  We propose some conjectures for asymptotic distribution of probabilistic
Burgers cellular automaton (PBCA) which is defined by a simple motion rule of
particles including a probabilistic parameter. Asymptotic distribution of
configurations converges to a unique steady state for PBCA. We assume some
conjecture on the distribution and derive the asymptotic probability expressed
by GKZ hypergeometric function. If we take a limit of space size to infinity, a
relation between density and flux of particles for infinite space size can be
evaluated. Moreover, we propose two extended systems of PBCA of which
asymptotic behavior can be analyzed as PBCA.
