  Recently Prosen and Mej\'ia-Monasterio (J. Phys. A: Math. Theor. 49 (2016)
185003) obtained exact nonequilibrium steady states of an integrable and
reversible cellular automaton driven by some stochastic boundary conditions. In
this paper, we explore the possible extensions of their method by generalizing
the boundary conditions. As the result, we find two cases where such an
extension is possible. One is the case where a special condition is satisfied
in a generalized boundary condition. The other is obtained by considering a
conserved quantity as energy and boundaries as heat reservoirs. The latter
includes the original solution as the special case. Properties of the both
solutions are discussed.
