The diffusion has been simulated by the "Monte Carlo method" on a random lattice. As in the "ant in the labyrinth" problem the particles move by stepping to allowed, randomly chosen neighboring fields. The particle interaction has been defined by the constraint that only one particle can occupy a site at a time. Biased diffusion means that one of the directions will be chosen with a greater probability than the others. It was shown that, with an increasing number of "walkers," the displacement of the particles first of all increases to a maximum value and then decreases. This "filling-up" effect will not occur with small bias fields and on lattices with a high concentration of allowed sites.