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Markov chain and state diagram

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data
    I have the following queuing system: http://img39.imageshack.us/img39/8264/immaginetd.jpg [Broken]
    that models voice traffic that come up with [tex]\alpha[/tex] e [tex]\beta[/tex] parameters, on both queue 1 and 2. When a source of voice is active causes traffic with exponential inter-arrival time which has the parameter of [tex]\lambda[/tex] . Service time is exponential too, with parameter [tex]\mu[/tex] . The scheduling policy is Round Robin (a packet from queue 1, then another packet from queue 2, and so on)work-conserving type (after serving a packet, from queue 1 there are no packet to serve from queue 2, the server remain serving packet from queue 1; and viceversa).
    I would like rappresent this system drawing Markov state transition diagram, but I don't know which are the probabilities of transition between states and also how "the ON OFF automata" affect the whole system.

    2. Relevant equations



    3. The attempt at a solution
    I think that a generical state has the form of (N1,N2,S) where N1 means number of users (packet) being in queue 1, and N2 numebr of users in queue 2. S [tex]\in[/tex] {1,2,[tex]\oslash[/tex](=empty set)} means who is being serving. So the initial state of the transitional state diagram could be (0,0,[tex]\oslash[/tex]) no one is being serving. If a packet (the first) is generated from queue 2 this is coded with a state of (0,1,2). But the label of the edge, that connect the initial state with this one, is surely not [tex]\lambda[/tex]. Which is the correct one? How the automata in the figure affect these transitions?
    Thank you all, and sorry for my english and mistakes I'm not native.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 2, 2009 #2
    Does anybody know what I'm speaking about of?
     
  4. Feb 21, 2011 #3
    u solve it?
    i have the same problem!!
     
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