The definition of semi-product of fractal is first put forward for the research of mutual relations between original fractal and its product of fractal when the transforms of IFS are incomplete.

Pointed out that we can acquire a fractal surface with roughness in one fragment by the fractal product,.

Using the quasi-reversibility property in each node,the precise product form solution of the stable distribution in special transition form is solved.

With their service rates depending on the size of batch service,first,we give the product form stationary distributions for network without negative signals using the quasi-reversibility in each node.

For such games, optimal mixed strategies having a special product form are searched for.

Sevaral operation characters in the lattice L of a product arrangement have been educed.

：The model of discrete- time queuing network system for tim e division multiple access (TDMA) protocol is presented in this paper, the performance of this protocol is analyzed by the method of product form equilibrium distribution.