The paper introduces a method of mathematical modeling of high scale road traffic
networks, where a new special hypermatrix
structure is intended to be used. The structure describes the inner-inner, inner-outer,
outer-outer relations, and laws
of a network area. The research examined the nonlinear equation system. The analysed
model can be applicable to the
testing and planning of large-scale road traffic networks, to the regulation of traffic
systems. The elaborated model is in
state space form where the states are vehicle densities on a particular lane and the
dynamics is described by a nonlinear
state constrained positive system. This model can be used directly for simulation
and analysis and as a starting point for
investigating various control strategies. The stability of the traffic over the network
can be analyzed by construction linear
Lyapunov function and the associated theory. The model points out that in intersection
control one must take the traffic
density values of both the input and the output sections into account. Generally the
control of any domain has to take the
density of input and output sections into consideration.
