  We present a general method for constructing integrable stochastic processes,
with two-step discrete time Floquet dynamics, from the transfer matrix
formalism. The models can be interpreted as a discrete time parallel update.
The method can be applied for both periodic and open boundary conditions. We
also show how the stationary distribution can be built as a matrix product
state. As an illustration we construct a parallel discrete time dynamics
associated with the R-matrix of the SSEP and of the ASEP, and provide the
associated stationary distributions in a matrix product form. We use this
general framework to introduce new integrable generalized exclusion processes,
where a fixed number of particles is allowed on each lattice site in opposition
to the (single particle) exclusion process models. They are constructed using
the fusion procedure of R-matrices (and K-matrices for open boundary
conditions) for the SSEP and ASEP. We develop a new method, that we named
"fused" matrix ansatz, to build explicitly the stationary distribution in a
matrix product form. We use this algebraic structure to compute physical
observables such as the correlation functions and the mean particle current.
