  Urban road transport is a major civilisational and economic challenge,
affecting the quality of life and economic activity. Addressing these
challenges requires a multidisciplinary approach and sustainable urban planning
strategies to mitigate the negative effects of traffic in cities. In this
paper, we introduce an extension of one of the most popular macroscopic traffic
simulation models, the Payne-Whitham model. We investigate how this model,
originally designed to model highway traffic on straight road segments, can be
adapted to more realistic conditions with arbitrary road network graphs and
multiple intersections with traffic signals. Furthermore, we showcase the
practical application of this extension in experiments aimed at optimising
traffic signal settings. For computational reasons, these experiments involve
the adoption of surrogate models for approximating our extended Payne-Whitham
model, and subsequently, we utilise the Differential Evolution optimization
algorithm, resulting in the identification of traffic signal settings that
enhance the average speed of cars and decrease the total length of queues,
thereby facilitating smoother traffic flow.
