Question: Modulated Markov Rate Process

Dear All,

I have a question related to Modulated Markov Rate Process (MMRP). Please see MMRP and here. For more information see this

In this kind of markov chain it is necessary to have ON and OFF state that separte by a exponential distribution. Also the number of items as mentioned in the figures has a Geometric distribution. The transmission rate is constant. So the arrival rate is continuous and departure is discerete.

How is it possible to have such a markov chain?

If we do not have ON and OFF state, is it possible to have similar Markov chain?

I mean if we have poisson arrival for n files (let say) with rate \lambda and the file size is Geometric with parameter \theta. It means that the averrage file size is 1 over \theta. After a request for a file, packets will be requested with constant rate \mui. Then can we have a markov chain like the markov chain that I uploaded as a file. Please pay attention that the arrival is cintinuous and departure is discerete (geometric multiply by a constant)

Best Regards,

Saeid