Communications in Mathematical Sciences

Volume 6 (2008)

Number 3

Circulation of car traffic in congested urban areas

Pages: 765 – 784



Annunziata Cascone

Ciro D'Apice

Benedetto Piccoli

Luigi Rarità


The aim of this work is to understand how urban traffic behavior, especially in cases of congestion, can be improved by an accurate choice of traffic coefficients. For this, we define three cost functionals that measure average velocity, average travelling time and total flux of cars. The global optimal control problem for a complex network is difficult to solve both from analytical and numerical points of view. Thus, we focus on a simple junction with one incoming road and two outgoing roads (junctions of 1×2 type), obtaining exact solutions to a simple optimization problem. Then, we use such results at each node of the network. The traffic evolution of some networks is then studied via simulations. In particular, it is shown that an appropriate choice of the traffic distributions can be useful in order to improve network conditions.


Traffic flows on road networks; conservation laws; optimal control

2010 Mathematics Subject Classification

35L65, 49J20, 76N25

Full Text (PDF format)