  We present in this article an algebraic approach to model and simulate road
traffic networks. By defining a set of road traffic systems and adequate
concatenating operators in that set, we show that large regular road networks
can be easily modeled and simulated. We define elementary road traffic systems
which we then connect to each other and obtain larger systems. For the traffic
modeling, we base on the LWR first order traffic model with piecewise-linear
fundamental traffic diagrams. This choice permits to represent any traffic
system with a number of matrices in specific algebraic structures. For the
traffic control on intersections, we consider two cases: intersections
controlled with a priority rule, and intersections controlled with traffic
lights. Finally, we simulate the traffic on closed regular networks, and derive
the macroscopic fundamental traffic diagram under the two cases of intersection
control.
