# Markov chain and state diagram

1. Sep 30, 2009

### Fabio_vox

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 $$\alpha$$ e $$\beta$$ 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 $$\lambda$$ . Service time is exponential too, with parameter $$\mu$$ . 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 $$\in$$ {1,2,$$\oslash$$(=empty set)} means who is being serving. So the initial state of the transitional state diagram could be (0,0,$$\oslash$$) 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 $$\lambda$$. 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. Oct 2, 2009

### Fabio_vox

Does anybody know what I'm speaking about of?

3. Feb 21, 2011

### sbirulicchio

u solve it?
i have the same problem!!