<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" id="m0079">

  <name xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Ethernet Packet Size</name>

  <metadata xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
  <md:version xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2.5</md:version>
  <md:created xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2000/08/02</md:created>
  <md:revised xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">2006/05/18 04:54:13.342 GMT-5</md:revised>
  <md:authorlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
      <md:author xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="dhj">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Don</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Johnson</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">dhj@rice.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="dhj">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Don</md:firstname>
      
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Johnson</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">dhj@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="kashent">
      <md:firstname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Indra</md:firstname>
      <md:othername xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Neel</md:othername>
      <md:surname xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">Datta</md:surname>
      <md:email xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">kashent@alumni.rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">capacity</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">ethernet</md:keyword>
    <md:keyword xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">packet size</md:keyword>
  </md:keywordlist>

  <md:abstract xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">(Blank Abstract)</md:abstract>
</metadata>

  <content xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">

    <para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="pa1">A subtle consideration in Ethernet is the minimum packet size  
      <m:math>
	<m:ci><m:msub>
	    <m:mi>P</m:mi>
	    <m:mi>min</m:mi>
	  </m:msub></m:ci>
      </m:math>.
      The time required to transmit such packets equals  
      <m:math>
	<m:apply>
	  <m:divide/>
	  <m:ci><m:msub>
	      <m:mi>P</m:mi>
	    <m:mi>min</m:mi>
	    </m:msub></m:ci>
	  <m:ci>C</m:ci>
	</m:apply>
      </m:math>, where <m:math><m:ci>C</m:ci></m:math> is the
      Ethernet's capacity in bps. Ethernet now comes in two different
      types, each with individual specifications, the most
      distinguishing of which is capacity: 10 Mbps and
      100 Mbps. If the minimum transmission time is such that the
      beginning of the packet has not propagated the full length of
      the Ethernet before the end-of-transmission, it is possible that
      two computers will begin transmission at the same time and, by
      the time their transmissions cease, the other's packet will not
      have propagated to the other. In this case, computers in-between
      the two will sense a collision, which renders both computer's
      transmissions senseless to them, without the two transmitting
      computers knowing a collision has occurred at all!  For Ethernet
      to succeed, we must have the minimum packet transmission time
      exceed <emphasis xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">twice</emphasis> the voltage propagation time.
      
      <equation xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="time">
	<m:math>
	  <m:apply>
	    <m:gt/>
	    <m:apply>
	      <m:divide/>
	      <m:ci><m:msub>
		  <m:mi>P</m:mi>
		  <m:mi>min</m:mi>
		</m:msub></m:ci>
	      <m:ci>C</m:ci>
	    </m:apply>
	    <m:apply>
	      <m:divide/>
	      <m:apply>
		<m:times/>
		<m:cn>2</m:cn>
		<m:ci>L</m:ci>
	      </m:apply>
	      <m:ci>c</m:ci>
	    </m:apply>
	  </m:apply>
	  <m:mtext>  or   </m:mtext>
	  <m:apply>
	    <m:gt/>
	    <m:ci><m:msub>
		<m:mi>P</m:mi>
		<m:mi>min</m:mi>
	      </m:msub></m:ci>
	    <m:apply>
	      <m:divide/>
	      <m:apply>
		<m:times/>
		<m:cn>2</m:cn>
		<m:ci>L</m:ci>
		<m:ci>C</m:ci>
	      </m:apply>
	      <m:ci>c</m:ci>
	    </m:apply>
	  </m:apply>
	</m:math>
      </equation>
      Thus, for the 10 Mbps Ethernet having a 1 km maximum
      length specification, the minimum packet size is about 70 bits.
    </para>

    <exercise xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="exer1">
      <problem xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
	<para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="exer1a">The 100 Mbps Ethernet was designed more
	  recently than the 10 Mbps alternative.  To maintain the
	  same minimum packet size as the earlier, slower version,
	  what should its length specification be?  Why should the
	  minimum packet size remain the same?
	</para>
      </problem>

      <solution xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/">
	<para xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="exer1b">
	  The cable must be a factor of ten shorter: It cannot exceed
	  100 m. Different minimum packet sizes means different
	  packet formats, making connecting old and new systems
	  together more complex than need be.
	</para>
      </solution>
    </exercise>
    
  </content>
</document>
