  Summary: Traffic light coordination is a complex problem. In this paper, we
extend previous work on an abstract model of city traffic to allow for multiple
street intersections. We test a self-organizing method in our model, showing
that it is close to theoretical optima and superior to a traditional method of
traffic light coordination.
  Abstract: The elementary cellular automaton following rule 184 can mimic
particles flowing in one direction at a constant speed. This automaton can
therefore model highway traffic. In a recent paper, we have incorporated
intersections regulated by traffic lights to this model using exclusively
elementary cellular automata. In such a paper, however, we only explored a
rectangular grid. We now extend our model to more complex scenarios employing
an hexagonal grid. This extension shows first that our model can readily
incorporate multiple-way intersections and hence simulate complex scenarios. In
addition, the current extension allows us to study and evaluate the behavior of
two different kinds of traffic light controller for a grid of six-way streets
allowing for either two or three street intersections: a traffic light that
tries to adapt to the amount of traffic (which results in self-organizing
traffic lights) and a system of synchronized traffic lights with coordinated
rigid periods (sometimes called the "green wave" method). We observe a tradeoff
between system capacity and topological complexity. The green wave method is
unable to cope with the complexity of a higher-capacity scenario, while the
self-organizing method is scalable, adapting to the complexity of a scenario
and exploiting its maximum capacity. Additionally, in this paper we propose a
benchmark, independent of methods and models, to measure the performance of a
traffic light controller comparing it against a theoretical optimum.
