title: TCP Connection theory : Minimum rate of sequence numbers
body: <p>(Asking this question here because <a href="http://cs.stackexchange.com">cs stack exhange</a> has only 50 followers for Computer Networks tag and has no tag for TCP)</p>
  
  <p>At a particular national level examination, for post-graduate university admissions in my country, the following question was asked:</p>
  
  <p>"While opening a TCP connection, the initial sequence number is to be derived 
  using a time-of-day (ToD) clock that keeps running even when the host is down. 
  The low order 32 bits of the counter of the ToD clock is to be used for the initial 
  sequence numbers. The clock counter increments once per millisecond. The 
  maximum packet lifetime is given to be 64s. </p>
  
  <p>"Which one of the choices given below is closest to the minimum permissible rate 
      at which sequence numbers used for packets of a connection can increase? </p>
  
  <pre><code> (A) 0.015/s (B) 0.064/s (C) 0.135/s (D) 0.327/s"
  </code></pre>
  
  <p>The answer apparently is (B) 0.064/s</p>
  
  <ul>
  <li>Normally, TCP <strong>maximum</strong> connection speed is governed by the packet lifetime. If you use 32 bits  for the sequence number, then the numbers will get repeated after 2^32 counts, because of wrap around. </li>
  <li>If you send a packet with number X, then after 2^32 bytes are sent, the number X will get reassigned to some other packet. When the second packet with number X enters the connection, the first one shouldn't be in the network (to avoid duplication). So sequence numbers should <strong>not</strong> be repeated <strong>before</strong> a packet lifetime.</li>
  </ul>
  
  <p><em>That</em> governs the <em>maximum</em> rate.</p>
  
  <p>However, as asked in the problem, we need to find the <em>minimum</em> rate.</p>
  
  <p>(btw, even if sequence numbers are changed once in every 64 seconds (1 seq no. in 64 seconds) , then the number of sequence values in 1 second = 1/64 = 0.015...which is option A, but that's not the correct answer either , apparently.)</p>
  
  <p>My questions:</p>
  
  <ol>
  <li>What factor governs the minimum rate in general, or in this particular question?</li>
  <li>Why 0.064/s, as in what happens if sequence numbers change slower than that? How to solve this question to arrive at 0.064/s ?</li>
  </ol>
  
  <p>I know it's more of a theoretical question, but it has been really nagging me for a long time.. 
  Any help is highly appreciated. (including proof that this question and/or the answer is wrong. The only reason this question is worth pondering over, is that it was asked in an important and highly valued  nationwide examination.)</p>