  In this paper, we study the phenomenon of concentration and the formation of
delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to
the Aw-Rascle traffic model. It is proved that as the adiabatic exponent
vanishes, the limit of solutions tends to a special delta-shock rather than the
classical one to the zero pressure gas dynamics. In order to further study this
problem, we consider a perturbed Aw-Rascle model and proceed to investigate the
limits of solutions. We rigorously proved that, as $\gamma$ tends to one, any
Riemann solution containing two shock waves tends to a delta-shock to the zero
pressure gas dynamics in the distribution sense. Moreover, some representative
numerical simulations are exhibited to confirm the theoretical analysis.
