \(\mathbb{V}\),
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\item a mapping from physical ports and VLANs to two distinct symbols pronounced
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``tagged'' and ``untagged'' repectively
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\( t : \mathbb{P} \times \mathbb{V} \rightarrow \{ \tau, \upsilon \} \),
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\item a mapping from physical ports and VLANs to VLANs (Port PVID)
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\( v : \mathbb{P} \times \mathbb{V} \rightarrow \mathbb{V} \)
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with \(v(p, q) \mapsto q\) when \(q \neq \epsilon\),
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\item a mapping from addresses and VLANs to physical ports (ARP Table)
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\( a : \mathbb{A} \times \mathbb{V} \rightarrow \mathbb{P} \) and
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\item the broadcast address \(\beta \in \mathbb{A}\)
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\item the empty VLAN tag \(\epsilon \in \mathbb{V}\)
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\end{itemize}
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A Frame processed by a Switch \(\mathcal{S}\)
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is a tuple \( \mathcal{F}_\mathcal{S} = (d, q) \)
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consisting of a destination address \(d \in \mathbb{A} \) and a VLAN tag \( q \in \mathbb{V} \).
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When a Frame \( \mathcal{F}_\mathcal{S}' = (d, q') \)
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enters a port \( p \in \mathbb{P}\)
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the Switch first ensures the Packet has a VLAN tag for internal processing
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assigned by creating a new Frame \( \mathcal{F}_\mathcal{S} = (d, q)\) with \(q = v(p, q')\).
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\subsection{Broadcast processing}
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When the Frame's destination address \( d = \beta \)
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the Switch creates a new Frame for each port
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\( p \in \{\, p \mid t(p, \_) \,\} \)
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in the following manner:
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\begin{equation}\label{eq:egress}
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\mathcal{F}_{\mathcal{S}, p}^{e} =
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\left\{
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\begin{array}{ll}
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(d,q) & \mbox{if } t(p, q) = \tau \\
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(d, \epsilon) & \mbox{if } t(p, q) = \upsilon\\
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\end{array}
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\right.
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\end{equation}
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\( \mathcal{F}_{\mathcal{S}, p}^{e} \)
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is then transmitted out port \(p\) and processing of this Frame is complete.
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\subsection{Unicast processing}
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When the Frame's destination address \(d\) is not the broadcast address the Switch first determines the egress port \(p = a(d, q)\). Then a new Frame is created as in equation \ref{eq:egress}. \( \mathcal{F}_{\mathcal{S}, p}^{e} \)
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is then transmitted out port \(p\) and processing of this Frame is complete.
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\end{document}
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