  A system of agents moving along a road in both directions is studied
numerically within a cellular-automata formulation. An agent steps to the right
with probability $q$ or to the left with $1-q$ when encountering other agents.
Our model is restricted to two agent types, traffic-rule abiders ($q=1$) and
traffic-rule ignorers ($q=1/2$). The traffic flow, resulting from the
interaction between these two types of agents, is obtained as a function of
density and relative fraction. The risk for jamming at a fixed density, when
starting from a disordered situation, is smaller when every agent abides by a
traffic rule than when all agents ignore the rule. Nevertheless, the absolute
minimum occurs when a small fraction of ignorers are present within a majority
of abiders. The characteristic features for the spatial structure of the flow
pattern are obtained and discussed.
