  We propose a road layout and traffic model, based on last passage percolation
(LPP). An easy naive argument shows that coalescence of traffic trajectories is
essential to be considered when observing traffic networks around us. This is a
fundamental feature in first passage percolation (FPP) models where nearby
geodesics naturally coalesce in search of the easiest passage through the
landscape. Road designers seek the same in pursuing cost savings, hence FPP
geodesics are straightforward candidates to model road layouts. Unfortunately
no detailed knowledge is rigorously available on FPP geodesics. To address
this, we use exponential LPP instead to build a stochastic model of road
traffic and prove certain characteristics thereof. Cars start from every point
of the lattice and follow half-infinite geodesics in random directions.
Exponential LPP is known to be in the KPZ universality class and it is widely
expected that FPP shares very similar properties, hence our findings should
equally apply to FPP-based modelling. We address several traffic-related
quantities of this model and compare our theorems to real life road networks.
