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Analysis of generalized optimal current lattice model for traffic flow. (English) Zbl 1153.82327
Summary: A generalized optimal current lattice model (GOCLM) for traffic flow is proposed to describe the motion of the dynamical traffic flow with a consideration of multi-interaction of the front lattice sites. In order to verify the reasonability of the new model, the stability condition is obtained by the use of linear stability theory. The modified KdV (Korteweg-de Vries) equation is derived by the use of the nonlinear analysis method and the kink-antikink soliton solution is obtained near the critical point. The propagation velocities of density waves are calculated for different numbers of the front interactions. A numerical simulation is carried out to check out the performance of GOCLM for traffic flow. The simulation results show that GOCLM is better than the previous models in suppressing the traffic jams.

82C20Dynamic lattice systems and systems on graphs
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
90B20Traffic problems
82C27Dynamic critical phenomena
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