This article shows how the evolution of multi-commodity traffic flows
over complex networks can be predicted over time, based on a simple ma
croscopic computer representation of traffic flow that is consistent w
ith the kinematic wave theory under all traffic conditions. The method
does not use ad hoc procedures to treat special situations. After a b
rief review of the basic model for one link, the article describes how
three-legged junctions can be modeled. It then introduces a numerical
procedure for networks, assuming that a time-varying origin-destinati
on (O-D) table is given and that the proportion of turns at every junc
tion is known. These assumptions are reasonable for numerical analysis
of disaster evacuation plans. The results are then extended to the ca
se where, instead of the turning proportions, the best routes to each
destination from every junction are known at all times. For technical
reasons explained in the text, the procedure is more complicated in th
is case, requiring more computer memory and more time for execution. T
he effort is estimated to be about an older of magnitude greater than
for the static traffic assignment problem on a network of the same siz
e. The procedure is ideally suited for parallel computing. It is hoped
that the results in the article wilt lead to more realistic models of
freeway flow, disaster evacuations and dynamic traffic assignment for
the evening commute.