Abstract:
The phenomenon of passing on a two-
dimensional network has been studied through lat-
tice hydrodynamic approach. Near the critical point,
the effect of passing is investigated theoretically and
numerically. The modified Korteweg–de Vries equa-
tion near the critical point is derived using the reduc-
tion perturbation method through nonlinear analysis.
Analytically, it is shown that for all possible configura-
tions of vehicle, the stable region significantly reduces
with an increase in the passing rate. It is shown that
the jamming transition occurs among no jam to chaotic
jam for any configuration of vehicles for larger rate of
passing constant, while for smaller rate of passing, the
jamming transitions occur from no jam to chaotic jam
through kink jam for any configuration of vehicles. The
results show that the modified model is able to explain
the complex phenomena of traffic flow at a better level
of accuracy than the most of the existing models. Sim-
ulation results are found consistent with the theoretical
findings, which confirm that the passing plays a signif-
icant role in a two-dimensional traffic system.
