Matchment of a MMP with a Two-state Semi-MMP

In general, suppose the controlling process of the single source for ATM MUX be a two-state Markov chain in the fluid mode, the superposition to the ATM MUX is a MMP whose controlling process is a muti-state, continuous, irreducible MC.It is inconvenient to study the content of the buffer because of the large number of state. To solve this problem, this paper gives a method to match the MMP with a simple two-state semi-MMP.