1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Balanced Sequences and Optimal Routing

  1. Jan 16, 2006 #1
    I've been reading the paper on Balanced Sequences and Optimal Routing (Altman, Gaujal, Hordijk; 2000). However, there are a couple of proofs given that I don't quite follow. There are statements made that are assumed to trivially follow, but I can't see how and am hoping someone will be able to help me.

    The first is in the proof of Proposition 2.16. The fact that l_i >= (n-1)l_1 + n is easily shown, but 'on the other hand' l_i <= n(l_1) - 3 does not seem to follow from any similar method.

    The second is in the proof of Theorem 2.21, Step (2). Where does the fact that |s_1| >= max{4, 2(n+m)+1} come from. (Obviously the 4 is trivial, but I do not understand the 2(n+m)+1)

    The paper is attached; I hope that someone with a better understanding than me will be able to follow the proofs and let me know where I'm missing something obvious!


    Attached Files:

    • 48-2.pdf
      File size:
      196.3 KB
  2. jcsd
  3. Apr 8, 2006 #2


    User Avatar

    A question

    Sorry not to provide any answer to your questions? But if you don't mind, I hav a question about that paper on Balanced sequences and optimal routing. I hav been looking for some partical applications of the results presented in that paper, but unfornately I havn't been abled to find a good one, so far. May be it is due to my lack of knowledge about queuing networks.
    Therefore, I will be more than please, if you can provide me with an application, or any link or article where I will be able to find some.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Balanced Sequences and Optimal Routing
  1. Is this a sequence? (Replies: 1)

  2. Optimization Problem (Replies: 3)

  3. Optimal Frequency (Replies: 1)

  4. Optimization problem (Replies: 10)