A new stochastic discrete space-time model of multiple random walkers is proposed to simulate one-and two-dimensional many body interacting lattice gas systems. A very simple rule set which prohibits the multiple occupancy of lattice sites by the random walkers while conserving their number is used to define the dynamics of the walkers. We found a linear time dependence for the mean squared end-to-end distances of the two-dimensional random walkers system. Extensions of the model to a wide variety of diffusive systems are noted.